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Resources to Help You Solve Math Equations
Whether you love math or suffer through every single problem, there are plenty of resources to help you solve math equations. Skip the tutor and log on to load these awesome websites for a fantastic free equation solver or simply to find answers for solving equations on the Internet.
Stand By for Automatic Math Solutions at Quick Math
The Quick Math website offers easy answers for solving equations along with a simple format that makes math a breeze. Load the website to browse tutorials, set up a polynomial equation solver, or to factor or expand fractions. From algebra to calculus and graphs, Quick Math provides not just the answers to your tough math problems but a step-by-step problem-solving calculator. Use the input bar to enter your equation, and click on the “simplify” button to explore the problem and its solution. Choose some sample problems to practice your math skills, or move to another tab for a variety of math input options. Quick Math makes it easy to learn how to solve this equation even when you’re completely confused.
Modern Math Answers Come From Mathway
Mathway offers a free equation solver that sifts through your toughest math problems — and makes math easy. Simply enter your math problem into the Mathway calculator, and choose what you’d like the math management program to do with the problem. Pick from math solutions that include graphing, simplifying, finding a slope or solving for a y-intercept by scrolling through the Mathway drop-down menu. Use the answers for solving equations to explore different types of solutions, or set the calculator to offer the best solution for your particular math puzzle. Mathway offers the option to create an account, to sign in or sign up for additional features or to simply stick with the free equation solver.
Wyzant — Why Not?
Wyzant offers a variety of answers when it comes to “how to solve this equation” questions. Sign up to find a tutor trained to offer online sessions that increase your math understanding, or jump in with the calculator that helps you simplify math equations. A quick-start guide makes it easy to understand exactly how to use the Wyzant math solutions pages, while additional resources provide algebra worksheets, a polynomial equation solver, math-related blogs to promote better math skills and lesson recording. Truly filled with math solutions, Wyzant provides more than just an equation calculator and actually connects you with people who are trained to teach the math you need. Prices for tutoring vary greatly, but access to the website and its worksheets is free.
Take in Some WebMath
Log onto the WebMath website, and browse through the tabs that include Math for Everyone, Trig and Calculus, General Math and even K-8 Math. A simple drop-down box helps you to determine what type of math help you need, and then you easily add your problem to the free equation solver. WebMath provides plenty of options for homeschoolers with lesson plans, virtual labs and family activities.
Khan Academy Offers More Than Answers
A free equation solver is just the beginning when it comes to awesome math resources at Khan Academy. Free to use and filled with videos that offer an online teaching experience, Khan Academy helps you to simplify math equations, shows you how to solve equations and provides full math lessons from Kindergarten to SAT test preparation. Watch the video for each math problem, explore the sample problems, and increase your math skills right at home with Khan Academy’s easy-to-follow video learning experience. Once you’ve completed your math video, move onto practice problems that help to increase your confidence in your math skills.
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120 Math Word Problems To Challenge Students Grades 1 to 8
Make solving math problems fun!
With Prodigy's assessment tools, you can engage your students that adapts for your curriculum, lesson and student needs.
- Teaching Tools
- Subtraction
- Multiplication
- Mixed operations
- Ordering and number sense
- Comparing and sequencing
- Physical measurement
- Ratios and percentages
- Probability and data relationships
You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.
A jolt of creativity would help. But it doesn’t come.
Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.
This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes.
There are 120 examples in total.
The list of examples is supplemented by tips to create engaging and challenging math word problems.
120 Math word problems, categorized by skill
Addition word problems.
Best for: 1st grade, 2nd grade
1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?
2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?
3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?
4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?
5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?
6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?
7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?
8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?
Subtraction word problems
Best for: 1st grade, second grade
9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?
10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?
11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?
Practice math word problems with Prodigy Math
Join millions of teachers using Prodigy to make learning fun and differentiate instruction as they answer in-game questions, including math word problems from 1st to 8th grade!
12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?
13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?
14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?
15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?
16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?
Multiplication word problems
Best for: 2nd grade, 3rd grade
17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?
18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?
19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?
20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?
21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?
Division word problems
Best for: 3rd grade, 4th grade, 5th grade
22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?
23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?
24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?
25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?
26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?
Mixed operations word problems
27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?
28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?
29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?
30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?
Ordering and number sense word problems
31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?
32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?
33. Composing Numbers: What number is 6 tens and 10 ones?
34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?
35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?
Fractions word problems
Best for: 3rd grade, 4th grade, 5th grade, 6th grade
36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?
37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?
38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?
39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?
40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?
41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?
42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?
43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?
44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.
45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?
46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.
Decimals word problems
Best for: 4th grade, 5th grade
47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?
48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?
49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?
50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?
51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?
52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?
Comparing and sequencing word problems
Best for: Kindergarten, 1st grade, 2nd grade
53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?
54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?
55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?
56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?
57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?
58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?
59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?
Time word problems
66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?
69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?
70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?
71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?
Money word problems
Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade
60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?
61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?
62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?
63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?
64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?
65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?
67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.
68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?
Physical measurement word problems
Best for: 1st grade, 2nd grade, 3rd grade, 4th grade
72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?
73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?
74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?
75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?
76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?
77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?
78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?
79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?
80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?
81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?
Ratios and percentages word problems
Best for: 4th grade, 5th grade, 6th grade
82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?
83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?
84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?
85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?
86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?
87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?
88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?
Probability and data relationships word problems
Best for: 4th grade, 5th grade, 6th grade, 7th grade
89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?
90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?
91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.
92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?
93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?
94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?
95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .
Geometry word problems
Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade
96. Introducing Perimeter: The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?
97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?
98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?
99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?
100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?
101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?
102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?
103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?
104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?
105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?
106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?
107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?
108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?
109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?
110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?
111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?
112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?
113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?
114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?
Variables word problems
Best for: 6th grade, 7th grade, 8th grade
115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?
116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.
117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.
118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.
119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.
120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?
How to easily make your own math word problems & word problems worksheets
Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:
- Link to Student Interests: By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
- Make Questions Topical: Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
- Include Student Names: Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
- Be Explicit: Repeating keywords distills the question, helping students focus on the core problem.
- Test Reading Comprehension: Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
- Focus on Similar Interests: Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
- Feature Red Herrings: Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.
A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.
Final thoughts about math word problems
You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.
Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.
The result?
A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.
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30 Problem Solving Maths Questions And Answers For GCSE
Martin noon.
Problem solving maths questions can be challenging for GCSE students as there is no ‘one size fits all’ approach. In this article, we’ve compiled tips for problem solving, example questions, solutions and problem solving strategies for GCSE students.
Since the current GCSE specification began, there have been many problem solving exam questions which take elements of different areas of maths and combine them to form new maths problems which haven’t been seen before.
While learners can be taught to approach simply structured problems by following a process, questions often require students to make sense of lots of new information before they even move on to trying to solve the problem. This is where many learners get stuck.
How to teach problem solving
6 tips to tackling problem solving maths questions, 10 problem solving maths questions (foundation tier), 10 problem solving maths questions (foundation & higher tier crossover), 10 problem solving maths questions (higher tier).
In the Ofsted maths review , published in May 2021, Ofsted set out their findings from the research literature regarding the sort of curriculum and teaching that best supports all pupils to make good progress in maths throughout their time in school.
