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How to Solve Math Problems

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This article was co-authored by Daron Cam . Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary's College. wikiHow marks an article as reader-approved once it receives enough positive feedback. In this case, 84% of readers who voted found the article helpful, earning it our reader-approved status. This article has been viewed 557,594 times.

Although math problems may be solved in different ways, there is a general method of visualizing, approaching and solving math problems that may help you to solve even the most difficult problem. Using these strategies can also help you to improve your math skills overall. Keep reading to learn about some of these math problem solving strategies.

Understanding the Problem

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Developing a Plan

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Solving the Problem

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To solve a math problem, try rewriting the problem in your own words so it's easier to solve. You can also make a drawing of the problem to help you figure out what it's asking you to do. If you're still completely stuck, try solving a different problem that's similar but easier and then use the same steps to solve the harder problem. Even if you can't figure out how to solve it, try to make an educated guess instead of leaving the question blank. To learn how to come up with a solid plan to use to help you solve a math problem, scroll down! Did this summary help you? Yes No

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StatAnalytica

Top 3 Tips on How to Solve Math Problems

how-to-solve-math-problems

Math can be used in various aspects of life, starting from measuring the distance of the destination from home and measuring the shortest route from destination to home, and so on. Therefore, it is always necessary that you must know why math is so important and how to solve math problems. Below, we have listed the math importance along with the necessary details like what math is, types of maths, and how to solve math problems. All these will help you to know the necessary details about maths.

What is Math?

Table of Contents

Geometric Shapes, equations, function, and numbers. Some branches of mathematics are identified by the use of strict proofs based on assumptions. That is called math.

Types of Math

There are two types of math. We discuss below:

1. Pure Mathematics: This is the resolution of the mathematics which details without actual thought into direct applications such as Finance, Economics, and much more. These are following different types of pure mathematics:

2. Applied Mathematics: it is a mathematical calculation approach to solve the problems of mathematics that deal with subjects like physical science, computer science, engineering, and much more. In other words, we can say that this branch deals with daily life problems such as measuring the speed of your vehicle, etc.

Some common reasons: Why is math so important?

To understand more about why is math so important; let’s look at a trick called the “ 10 Rule Formula.”

How to solve math problems: Different techniques for different type of problem

How to solve math problems related to common factors.

Common factors are the number(s) that divide the specific number exactly.

For example:

Calculate the common factor of 5 and 10.

[Now, you can see that each common factor (that is 1 and 5) divides the provided math problem numbers 5 and 10 exactly ].

How to solve geometry math problems?

To solve the geometry math problems, you need to follow the following steps:

Calculate the area of the rectangle of length 10 cm and width 5 cm.

As length and width are given in cm, do not forget to write the SI unit in the final answer, which is 50 cm.

How to solve trigonometric equations

Trigonometric functions can be used for various purposes, like for planning urban issues. To solve the basic trigonometric problems, you need to follow the below-mentioned steps:

Solve sin(x) + 2 = 3 in interval 0° ≤ x < 360°.

sin( x ) + 2 = 3

sin( x ) = 3 – 2 = 1

We know that sine 1 (+ve value) lies in the first quadrant that is between 0 degrees to 90 degrees. Moreover, we are well versed that sin (90) = 1. Therefore, the answer will be:

x = 90 degrees.

A real-life example: How to use mathematics to solve urban problems?

It has been seen that mathematics has various applications in solving urban issues. Moreover, there are various branches of mathematics in which urban problems can be solved, such as trigonometric functions that are used to determine the roof inclinations (to make a bungalow in the urban area), and much more.

The basic math concepts that we use to solve the urban problems are:

Now, the question is how to use math for solving urban problems. Urban designers use mathematics as they need to design the appearance, functionalities, and arrangements of the city and town. Apart from this, with the help of using mathematical concepts, urban designers can easily shape and secure public areas.

Let take an example of it

Suppose an urban designer plans to make an avenue (the road that has trees on both sides). During the plantation of trees, he attaches a tree with the wire that is connected with a knot with a wooden stake. The tree wire length is 8 feet, and the angle between the connected knot tree and the wooden stake is 42º. Now, the designer needs to calculate the height of the connecting point of the knotted tree so that he can tie a knot at the same distance to balance the tree during plantation.

math-example

Hence, sin (42 degrees) = x/8 (feet)

0.669 = x/8

x = 5.4 feet.