Regarding the teaching of problem solving skills, these were their recommendations:
- Teachers could use a curricular approach that better engineers success in problem-solving by teaching the useful combinations of facts and methods, how to recognise the problem types and the deep structures that these strategies pair to.
- Strategies for problem-solving should be topic specific and can therefore be planned into the sequence of lessons as part of the wider curriculum. Pupils who are already confident with the foundational skills may benefit from a more generalised process involving identifying relationships and weighing up features of the problem to process the information.
- Worked examples, careful questioning and constructing visual representations can help pupils to convert information embedded in a problem into mathematical notation.
- Open-ended problem solving tasks do not necessarily mean that the activity is the ‘ideal means of acquiring proficiency’. While enjoyable, open ended problem-solving activities may not necessarily lead to improved results.
There is no ‘one size fits all’ approach to successfully tackling problem solving maths questions however, here are 6 general tips for students facing a problem solving question:
- Read the whole question, underline important mathematical words, phrases or values.
- Annotate any diagrams, graphs or charts with any missing information that is easy to fill in.
- Think of what a sensible answer may look like. E.g. Will the angle be acute or obtuse? Is £30,000 likely to be the price of a coat?
- Tick off information as you use it.
- Draw extra diagrams if needed.
- Look at the final sentence of the question. Make sure you refer back to that at the end to ensure you have answered the question fully.
There are many online sources of mathematical puzzles and questions that can help learners improve their problem-solving skills. Websites such as NRICH and our blog on SSDD problems have some great examples of KS2, KS3 and KS4 mathematical problems.
In this article, we’ve focussed on GCSE questions and compiled 30 problem solving maths questions and solutions suitable for Foundation and Higher tier students. Additionally, we have provided problem solving strategies to support your students for some questions. For the full set of questions, solutions and strategies in a printable format, please download our 30 Problem Solving Maths Questions, Solutions & Strategies.
These first 10 questions and solutions are similar to Foundation questions. For the first three, we’ve provided some additional strategies.
In our downloadable resource, you can find strategies for all 10 Foundation questions .
1) L-shape perimeter
Here is a shape:
Sarah says, “There is not enough information to find the perimeter.”
Is she correct? What about finding the area?
- Try adding more information – giving some missing sides measurements that are valid.
- Change these measurements to see if the answer changes.
- Imagine walking around the shape if the edges were paths. Could any of those paths be moved to another position but still give the same total distance?
The perimeter of the shape does not depend on the lengths of the unlabelled edges.
Edge A and edge B can be moved to form a rectangle, meaning the perimeter will be 22 cm. Therefore, Sarah is wrong.
The area, however, will depend on those missing side length measurements, so we would need more information to be able to calculate it.
2) Find the missing point
Here is a coordinate grid with three points plotted. A fourth point is to be plotted to form a parallelogram. Find all possible coordinates of the fourth point.
- What are the properties of a parallelogram?
- Can we count squares to see how we can get from one vertex of the parallelogram to another? Can we use this to find the fourth vertex?
There are 3 possible positions.
3) That rating was a bit mean!
The vertical line graph shows the ratings a product received on an online shopping website. The vertical line for 4 stars is missing.
If the mean rating is 2.65, use the information to complete the vertical line graph.
Strategies
- Can the information be put into a different format, either a list or a table?
- Would it help to give the missing frequency an algebraic label, x ?
- If we had the data in a frequency table, how would we calculate the mean?
- Is there an equation we could form?
Letting the frequency of 4 star ratings be x , we can form the equation \frac{45+4x}{18+x} =2.65
Giving x=2
4) Changing angles
The diagram shows two angles around a point. The sum of the two angles around a point is 360°.
Peter says “If we increase the small angle by 10% and decrease the reflex angle by 10%, they will still add to 360°.”
Explain why Peter might be wrong.
Are there two angles where he would be correct?
Peter is wrong, for example, if the two angles are 40° and 320°, increasing 40° by 10% gives 44°, decreasing 320° by 10% gives 288°. These sum to 332°.
10% of the larger angle will be more than 10% of the smaller angle so the sum will only ever be 360° if the two original angles are the same, therefore, 180°.
5) Base and power
The integers 1, 2, 3, 4, 5, 6, 7, 8 and 9 can be used to fill in the boxes.
How many different solutions can be found so that no digit is used more than once?
There are 8 solutions.
6) Just an average problem
Place six single digit numbers into the boxes to satisfy the rules.
The mean is 5 \frac{1}{3}
The median is 5
The mode is 3.
How many different solutions are possible?
There are 4 solutions.
2, 3, 3, 7, 8, 9
3, 3, 4, 6, 7, 9
3, 3, 3, 7, 7, 9
3, 3, 3, 7, 8, 8
7) Square and rectangle
The square has an area of 81 cm 2 . The rectangle has the same perimeter as the square.
Its length and width are in the ratio 2:1.
Find the area of the rectangle.
The sides of the square are 9 cm giving a perimeter of 36 cm.
We can then either form an equation using a length 2x and width x .
Or, we could use the fact that the length and width add to half of the perimeter and share 18 in the ratio 2:1.
The length is 12 cm and the width is 6 cm, giving an area of 72 cm 2 .
8) It’s all prime
The sum of three prime numbers is equal to another prime number.
If the sum is less than 30, how many different solutions are possible?
There are 5 solutions.
2 can never be used as it would force two more odd primes into the sum to make the total even.
9) Unequal share
Bob and Jane have £10 altogether. Jane has £1.60 more than Bob. Bob spends one third of his money. How much money have Bob and Jane now got in total?
Initially Bob has £4.20 and Jane has £5.80. Bob spends £1.40, meaning the total £10 has been reduced by £1.40, leaving £8.60 after the subtraction.
10) Somewhere between
Fred says, “An easy way to find any fraction which is between two other fractions is to just add the numerators and add the denominators.” Is Fred correct?
Solution
Fred is correct. His method does work and can be shown algebraically which could be a good problem for higher tier learners to try.
If we use these two fractions \frac{3}{8} and \frac{5}{12} , Fred’s method gives us \frac{8}{20} = \frac{2}{5}
\frac{3}{8} = \frac{45}{120} , \frac{2}{5} = \frac{48}{120} , \frac{5}{12} = \frac{50}{120} . So \frac{3}{8} < \frac{2}{5} < \frac{5}{12}
The next 10 questions are crossover questions which could appear on both Foundation and Higher tier exam papers. We have provided solutions for each and, for the first three questions, problem solving strategies to support learners.
11) What’s the difference?
An arithmetic sequence has an nth term in the form an+b .
4 is in the sequence.
16 is in the sequence.
8 is not in the sequence.
-2 is the first term of the sequence.
What are the possible values of a and b ?
- We know that the first number in the sequence is -2 and 4 is in the sequence. Can we try making a sequence to fit? Would using a number line help?
- Try looking at the difference between the numbers we know are in the sequence.
If we try forming a sequence from the information, we get this:
We can now try to fill in the missing numbers, making sure 8 is not in the sequence. Going up by 2 would give us 8, so that won’t work.
The only solutions are 6 n -8 and 3 n -5.
12) Equation of the hypotenuse
The diagram shows a straight line passing through the axes at point P and Q .
Q has coordinate (8, 0). M is the midpoint of PQ and MQ has a length of 5 units.
Find the equation of the line PQ .
- We know MQ is 5 units, what is PQ and OQ ?
- What type of triangle is OPQ ?
- Can we find OP if we know PQ and OQ ?
- A line has an equation in the form y=mx+c . How can we find m ? Do we already know c ?
PQ is 10 units. Using Pythagoras’ Theorem OP = 6
The gradient of the line will be \frac{-6}{8} = -\frac{3}{4} and P gives the intercept as 6.
13) What a waste
Harry wants to cut a sector of radius 30 cm from a piece of paper measuring 30 cm by 20 cm.
What percentage of the paper will be wasted?
- What information do we need to calculate the area of a sector? Do we have it all?
- Would drawing another line on the diagram help find the angle of the sector?
The angle of the sector can be found using right angle triangle trigonometry.
The angle is 41.81°.
This gives us the area of the sector as 328.37 cm 2 .
The area of the paper is 600 cm 2 .
The area of paper wasted would be 600 – 328.37 = 271.62 cm 2 .
The wasted area is 45.27% of the paper.
14) Tri-polygonometry
The diagram shows part of a regular polygon and a right angled triangle. ABC is a straight line. Find the sum of the interior angles of the polygon.
Finding the angle in the triangle at point B gives 30°. This is the exterior angle of the polygon. Dividing 360° by 30° tells us the polygon has 12 sides. Therefore, the sum of the interior angles is 1800°.
15) That’s a lot of Pi
A block of ready made pastry is a cuboid measuring 3 cm by 10 cm by 15 cm.
Anne is making 12 pies for a charity event. For each pie, she needs to cut a circle of pastry with a diameter of 18 cm from a sheet of pastry 0.5 cm thick.
How many blocks of pastry will Anne need to buy?
The volume of one block of pastry is 450 cm 3 .
The volume of one cylinder of pastry is 127.23 cm 3 .
12 pies will require 1526.81 cm 3 .
Dividing the volume needed by 450 gives 3.39(…).
Rounding this up tells us that 4 pastry blocks will be needed.
16) Is it right?
A triangle has sides of (x+4) cm, (2x+6) cm and (3x-2) cm. Its perimeter is 80 cm.
Show that the triangle is right angled and find its area.
Forming an equation gives 6x+8=80
This gives us x=12 and side lengths of 16 cm, 30 cm and 34 cm.
Using Pythagoras’ Theorem
16 2 +30 2 =1156
Therefore, the triangle is right angled.
The area of the triangle is (16 x 30) ÷ 2 = 240 cm 2 .
17) Pie chart ratio
The pie chart shows sectors for red, blue and green.
The ratio of the angles of the red sector to the blue sector is 2:7.
The ratio of the angles of the red sector to the green sector is 1:3.
Find the angles of each sector of the pie chart.
Multiplying the ratio of red : green by 2, it can be written as 2:6.
Now the colour each ratio has in common, red, has equal parts in each ratio.
The ratio of red:blue is 2:7, this means red:blue:green = 2:7:6.
Sharing 360° in this ratio gives red:blue:green = 48°:168°:144°.
18) DIY Simultaneously
Mr Jones buys 5 tins of paint and 4 rolls of decorating tape. The total cost was £167.
The next day he returns 1 unused tin of paint and 1 unused roll of tape. The refund amount is exactly the amount needed to buy a fan heater that has been reduced by 10% in a sale. The fan heater normally costs £37.50.
Find the cost of 1 tin of paint.
The sale price of the fan heater is £33.75. This gives the simultaneous equations
p+t = 33.75 and 5 p +4 t = 167.
We only need the price of a tin of paint so multiplying the first equation by 4 and then subtracting from the second equation gives p =32. Therefore, 1 tin of paint costs £32.
19) Triathlon pace
Jodie is competing in a Triathlon.
A triathlon consists of a 5 km swim, a 40 km cycle and a 10 km run.
Jodie wants to complete the triathlon in 5 hours.
She knows she can swim at an average speed of 2.5 km/h and cycle at an average speed of 25 km/h. There are also two transition stages, in between events, which normally take 4 minutes each.
What speed must Jodie average on the final run to finish the triathlon in 5 hours?
Dividing the distances by the average speeds for each section gives times of 2 hours for the swim and 1.6 hours for the cycle, 216 minutes in total. Adding 8 minutes for the transition stages gives 224 minutes. To complete the triathlon in 5 hours, that would be 300 minutes. 300 – 224 = 76 minutes. Jodie needs to complete her 10 km run in 76 minutes, or \frac{19}{15} hours. This gives an average speed of 7.89 km/h.
20) Indices
a 2x × a y =a 3
(a 3 ) x ÷ a 4y =a 32
Find x and y .
Forming the simultaneous equations
Solving these gives
This final set of 10 questions would appear on the Higher tier only. Here we have just provided the solutions. Try asking your learners to discuss their strategies for each question.
21) Angles in a polygon
The diagram shows part of a regular polygon.
A , B and C are vertices of the polygon.
The size of the reflex angle ABC is 360° minus the interior angle.
Show that the sum of all of these reflex angles of the polygon will be 720° more than the sum of its interior angles.
Each of the reflex angles is 180 degrees more than the exterior angle: 180 + \frac{360}{n}
The sum of all of these angles is n (180 + \frac{360}{n} ).
This simplifies to 180 n + 360
The sum of the interior angles is 180( n – 2) = 180 n – 360
The difference is 180 n + 360 – (180 n -360) = 720°
22) Prism and force (Non-calculator)
The diagram shows a prism with an equilateral triangle cross-section.
When the prism is placed so that its triangular face touches the surface, the prism applies a force of 12 Newtons resulting in a pressure of \frac{ \sqrt{3} }{4} N/m^{2}
Given that the prism has a volume of 384 m 3 , find the length of the prism.
Pressure = \frac{Force}{Area}
Area = 12÷ \frac{ \sqrt{3} }{4} = 16\sqrt{3} m 2
Therefore, the length of the prism is 384 ÷ 16\sqrt{3} = 8\sqrt{3} m
23) Geometric sequences (Non-calculator)
A geometric sequence has a third term of 6 and a sixth term of 14 \frac{2}{9}
Find the first term of the sequence.
The third term is ar 2 = 6
The sixth term is ar 5 = \frac{128}{9}
Diving these terms gives r 3 = \frac{64}{27}
Giving r = \frac{4}{3}
Dividing the third term twice by \frac{4}{3} gives the first term a = \frac{27}{8}
24) Printing factory
A printing factory is producing exam papers. When all 10 of its printers are working, it can produce all of the exam papers in 12 days.
For the first two days of printing, 3 of the printers are broken.
At the beginning of the third day it is discovered that 2 more printers have broken down, so the factory continues to print with the reduced amount of printers for 3 days. The broken printers are repaired and now all printers are available to print the remaining exams.
How many days in total does it take the factory to produce all of the exam papers?
If we assume one printer prints 1 exam paper per day, 10 printers would print 120 exam papers in 12 days. Listing the number printed each day for the first 5 days gives:
Day 5: 5
This is a total of 29 exam papers.