It means the designer needs to tie a knot on the other tree at the height of 5.4 feet to balance the tree.

If you are looking for the solution for How to Understand and solve the maths problem by reading the book, then you can follow the below- mentioned steps. These steps are:

Here we will give you some tricks and tips which can be very useful in solving the math problems.

Step by step, you will know about every prospective in which you will about How to Solve Math Problems:-

1. Knowing the Problem

Analyze type of problem.

You first have to know about the difficulty and brainstorm to get the idea to solve it very quickly. If you are taking some time to identify the problem, that’s not the point, but you will solve it quickly if you recognize it instantly.

Read it carefully

 Read the problem until you get some hint from it and get some logic to solve it. Maths is a subject which is based on the logic so that you have to get points to explain.

Summarize the difficulty

To summarize the problem to your mind, you can write or speak out. By doing this, your account will be able to think about the issue and can get solutions. After this, you will get the problem in your own words, and you can now solve it in your words or your way quickly.

Outline the problem

There are many problems in math, and some have drawable solutions, or you can get help to outline the issue. See the weather the diagram is showing the exact problem asked in the question. If it relates to the challenge, then go ahead or re-read your question.

Study the examples

By study, the examples that are the same as the problem can be solved by following the same patterns. Creating a table can also help to support the design equal to the example.

2. Outline the answers

Write the things you need to get the answer.

First, you will need the formula to solve the problem. Here you need to spend some time reviewing concepts in your textbooks that will help you solve the problem. Make a list that follows the question pattern, giving a full organization to get the answer. By doing this, you can get an estimate of the solution without solving the whole problem.

Easier to harder

If you are tying any problem that is hard one, then leave it and do the easier one, which is similar to earlier. This will help you to understand the concept and pattern of the problem.

Using a graphical calculator

If you are facing a graphical problem in pre-calculus work than you can also take the help of graphical calculator. There is some tips to use the graphical calculator:

3. The last step is problem-solving

There are three simple steps, which are followed for problem-solving.  Steps are given below:

Go with your plan

Your plan makes your answer proceed smoothly. Moreover, there are higher chances of getting accurate answers.

Another method implement

If your estimate does not match with the answer, then use another way or a method to get a satisfying solution to the problem. Find your mistake, make it correct, and implement the technique again.

See the problem again

After solving the problem, go back to your question again and reflect on it. It will give you the idea to see a similar problem again and solve it quickly.

From the above discussion, you’ve now got clarity about how to solve math problems. Follow these tips while practicing your math. If you want math homework help then you can get the math homework helpers here.

FAQs Related With How to Solve Math Problems

What are the types of math.

There are two types of math. We discuss below: 1.Pure Mathematics 2.Applied Mathematics

How to solve math problems?

The following steps can help you in solving math problems: 1. Knowing the Problem 2.Develop the plan to solve it 3. The last step is problem-solving

How do you solve math problems?

Four steps help you solve any math problems quickly:   Read the problem carefully, understand it, and recognize the type of problem.  Try to draw and review the math problem.  Create a plan to solve it.  Use the relevant formulas to solve the problem.

What are the 7 hardest math problems?

There are 6 math problems that have not solved till the date of July 2020:   Hodge conjecture. P versus NP. Yang-Mills existence and mass gap. Birch and Swinnerton-Dyer conjecture. Riemann hypothesis. Navier–Stokes existence and smoothness.

Why do I struggle with math so much?

Math resembles one of the toughest subjects as it needs time as well as energy. Many students don’t have enough time to “get” math lessons. At the same time, several of them get into more complex concepts. Therefore, the reason why you struggle with math can vary from person to person’s mental abilities.

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How to Solve Math Problems Faster: 15 Techniques to Show Students

how do you solve this type of math problem

“Test time. No calculators.”

You’ll intimidate many students by saying this, but teaching techniques to solve math problems with ease and speed can make it less daunting.

This can also  make math more rewarding . Instead of relying on calculators, students learn strategies that can improve their concentration and estimation skills while building number sense. And, while there are educators who  oppose math “tricks”  for valid reasons, proponents point to benefits such as increased confidence to handle difficult problems.

Here are 15 techniques to show students,  helping them solve math problems faster:

Addition and Subtraction

1. two-step addition.

how do you solve this type of math problem

Many students struggle when learning to add integers of three digits or higher together, but changing the process’s steps can make it easier.

The first step is to  add what’s easy.  The second step is to  add the rest.

Let’s say students must find the sum of 393 and 89. They should quickly see that adding 7 onto 393 will equal 400 — an easier number to work with. To balance the equation, they can then subtract 7 from 89.

Broken down, the process is:

With this fast technique, big numbers won’t look as scary now.

2. Two-Step Subtraction

There’s a similar method for subtraction.

Remove what’s easy. Then remove what’s left.

Suppose students must find the difference of 567 and 153. Most will feel that 500 is a simpler number than 567. So, they just have to take away 67 from the minuend — 567 — and the subtrahend — 153 — before solving the equation.

Here’s the process:

Instead of two complex numbers, students will only have to tackle one.

how do you solve this type of math problem

3. Subtracting from 1,000

You can  give students confidence  to handle four-digit integers with this fast technique.

To subtract a number from 1,000, subtract that number’s first two digits from 9. Then, subtract the final digit from 10.

Let’s say students must solve 1,000 – 438.  Here are the steps:

This also applies to 10,000, 100,000 and other integers that follow this pattern.

Multiplication and Division

4. doubling and halving.

how do you solve this type of math problem

When students have to multiply two integers, they can speed up the process when one is an even number. They just need to  halve the even number and double the other number.

Students can stop the process when they can no longer halve the even integer, or when the equation becomes manageable.

Using 33 x 48 as an example,  here’s the process:

The only prerequisite is understanding the 2 times table.

5. Multiplying by Powers of 2

This tactic is a speedy variation of doubling and halving.

It simplifies multiplication if a number in the equation is a power of 2, meaning it works for 2, 4, 8, 16 and so on.

Here’s what to do:  For each power of 2 that makes up that number, double the other number.

For example, 9 x 16 is the same thing as 9 x (2 x 2 x 2 x 2) or 9 x 24. Students can therefore double 9 four times to reach the answer:

Unlike doubling and halving, this technique demands an understanding of exponents along with a strong command of the 2 times table.

how do you solve this type of math problem

6. Multiplying by 9

For most students, multiplying by 9 — or 99, 999 and any number that follows this pattern — is difficult compared with multiplying by a power of 10.

But there’s an easy tactic to solve this issue, and  it has two parts.

First, students round up the 9  to 10. Second, after solving the new equation, they subtract the number they just multiplied by 10 from the answer.

For example, 67 x 9 will lead to the same answer as 67 x 10 – 67. Following the order of operations will give a result of 603. Similarly, 67 x 99 is the same as 67 x 100 – 67.

Despite more steps, altering the equation this way is usually faster.

7. Multiplying by 11

how do you solve this type of math problem

There’s an easier way for multiplying two-digit integers by 11.

Let’s say students must find the product of 11 x 34.

The idea is to put a space between the digits, making it 3_4. Then, add the two digits together and put the sum in the space.

The answer is 374.

What happens if the sum is two digits? Students would put the second digit in the space and add 1 to the digit to the left of the space.  For example:

It’s multiplication without having to multiply.

8. Multiplying Even Numbers by 5

This technique only requires basic division skills.

There are two steps,  and 5 x 6 serves as an example. First, divide the number being multiplied by 5 — which is 6 — in half. Second, add 0 to the right of number.

The result is 30, which is the correct answer.

It’s an ideal, easy technique for students mastering the 5 times table.

9. Multiplying Odd Numbers by 5

This is another time-saving tactic that works well when teaching students the 5 times table.

This one has three steps,  which 5 x 7 exemplifies.

First, subtract 1 from the number being multiplied by 5, making it an even number. Second, cut that number in half — from 6 to 3 in this instance. Third, add 5 to the right of the number.