91 exam papers are remaining with 10 printers now able to produce a total of 10 exam papers each day. 10 more days would be required to complete the job.
Therefore, 15 days in total are required.
25) Circles
The diagram shows a circle with equation x^{2}+{y}^{2}=13 .
A tangent touches the circle at point P when x=3 and y is negative.
The tangent intercepts the coordinate axes at A and B .
Find the length AB .
Using the equation x^{2}+y^{2}=13 to find the y value for P gives y=-2 .
The gradient of the radius at this point is - \frac{2}{3} , giving a tangent gradient of \frac{3}{2} .
Using the point (3,-2) in y = \frac {3}{2} x+c gives the equation of the tangent as y = \frac {3}{2} x – \frac{13}{2}
Substituting x=0 and y=0 gives A and B as (0 , -\frac {13}{2}) and ( \frac{13}{3} , 0)
Using Pythagoras’ Theorem gives the length of AB as ( \frac{ 13\sqrt{13} }{6} ) = 7.812.
26) Circle theorems
The diagram shows a circle with centre O . Points A, B, C and D are on the circumference of the circle.
EF is a tangent to the circle at A .
Angle EAD = 46°
Angle FAB = 48°
Angle ADC = 78°
Find the area of ABCD to the nearest integer.
The Alternate Segment Theorem gives angle ACD as 46° and angle ACB as 48°.
Opposite angles in a cyclic quadrilateral summing to 180° gives angle ABC as 102°.
Using the sine rule to find AC will give a length of 5.899. Using the sine rule again to find BC will give a length of 3.016cm.
We can now use the area of a triangle formula to find the area of both triangles.
0.5 × 5 × 5.899 × sin (46) + 0.5 × 3.016 × 5.899 × sin (48) = 17 units 2 (to the nearest integer).
27) Quadratic function
The quadratic function f(x) = -2x^{2} + 8x +11 has a turning point at P .
Find the coordinate of the turning point after the transformation -f(x-3) .
There are two methods that could be used. We could apply the transformation to the function and then complete the square, or, we could complete the square and then apply the transformation.
Here we will do the latter.
This gives a turning point for f(x) as (2,19).
Applying -f(x-3) gives the new turning point as (5,-19).
28) Probability with fruit
A fruit bowl contains only 5 grapes and n strawberries.
A fruit is taken, eaten and then another is selected.
The probability of taking two strawberries is \frac{7}{22} .
Find the probability of taking one of each fruit.
There are n+5 fruits altogether.
P(Strawberry then strawberry)= \frac{n}{n+5} × \frac{n-1}{n+4} = \frac{7}{22}
This gives the quadratic equation 15n^{2} - 85n - 140 = 0
This can be divided through by 5 to give 3n^{2} - 17n- 28 = 0
This factorises to (n-7)(3n + 4) = 0
n must be positive so n = 7.
The probability of taking one of each fruit is therefore, \frac{5}{12} × \frac{7}{11} + \frac {7}{12} × \frac {5}{11} = \frac {70}{132}
29) Ice cream tub volume
An ice cream tub in the shape of a prism with a trapezium cross-section has the dimensions shown. These measurements are accurate to the nearest cm.
An ice cream scoop has a diameter of 4.5 cm to the nearest millimetre and will be used to scoop out spheres of ice cream from the tub.
Using bounds find a suitable approximation to the number of ice cream scoops that can be removed from a tub that is full.
We need to find the upper and lower bounds of the two volumes.
Upper bound tub volume = 5665.625 cm 3
Lower bound tub volume = 4729.375 cm 3
Upper bound scoop volume = 49.32 cm 3
Lower bound scoop volume = 46.14 cm 3
We can divide the upper bound of the ice cream tub by the lower bound of the scoop to get the maximum possible number of scoops.
Maximum number of scoops = 122.79
Then divide the lower bound of the ice cream tub by the upper bound of the scoop to get the minimum possible number of scoops.
Minimum number of scoops = 95.89
These both round to 100 to 1 significant figure, Therefore, 100 scoops is a suitable approximation the the number of scoops.
30) Translating graphs
The diagram shows the graph of y = a+tan(x-b ).
The graph goes through the points (75, 3) and Q (60, q).
Find exact values of a , b and q .
The asymptote has been translated to the right by 30°.
Therefore, b=30
So the point (45,1) has been translated to the point (75,3).
Therefore, a=2
We hope these problem solving maths questions will support your GCSE teaching. To get all the solutions and strategies in a printable form, please download the complete resource .
Looking for additional support and resources? You are welcome to download any of the secondary maths resources from Third Space Learning’s resource library for free. There is a section devoted to GCSE maths revision with plenty of maths worksheets and GCSE maths questions . There are also maths tests for KS3, including a Year 7 maths test , a Year 8 maths test and a Year 9 maths test Other valuable maths practice and ideas particularly around reasoning and problem solving at secondary can be found in our KS3 and KS4 maths blog articles. Try these fun maths problems for KS2 and KS3, KS3 maths games and 30 problem solving maths questions . For children who need more support, our maths intervention programmes for KS3 achieve outstanding results through a personalised one to one tuition approach.
Do you have students who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of students across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to plug gaps and boost progress. Since 2013 we’ve helped over 150,000 primary and secondary students become more confident, able mathematicians. Find out more about our GCSE Maths tuition or request a personalised quote for your school to speak to us about your school’s needs and how we can help.
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1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 145. So after completing the 1st week she will get $ (x+145). Similarly after completing the 2nd week she will get $ (x + 145) + $ 145. = $ (x + 145 + 145) = $ (x + 290) So in this way end of every week her salary will increase by $ 145.
3. Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he: (a) broke even, (b) lost 4 cents, (c) gained 4 cents, (d) lost 10 cents, (e) gained 10 cents Solution:
Selling price of the first pipe = $1.20
Profit = 20%
Let’s try to find the cost price of the first pipe
CP = Selling price - Profit
CP = 1.20 - 20% of CP
CP = 1.20 - 0.20CP
CP + 0.20CP = 1.20
1.20CP = 1.20
CP = \(\frac{1.20}{1.20}\)
Selling price of the Second pipe = $1.20
Let’s try to find the cost price of the second pipe
CP = Selling price + Loss
CP = 1.20 + 20% of CP
CP = 1.20 + 0.20CP
CP - 0.20CP = 1.20
0.80CP = 1.20
CP = \(\frac{1.20}{0.80}\)
Therefore, total cost price of the two pipes = $1.00 + $1.50 = $2.50
And total selling price of the two pipes = $1.20 + $1.20 = $2.40
Loss = $2.50 – $2.40 = $0.10
Therefore, Mr. Jones loss 10 cents.