The answer is 35.

Who needs a calculator?

10. Squaring a Two-Digit Number that Ends with 1

how do you solve this type of math problem

Squaring a high two-digit number can be tedious, but there’s a shortcut if 1 is the second digit.

There are four steps to this shortcut,  which 812 exemplifies:

This work-around eliminates the difficulty surrounding the second digit, allowing students to work with multiples of 10.

11. Squaring a Two-Digit Numbers that Ends with 5

Squaring numbers ending in 5 is easier, as there are  only two parts of the process.

First, students will always make 25 the product’s last digits.

Second, to determine the product’s first digits, students must multiply the number’s first digit — 9, for example — by the integer that’s one higher — 10, in this case.

So, students would solve 952 by designating 25 as the last two digits. They would then multiply 9 x 10 to receive 90. Putting these numbers together, the  result is 9,025.

Just like that, a hard problem becomes easy multiplication for many students.

12. Calculating Percentages

Cross-multiplication is an  important skill  to develop, but there’s an easier way to calculate percentages.

For example, if students want to know what 65% of 175 is, they can multiply the numbers together and move the decimal place two digits to the left.

The result is 113.75, which is indeed the correct answer.

This shortcut is a useful timesaver on tests and quizzes.

13. Balancing Averages

how do you solve this type of math problem

To determine the average among a set of numbers, students can balance them instead of using a complex formula.

Suppose a student wants to volunteer for an average of 10 hours a week over a period of four weeks. In the first three weeks, the student worked for 10, 12 and 14 hours.

To determine the number of hours required in the fourth week, the student must  add how much he or she surpassed or missed the target average  in the other weeks:

To learn the number of hours for the final week, the student must  subtract the sum from the target average:

With practice, this method may not even require pencil and paper. That’s how easy it is. 

how do you solve this type of math problem

Word Problems

14. identifying buzzwords.

Students who struggle to translate  word problems  into equations will benefit from learning how to spot buzzwords — phrases that indicate specific actions.

This isn’t a trick. It’s a tactic.

Teach students to look for these buzzwords,  and what skill they align with in most contexts:

Be sure to include buzzwords that typically appear in their textbooks (or other classroom  math books ), as well as ones you use on tests and assignments.

As a result, they should have an  easier time processing word problems .

15. Creating Sub-Questions

how do you solve this type of math problem

For complex word problems, show students how to dissect the question by answering three specific sub-questions.

Each student should ask him or herself:

These sub-questions help students avoid overload.

Instead of writing and analyzing each detail of the question, they’ll be able to identify key information. If you identify students who are struggling with these, you can use  peer learning  as needed.  

For more fresh approaches to teaching math in your classroom, consider treating your students to a range of  fun math activities .

Final Thoughts About these Ways to Solve Math Problems Faster

Showing these 15 techniques to students can give them the  confidence to tackle tough questions .

They’re also  mental math  exercises, helping them build skills related to focus, logic and critical thinking.

A rewarding class equals an  engaging class . That’s an easy equation to remember.

> Create or log into your teacher account on Prodigy  — a free, adaptive math game that adjusts content to accommodate player trouble spots and learning speeds. Aligned to US and Canadian curricula, it’s loved by more than 500,000 teachers and 15 million students.

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Our online math calculator can answer a number of problems in a wide range of subjects, not just strictly math. Below is a list of the available subjects that are covered by the math word problem solver.

Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.

Basic Math Solutions

Below are examples of basic math problems that can be solved.

Math Word Problem Solutions

Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

Pre-Algebra Solutions

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  16. Top 3 Tips on How to Solve Math Problems

    Four steps help you solve any math problems quickly: Read the problem carefully, understand it, and recognize the type of problem. Try to draw and review the math problem. Create a plan to solve it. Use the relevant formulas to solve the problem.

  17. 15 Techniques to Solve Math Problems Faster

    Square the integer, which is now an easier number: 80 x 80 = 6,400. Add the integer with the resulting square twice: 6,400 + 80 + 80 = 6,560. Add 1: 6,560 + 1 = 6,561. This work-around eliminates the difficulty surrounding the second digit, allowing students to work with multiples of 10.

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