Answer: (d)
5. A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at: (a) 6 % , (b) 6.1 %, (c) 6.2 %, (d) 6.3 %, (e) 6.4 % Solution: Income from $ 4000 at 5 % in one year = $ 4000 of 5 %. = $ 4000 × 5/100. = $ 4000 × 0.05. = $ 200. Income from $ 3500 at 4 % in one year = $ 3500 of 4 %. = $ 3500 × 4/100. = $ 3500 × 0.04. = $ 140. Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340. Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340. = $ 160. Total invested amount = $ 4000 + $ 3500 = $7500. Remaining invest amount = $ 10000 - $ 7500 = $ 2500. We know that, Interest = Principal × Rate × Time Interest = $ 160, Principal = $ 2500, Rate = r [we need to find the value of r], Time = 1 year. 160 = 2500 × r × 1. 160 = 2500r 160/2500 = 2500r/2500 [divide both sides by 2500] 0.064 = r r = 0.064 Change it to a percent by moving the decimal to the right two places r = 6.4 % Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year. Answer: (e) 6. Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was: (a) three times as much, (b) twice as much, (c) the same, (d) half as much, (e) a third as much Solution: Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr. We know that Speed = Distance/Time. Or, Time = Distance/Speed. So, times taken to covered a distance of 50 miles on his first trip = 50/x hr. And times taken to covered a distance of 300 miles on his later trip = 300/3x hr. = 100/x hr. So we can clearly see that his new time compared with the old time was: twice as much. Answer: (b)
Unsolved Questions:
1. Fahrenheit temperature F is a linear function of Celsius temperature C. The ordered pair (0, 32) is an ordered pair of this function because 0°C is equivalent to 32°F, the freezing point of water. The ordered pair (100, 212) is also an ordered pair of this function because 100°C is equivalent to 212° F, the boiling point of water.
2. A sports field is 300 feet long. Write a formula that gives the length of x sports fields in feet. Then use this formula to determine the number of sports fields in 720 feet.
3. A recipe calls for 2 1/2 cups and I want to make 1 1/2 recipes. How many cups do I need?
4. Mario answered 30% of the questions correctly. The test contained a total of 80 questions. How many questions did Mario answer correctly?
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Solving Word Questions
With LOTS of examples!
In Algebra we often have word questions like:
Example: Sam and Alex play tennis.
On the weekend Sam played 4 more games than Alex did, and together they played 12 games.
How many games did Alex play?
How do we solve them?
The trick is to break the solution into two parts:
Turn the English into Algebra.
Then use Algebra to solve.
Turning English into Algebra
To turn the English into Algebra it helps to:
- Read the whole thing first
- Do a sketch if possible
- Assign letters for the values
- Find or work out formulas
You should also write down what is actually being asked for , so you know where you are going and when you have arrived!
Also look for key words:
Thinking Clearly
Some wording can be tricky, making it hard to think "the right way around", such as:
Example: Sam has 2 dollars less than Alex. How do we write this as an equation?
- Let S = dollars Sam has
- Let A = dollars Alex has
Now ... is that: S − 2 = A
or should it be: S = A − 2
or should it be: S = 2 − A
The correct answer is S = A − 2
( S − 2 = A is a common mistake, as the question is written "Sam ... 2 less ... Alex")
Example: on our street there are twice as many dogs as cats. How do we write this as an equation?
- Let D = number of dogs
- Let C = number of cats
Now ... is that: 2D = C
or should it be: D = 2C
Think carefully now!
The correct answer is D = 2C
( 2D = C is a common mistake, as the question is written "twice ... dogs ... cats")
Let's start with a really simple example so we see how it's done:
Example: A rectangular garden is 12m by 5m, what is its area ?
Turn the English into Algebra:
- Use w for width of rectangle: w = 12m
- Use h for height of rectangle: h = 5m
Formula for Area of a Rectangle : A = w × h
We are being asked for the Area.
A = w × h = 12 × 5 = 60 m 2
The area is 60 square meters .
Now let's try the example from the top of the page:
Example: Sam and Alex play Tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play?
- Use S for how many games Sam played
- Use A for how many games Alex played
We know that Sam played 4 more games than Alex, so: S = A + 4
And we know that together they played 12 games: S + A = 12
We are being asked for how many games Alex played: A
Which means that Alex played 4 games of tennis.
Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. Yes!
A slightly harder example:
Example: Alex and Sam also build tables. Together they make 10 tables in 12 days. Alex working alone can make 10 in 30 days. How long would it take Sam working alone to make 10 tables?
- Use a for Alex's work rate
- Use s for Sam's work rate
12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10
30 days of Alex alone is also 10 tables: 30a = 10
We are being asked how long it would take Sam to make 10 tables.
30a = 10 , so Alex's rate (tables per day) is: a = 10/30 = 1/3
Which means that Sam's rate is half a table a day (faster than Alex!)
So 10 tables would take Sam just 20 days.
Should Sam be paid more I wonder?
And another "substitution" example:
Example: Jenna is training hard to qualify for the National Games. She has a regular weekly routine, training for five hours a day on some days and 3 hours a day on the other days. She trains altogether 27 hours in a seven day week. On how many days does she train for five hours?
- The number of "5 hour" days: d
- The number of "3 hour" days: e
We know there are seven days in the week, so: d + e = 7
And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27
We are being asked for how many days she trains for 5 hours: d
The number of "5 hour" days is 3
Check : She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.
3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours
Some examples from Geometry:
Example: A circle has an area of 12 mm 2 , what is its radius?
- Use A for Area: A = 12 mm 2
- Use r for radius
And the formula for Area is: A = π r 2
We are being asked for the radius.
We need to rearrange the formula to find the area
Example: A cube has a volume of 125 mm 3 , what is its surface area?
Make a quick sketch:
- Use V for Volume
- Use A for Area
- Use s for side length of cube
- Volume of a cube: V = s 3
- Surface area of a cube: A = 6s 2
We are being asked for the surface area.
First work out s using the volume formula:
Now we can calculate surface area:
An example about Money:
Example: Joel works at the local pizza parlor. When he works overtime he earns 1¼ times the normal rate. One week Joel worked for 40 hours at the normal rate of pay and also worked 12 hours overtime. If Joel earned $660 altogether in that week, what is his normal rate of pay?
- Joel's normal rate of pay: $N per hour
- Joel works for 40 hours at $N per hour = $40N
- When Joel does overtime he earns 1¼ times the normal rate = $1.25N per hour
- Joel works for 12 hours at $1.25N per hour = $(12 × 1¼N) = $15N
- And together he earned $660, so:
$40N + $(12 × 1¼N) = $660
We are being asked for Joel's normal rate of pay $N.
So Joel’s normal rate of pay is $12 per hour
Joel’s normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660
More about Money, with these two examples involving Compound Interest
Example: Alex puts $2000 in the bank at an annual compound interest of 11%. How much will it be worth in 3 years?
This is the compound interest formula:
So we will use these letters:
- Present Value PV = $2,000
- Interest Rate (as a decimal): r = 0.11
- Number of Periods: n = 3
- Future Value (the value we want): FV
We are being asked for the Future Value: FV
Example: Roger deposited $1,000 into a savings account. The money earned interest compounded annually at the same rate. After nine years Roger's deposit has grown to $1,551.33 What was the annual rate of interest for the savings account?
The compound interest formula:
- Present Value PV = $1,000
- Interest Rate (the value we want): r
- Number of Periods: n = 9
- Future Value: FV = $1,551.33
We are being asked for the Interest Rate: r
So the annual rate of interest is 5%
Check : $1,000 × (1.05) 9 = $1,000 × 1.55133 = $1,551.33
And an example of a Ratio question:
Example: At the start of the year the ratio of boys to girls in a class is 2 : 1 But now, half a year later, four boys have left the class and there are two new girls. The ratio of boys to girls is now 4 : 3 How many students are there altogether now?
- Number of boys now: b
- Number of girls now: g
The current ratio is 4 : 3
Which can be rearranged to 3b = 4g
At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1
b + 4 g − 2 = 2 1
Which can be rearranged to b + 4 = 2(g − 2)
We are being asked for how many students there are altogether now: b + g
There are 12 girls !
And 3b = 4g , so b = 4g/3 = 4 × 12 / 3 = 16 , so there are 16 boys
So there are now 12 girls and 16 boys in the class, making 28 students altogether .
There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1
And now for some Quadratic Equations :
Example: The product of two consecutive even integers is 168. What are the integers?
Consecutive means one after the other. And they are even , so they could be 2 and 4, or 4 and 6, etc.
We will call the smaller integer n , and so the larger integer must be n+2
And we are told the product (what we get after multiplying) is 168, so we know:
n(n + 2) = 168
We are being asked for the integers
That is a Quadratic Equation , and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12.
Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES
Check 12: 12(12 + 2) = 12×14 = 168 YES
So there are two solutions: −14 and −12 is one, 12 and 14 is the other.
Note: we could have also tried "guess and check":
- We could try, say, n=10: 10(12) = 120 NO (too small)
- Next we could try n=12: 12(14) = 168 YES
But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12).
Example: You are an Architect. Your client wants a room twice as long as it is wide. They also want a 3m wide veranda along the long side. Your client has 56 square meters of beautiful marble tiles to cover the whole area. What should the length of the room be?
Let's first make a sketch so we get things right!:
- the length of the room: L
- the width of the room: W
- the total Area including veranda: A
- the width of the room is half its length: W = ½L
- the total area is the (room width + 3) times the length: A = (W+3) × L = 56
We are being asked for the length of the room: L
This is a quadratic equation , there are many ways to solve it, this time let's use factoring :
And so L = 8 or −14
There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!
So the length of the room is 8 m
L = 8, so W = ½L = 4
So the area of the rectangle = (W+3) × L = 7 × 8 = 56
There we are ...
... I hope these examples will help you get the idea of how to handle word questions. Now how about some practice?
Table of Contents
Introduction
Mathematics can be fun if you treat it the right way. Maths is nothing less than a game, a game that polishes your intelligence and boosts your concentration. Compared to older times, people have a better and friendly approach to mathematics which makes it more appealing. The golden rule is to know that maths is a mindful activity rather than a task.
There is nothing like hard math problems or tricky maths questions, it’s just that you haven’t explored mathematics well enough to comprehend its easiness and relatability. Maths tricky questions and answers can be transformed into fun math problems if you look at it as if it is a brainstorming session. With the right attitude and friends and teachers, doing math can be most entertaining and delightful.
Math is interesting because a few equations and diagrams can communicate volumes of information. Treat math as a language, while moving to rigorous proof and using logical reason for performing a particular step in a proof or derivation.
Treating maths as a language totally eradicates the concept of hard math problems or tricky maths questions from your mind. Introducing children to fun maths questions can create a strong love and appreciation for maths at an early age. This way you are setting up the child’s successful future. Fun math problems will urge your child to choose to solve it over playing bingo or baking.
Apparently, there are innumerable methods to make easy maths tricky questions and answers. This includes the inception of the ideology that maths is simpler than their fear. This can be done by connecting maths with everyday life. Practising maths with the aid of dice, cards, puzzles and tables reassures that your child effectively approaches Maths.
If you wish to add some fun and excitement into educational activities, also check out
- Check out some mind-blowing Math Magic Tricks!
- Mental Maths: How to Improve it?
Cuemath is one of the world's leading math learning platforms that offers LIVE 1-to-1 online math classes for grades K-12 . Our mission is to transform the way children learn math, to help them excel in school and competitive exams. Our expert tutors conduct 2 or more live classes per week, at a pace that matches the child's learning needs.
Fun Maths Questions with answers - PDF
Here is the Downloadable PDF that consists of Fun Math questions. Click the Download button to view them.
Here are some fun, tricky and hard to solve maths problems that will challenge your thinking ability.
Answer: is 3, because ‘six’ has three letters
What is the number of parking space covered by the car?
This tricky math problem went viral a few years back after it appeared on an entrance exam in Hong Kong… for six-year-olds. Supposedly the students had just 20 seconds to solve the problem!
Believe it or not, this “math” question actually requires no math whatsoever. If you flip the image upside down, you’ll see that what you’re dealing with is a simple number sequence.
Replace the question mark in the above problem with the appropriate number.
Which number is equivalent to 3^(4)÷3^(2)
This problem comes straight from a standardized test given in New York in 2014.
There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete?
This question comes directly from a second grader's math homework.
To figure out how many small dogs are competing, you have to subtract 36 from 49 and then divide that answer, 13 by 2, to get 6.5 dogs, or the number of big dogs competing. But you’re not done yet! You then have to add 6.5 to 36 to get the number of small dogs competing, which is 42.5. Of course, it’s not actually possible for half a dog to compete in a dog show, but for the sake of this math problem let’s assume that it is.
Add 8.563 and 4.8292.
Adding two decimals together is easier than it looks. Don’t let the fact that 8.563 has fewer numbers than 4.8292 trip you up. All you have to do is add a 0 to the end of 8.563 and then add like you normally would.
I am an odd number. Take away one letter and I become even. What number am I?
Answer: Seven (take away the ‘s’ and it becomes ‘even’).
Using only an addition, how do you add eight 8’s and get the number 1000?
Answer:
888 + 88 + 8 + 8 + 8 = 1000
Sally is 54 years old and her mother is 80, how many years ago was Sally’s mother times her age?
41 years ago, when Sally was 13 and her mother was 39.
Which 3 numbers have the same answer whether they’re added or multiplied together?
There is a basket containing 5 apples, how do you divide the apples among 5 children so that each child has 1 apple while 1 apple remains in the basket?
4 children get 1 apple each while the fifth child gets the basket with the remaining apple still in it.
There is a three-digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?
Fill in the question mark
Two girls were born to the same mother, at the same time, on the same day, in the same month and the same year and yet somehow they’re not twins. Why not?
Because there was a third girl, which makes them triplets!
A ship anchored in a port has a ladder which hangs over the side. The length of the ladder is 200cm, the distance between each rung in 20cm and the bottom rung touches the water. The tide rises at a rate of 10cm an hour. When will the water reach the fifth rung?
The tide raises both the water and the boat so the water will never reach the fifth rung.
The day before yesterday I was 25. The next year I will be 28. This is true only one day in a year. What day is my Birthday?
You have a 3-litre bottle and a 5-litre bottle. How can you measure 4 litres of water by using 3L and 5L bottles?
Solution 1 :
First, fill 3Lt bottle and pour 3 litres into 5Lt bottle.
Again fill the 3Lt bottle. Now pour 2 litres into the 5Lt bottle until it becomes full.
Now empty 5Lt bottle.
Pour remaining 1 litre in 3Lt bottle into 5Lt bottle.
Now again fill 3Lt bottle and pour 3 litres into 5Lt bottle.
Now you have 4 litres in the 5Lt bottle. That’s it.
Solution 2 :
First, fill the 5Lt bottle and pour 3 litres into 3Lt bottle.
Empty 3Lt bottle.
Pour remaining 2 litres in 5Lt bottle into 3Lt bottle.
Again fill the 5Lt bottle and pour 1 litre into 3 Lt bottle until it becomes full.
3 Friends went to a shop and purchased 3 toys. Each person paid Rs.10 which is the cost of one toy. So, they paid Rs.30 i.e. total amount. The shop owner gave a discount of Rs.5 on the total purchase of 3 toys for Rs.30. Then, among Rs.5, Each person has taken Rs.1 and remaining Rs.2 given to the beggar beside the shop. Now, the effective amount paid by each person is Rs.9 and the amount given to the beggar is Rs.2. So, the total effective amount paid is 9*3 = 27 and the amount given to beggar is Rs.2, thus the total is Rs.29. Where has the other Rs.1 gone from the original Rs.30?
The logic is payments should be equal to receipts. We cannot add the amount paid by persons and the amount given to the beggar and compare it to Rs.30.The total amount paid is ₹27. So, from ₹27, the shop owner received 25 rupees and beggar received ₹ 2. Thus, payments are equal to receipts.
How to get a number 100 by using four sevens (7’s) and a one (1)?
Answer 1: 177 – 77 = 100 ;
Answer 2: (7+7) * (7 + (1/7)) = 100
Move any four matches to get 3 equilateral triangles only (don’t remove matches)
Find the area of the red triangle.
To solve this fun maths question, you need to understand how the area of a parallelogram works. If you already know how the area of a parallelogram and the area of a triangle are related, then adding 79 and 10 and subsequently subtracting 72 and 8 to get 9 should make sense.
How many feet are in a mile?
Solve - 15+ (-5x) =0
What is 1.92÷3
A man is climbing up a mountain which is inclined. He has to travel 100 km to reach the top of the mountain. Every day He climbs up 2 km forward in the day time. Exhausted, he then takes rest there at night time. At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined. Then how many days does it take him to reach the mountain top?
If 72 x 96 = 6927, 58 x 87 = 7885, then 79 x 86 = ?
Answer:
Look at this series: 36, 34, 30, 28, 24, … What number should come next?
Look at this series: 22, 21, 23, 22, 24, 23, … What number should come next?
If 13 x 12 = 651 & 41 x 23 = 448, then, 24 x 22 =?
Look at this series: 53, 53, 40, 40, 27, 27, … What number should come next?
The ultimate goals of mathematics instruction are students understanding the material presented, applying the skills, and recalling the concepts in the future. There's little benefit in students recalling a formula or procedure to prepare for an assessment tomorrow only to forget the core concept by next week.
Teachers must focus on making sure that the students understand the material and not just memorize the procedures. After you learn the answers to a fun maths question, you begin to ask yourself how you could have missed something so easy. The truth is, most trick questions are designed to trick your mind, which is why the answers to fun maths questions are logical and easy.
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The home of mathematics education in New Zealand.
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- Teaching material
- Problem solving activities
Problem Solving
This section of the nzmaths website has problem-solving lessons that you can use in your maths programme. The lessons provide coverage of Levels 1 to 6 of The New Zealand Curriculum. The lessons are organised by level and curriculum strand. Accompanying each lesson is a copymaster of the problem in English and in Māori.
Choose a problem that involves your students in applying current learning. Remember that the context of most problems can be adapted to suit your students and your current class inquiry. Customise the problems for your class.
- Level 1 Problems
- Level 2 Problems
- Level 3 Problems
- Level 4 Problems
- Level 5 Problems
- Level 6 Problems
The site also includes Problem Solving Information . This provides you with practical information about how to implement problem solving in your maths programme as well as some of the philosophical ideas behind problem solving. We also have a collection of problems and solutions for students to use independently.
Examples for
Mathematical Word Problems
Math word problems is one of the most complex parts of the elementary math curriculum since translating text into symbolic math is required to solve the problem. Because the Wolfram Language has powerful symbolic computation ability, Wolfram|Alpha can interpret basic mathematical word problems and give descriptive results.
Word Problems
Solve a word problem and explore related facts.
Solve a word problem:
Related examples.
Math Word Problems
Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.
There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:
- Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
- Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
- Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
- Calculate : Use your strategy to solve the problem.
- Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.
Most Popular Math Word Problems this Week
Various Word Problems
Various word problems for students who have mastered basic arithmetic and need a further challenge.
Addition word problems
Subtraction word problems
Multiplication word problems
Division word problems
Multi-Step word problems
Copyright © 2005-2023 Math-Drills.com You may use the math worksheets on this website according to our Terms of Use to help students learn math.
40 Fun Math Questions with Answers
Learning math can be super fun if students are shown it in the right way. Students run away from hard math problems but don’t know that solving those questions can be fun and exciting . Solving math riddles and fun Math Questions is an interesting game that helps polish our aptitude and boosts our concentration and brainpower.
With time, the approaches to solving math and perception of the subject have changed a lot. These new perceptions of math have made the subject and its concepts more appealing. One only needs to know and understand that math is not just a subject or task; it is a mindful and fun-filled activity for the brain.
You can easily get 50+ Funny math questions – Download for free here!
Honestly, hard math questions or problems are all illusions; it is all about knowing and understanding the math sufficiently, its concepts, easiness, and relatability. If teachers have the right attitude and patience, solving and learning math can be most engaging, enjoyable, and delightful for the students. Here are some tricky and engaging yet funny math questions with answers for a fantastic brainstorming session.
Fun Math Questions For Students
- How can you make number six with these three matchsticks without cutting them?
100+ Free Math Worksheets, Practice Tests & Quizzes
Answer: Just move the first and the second matchstick in the shape of a V; it will form a six in roman number.
- Get five squares in the following gird. But you can only remove or move four matchsticks.
Answer: Remove the edge matchsticks from the middle row and column as shown in the picture.
- What will be the last number in the following series of numbers?
32, 45, 60, 77, ?
Answer: 8×4 =32, 9×5 = 45, 10×6 = 60, 11×7 = 77, 12×8 = 96.
Answer2: 32+13 = 45. 45+15 = 60, 60+17 = 77, 77+19 = 96.
So, the following number will be 96.
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- Solve this equation.
Answer: One Triangle = 10 as per the first equation
One Circle = 2 on solving the second equation
One Star = 1 on solving the equation third
So, the answer is 1.
- Find the correct answer to the equation.
Answer: 3 Apples = 30; So, 1 Apple = 10
As per the second equation, one banana = 1
As per the third equation, coconut half = 1
So, the half coconut + 1 Apple + 3 Banana = 12
- Fill the place for the question mark.
Answer: (8×4) – (6×2) = 20
(5×6) – (3×4) = 18
(9×4) – (5×3) = 21
- What goes into the empty box?
Answer: Seeing the rows
1+2= 3; 3+2= 5.
2+2= 4; 4+2=6.
Another way: See the columns
1 —> 2; 3 —> 4; 5 —>6
- Correct this equation but remember you can only move one stick.
Answer: Move the top right matchstick from the 8 and place it on — sign to make it + sign. The equation will be 9+6 = 15.
- Which number will be at the place of the question mark?
Answer: 2 Bananas = 30; so, 1 banana will be = 15
2 cherries + 2 cherries = 20; so, 1 cherry will be = 5
2 apples = 8; so, 1 apple will be = 4
Therefore; 1 banana + 1 cherry + 1 apple = 15 + 5 + 4 = 24
- Find the number for the blank space.
Answer: 8+6 =14; 14+8 = 22; 22+10 = 32; 32+12 = 42.
So, 42 will be the answer.
- Count the triangles.
- Can you solve this number puzzle?
Answer: (7*4) + (4*5) = 28+20 = 48;
(9*3) + (3*6) = 27+18 = 45;
(5*?) + (?*8) = 13*? = 6
- What is the missing number in the following grid?
Answer: (3 + 2) x 2 = 10
(1 + 9) x 2 = 20
(0 + 8) x 2 = 16
(7 + 5) x 2 = 24
So, the number is 6.
- Which numbers in pins should I stroke to get an exact 100 score?
Answer: Strike number 48, 39, 13 as 48 because 48+39+13 = 100.
- Find the appropriate number for the blank space in the grid.
Answer: On analyzing the grid, one can find that the fourth row contains the average of numbers in the first three rows.
So, (3+5+1) / 3 = 3 is the answer.
- Again, find the missing number?
Answer: Look carefully; these numbers are organized in groups of two digits,s such as 75, 34, and 68 in the first row and 83, 42, and 7. In the second row.
Now, the same sequence is followed with every digit. The first number from the digit is increased by one, and the second number is decreased by two. 6+1 = 7 and 8-2 = 6 in the last digit.
Therefore, the missing number is 6.
- What is the missing number in the given pie?
Answer: Just divide the pie in quarters and see the answer logic.
7+? = 11 →? =
18. Add only one matchstick to make the equation right.
Answer: Add the one matchstick to the plus sign between any 5 to make it 4.And 545+5 = 550.
- Find the next number for the below series with the help of the given dies. 19, 11, 11, 9, ?
Answer: 7+3+2 = 12
- How many other triangles does this triangle comprise?
Answer: 23, count them carefully and patiently.
- Find the answer to this puzzle picture?
Answer: The answer is 18.
Reason: 5*8 = 40; 8*3 = 24; and 5*6 = 30. So, 6*3 = 18.
- Which is heavier, one pound feathers or one pound iron piece?
Answer: Both are equally heavier.
- There are ten fishes in a tank; two of them drown, four swim away, and three fishes die. What is the number of fish present in the tank?
Answer: All ten fishes because no one has removed any fish from the tank.
- Find the answer if 2=6, 3=12, 4=20, 5=30, 6=42, 9=?
Answer: 2 = 2×3 = 6
3 = 3×4 = 12
4 = 4×5 = 20
5 = 5×6 = 30
6 = 6×7 = 42
7 = 7×8 = 56
8 = 8×9 = 72
9 = 9×10 = 90
So, 9 = 90.
- Guess the correct answer if 1+4 = 5; 2+5 = 12; 3+6 = 21; 8+11 = ?
Answer: 1+4 = 4×1+1 = 5
2+5 = 5×2+2 = 12
3+6 = 6×3+3 = 21
8+11 = 11×8+8 = 96
- How is this possible with numbers?
19+3 = 1622
Answer: These equations are written as the deviation of the numbers and then the addition of the numbers.
For example: 6+4 = (6-4)(6+4) = 210.
- Solve this equation to find X.
12/3 (5-3+2) + 2004 = X
Answer: X = 2004
- Solve this number quiz.
Answer: As per the sample equations, 2+3 = 2x(2+3) = 10; 7x(7+2) = 63; and so on.
So, 9+5 = 9(9+5) = 126.
- Solve this number mystery.
If 3, 2, 4 = 10
4, 3, 5 = 17
5, 4, 6 = 36
6, 5, 7 = 37
Answer: The hidden equation in these numbers is like 3X2+4 = 10 for the first one.
Similarly, 7X6+8 = 50
- Elon brought a container holding six chocolate bars. If he needs to divide the chocolate bars with his six friends so that all of them get one bar, the container still has a chocolate bar left. How did he do this?
Answer: It is possible because he had given one chocolate bar to five friends and one of his friends got a chocolate bar in the container. In this way, all his friends got chocolates, and one is still in the container.
- When I was four years old, my sister was half my age. Now, I am 18. How old is my sister now?
Answer: My sister’s age when I was 4 = half my age = 4/2 =2 years.
So, my sister is two years younger than me.
When I am 18, he will be 16 years old.
- Harry had six siblings. All of them have two years of age difference. The youngest is Jessy, his seven years old sister, while Harry is the most senior. Calculate Harry’s age.
Answer: The youngest sibling, Jessy, is seven years old. Harry has six siblings, which means they are a total of 7 siblings, and Harry is the eldest among them. All of them have two years of age difference, which means that adding six times two to seven can give us an answer. 7 + 2 + 2 + 2 + 2 + 2 + 2 = 19; so, Harry is 19.
- Place the correct symbol from *, +, -, /, in any order to balance the equation.
2 _ 1 _ 6 _ 6 = 48
Answer: 2 * 1 + 6 * 6 = 48
- Typically, the number is odd. But if you remove one letter from it, it will change to even. Guess the number.
Answer: The number is 7(seven). When its letter ‘s’ is removed, it becomes ‘even,’ but actually, 7 is an odd number.
- Angel visited a fair near her home. She traversed on her new bicycle presented by her father for winning the art contest. After reaching the fair, Angel noticed that 14 bicycles and tricycles were parked. The total number of wheels in the parking area is 38. Can you find the number of tricycles that were parked there?
Answer: Total bicycles and tricycles = 14
Total number of wheels = 38
All the cycles have minimum wheels, 14 X 2 = 28;
38 – 28 = 10
There are ten extra wheels other than bicycles, meaning ten tricycles.
- What three numbers give the same addition and multiplication operations result?
Answer: The three numbers are 1, 2, and 3; because, 1+2+3 = 6. And, 1*2*3 = 6.
- What will the following two numbers be in this numeric series?
22, 21, 23, 22, 24, 23, ?, ?
Answer: The following two numbers would be 25 and 24; the pattern of the series is the second number is one less than the first number, and the third number is two more than the second.
Another logic can be a consecutive number pattern formed by alternate numbers.
- A grandfather, two fathers, and two sons went to a theater together. How many tickets do they need to buy, assuming one for each?
Answer: They will need only three tickets because this is the trio of three generations: a grandfather, his son, and his grandchild (son’s son).
- John adds six to eight and gets the answer two; his teacher also accepts it. Why?
Answer: Because the question was on time. She asked to add six hours to 8 AM. So, he got the correct answer at 2 PM.
- Get the total of 1000 by adding only eight 8’s.
Answer: 888 + 88 + 8 + 8 + 8 = 1000
You may also like to read- How to divide fractions
These were some funny yet challenging math problems for students to brainstorm and recall the concepts, formulas, and procedures teachers have taught them in classes. Along with the learning benefits, these funny math questions can drive to the positive side of learning math, and they realize that math is neither complex nor a worthless subject.
Nevertheless, teachers should also understand that memorizing the procedures is not what students require. Therefore they should instead focus on creating an understanding of math and promote logical thinking in students.
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