problem solving comparing numbers

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Comparing Numbers Worksheets

Comparing and ordering numbers worksheets.

Our comparing numbers worksheets start off by focusing on comparing groups of objects rather than numbers . Later worksheets directly compare or order numbers without representations by pictured objects.

Topics include:

Kindergarten more than / less than worksheets

• Which group has more objects (using pictures, not numbers)
• Draw more (or less) objects than shown
• Which group has the most (or least) objects  (using pictures, not numbers)
• Count the object and circle the correct symbol (>, <, =)
• Circle the number which is greater (less)
• Compare the numbers and write in the correct symbol  (>, <, =)
• Circle the greatest (least) number
• Order the numbers from least to greatest (4 numbers)

Grade 1 comparing numbers worksheets

• Order 3 numbers least to greatest (0-30)
• Order 5 numbers least to greatest (0-100)
• Compare numbers as less than, greater than or equal to (<, >, =) 0-30
• Compare numbers as less than, greater than or equal to (<, >, =) 0-100

Grade 2 comparing and ordering numbers worksheets

• compare numbers up to 100 or 1,000
• order numbers up to 100 or 1,000

Grade 3 comparing and ordering numbers worksheets

• compare numbers up to 10,000 or 100,000
• order numbers up to 10,000 or 100,000

Grade 4 comparing and ordering numbers

• compare numbers up to 1 million
• order numbers up to 1 million

Related topics

Learning numbers worksheets

Counting worksheets

Sample Comparing Numbers Worksheet

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Comparison Word Problems

Related Pages Comparing & Ordering Numbers Comparing Numbers Worksheet More Word Problems Algebra Word Problems

In these lessons, we will learn how to solve comparison word problems using either bar models or comparison bars.

Printable Word Problem Worksheets for 1st Grade: Addition Word Problems Addition/Subtraction Word Problems Comparison Word Problems

The following diagrams show the three types of comparison word problems: Difference Unknown, Unknown Big Quantity, Unknown Small Quantity. Scroll down the page for examples and solutions.

Types of Comparison Word Problems

There are three main types of comparison word problems.

Difference Unknown Connie has 15 red marbles and 28 blue marbles. How many more blue marbles than red marbles does Connie have? This is a subtraction problem. 28 - 15 = 13

Unknown Big Quantity Connie has 15 red marbles and some blue marbles. She has 13 more blue marbles than red ones. How many blue marbles does Connie have? This is an addition problem. 15 + 13 = 28

Unknown Small Quantity Connie has 28 blue marbles. She has 13 more blue marbles than red ones. How many red marbles does Connie have? This is a subtraction problem. 28 -13 = 15

How to solve comparison word problems using Bar Models or Tape Diagrams?

This video explains how to use bar modeling in Singapore math to solve word problems that deal with comparing. This technique of using model drawings to solve word problems is recommended by the Common Core mathematics standards.

Example: Adam has 11 fewer lollipops than Hope. If Adam has 16 lollipops, how may lollipops does Hope have?

Bar Model (Comparison) This video employs a visual way to solve world problems using bar modeling. This type of word problem uses the comparison model. Because the part is missing, this is a subtraction problem.

Example: Cayla did 88 sit-ups in the morning. Nekira did 32 sit-ups at night. How many more sit-ups did Cayla do than Nekira?

How to solve comparison word problems using Comparison Bars?

This is another strategy that we can use for story problems that involves comparison.

• Bob has 14 crackers. Steve ate five fewer than Bob. How many did Steve eat?
• David has 5 marbles. Anna has 8 marbles. How many more does Anna have than David?
• Ellie has 9 goldfish. Laney has 5 more goldfish than Ellie. How many goldfish does Laney have?
• Mark earned $428 doing yard work. Troy earned $186. How much less did Troy earn?
• Billy has 679 gumballs. He has 278 more gumballs than Lee. How many gumballs does Lee have?
• Jake has 219 bottlecaps. Then, he found some more. Now he has 347 bottlecaps. How many bottlecaps did he find?

Comparison Bars

• Claire has 8 marbles. Sasha has 15 marbles. How many more marbles does Sasha have than Claire?
• Bill read 5 books. Beth read 2 more books than Bill. How many books did Beth read?
• Beth read 8 books. Bill read 3 fewer books than Beth. How many books did Bill read?

Example: The Nature Center has a collection of snakes. The redbelly snake in the collection is 9 inches long. The eastern ribbon snake is 21 inches long. How much longer is the eastern ribbon snake than the redbelly snake?

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Differentiated Math Fact Practice

4th Grade Resources

Problem Solving: Comparing Problems

What are Comparing Problems?

Three Types of Comparing Problems

• Comparing when the difference is unknown
• Comparing when the smaller part is unknown
• Comparing when the larger part is unknown

Comparing When the Difference is Unknown

Comparing when a part is unknown .

Larger Part Unknown

Smaller Part Unknown

Practice Comparing Problems

Wrapping Up . . .

• Teach students to VISUALIZE what is happening
• Provide students with a variety of STRATEGIES to use when solving
• Celebrate that we can solve problems in DIFFERENT ways and still get the same answer
• Focus on the CONTEXT
• PRACTICE, practice, practice by starting with concrete, hands-on opportunities and slowly moving more abstract.

The Problem Solving Series

• The 11 Types of Addition and Subtraction Problems
• How I Teach Problem Solving & The Joining Problems
• The Separating Problems
• Part-Part-Whole Problem Solving Group
• Comparing Problems and Wrap-Up

Save these Problem Solving Tips and Strategies

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Comparing Numbers Worksheets

Barrel toward our pdf comparing numbers worksheets for a wealth of material that helps practice comparing pictures, numbers, and measures with verve and tenacity! Let prekindergarten through 7th grade kids stay on until they improve their numeracy skills by comparing numbers using <, >, and = symbols. Take advantage of the included answer keys and try out some of our printables for free!

» Comparing Numbers up to 10

» Comparing 2-Digit Numbers

» Comparing 3-Digit Numbers

» Comparing 4-Digit Numbers

» Comparing Multi-Digit Numbers

Comparing Numbers - Objects

Casting around for interactive worksheets to boost kindergarten and grade 1 kids' comparing skills? These comparing numbers worksheets draw on everyday objects to make comparing numerals easy.

• Download the set

Comparing Numbers - Number Lines

Our pdfs are the ultimate in comparing numbers using the number line! Instruct children to read the number-line intervals and answer the questions comparing the position of the numbers at their own pace.

Comparing Numbers Using the Symbols >, <, or =

Delight as active learners whiz past their peers by swiftly placing the comparison symbols smaller than (<), larger than (>), and equal to (=) in each box and achieve excellence in comparing numbers up to 20.

Circling the Greater and Smaller Number

Direct the enthusiastic learners to circle the greater and smaller number in these 3-part exercises. We recommend these comparing numbers worksheets for the amazing young talent in kindergarten and 1st grade.

Counting and Comparing

Our printable practice worksheets, which thrive on mentally counting and comparing the number of real-world objects using the <, >, and = symbols, help children flourish into well-rounded math masters.

Comparing Numbers - Sticks

Comparing numbers using sticks allows students to "stick to the point" as they reassert their math-genie credentials by figuring the number of sticks in each set, comparing them, and circling the correct option.

Comparing Numbers Using Ten Frames

Let students flock around these pdf worksheets for a key upgrade, comparing numbers using ten frames. A bunch of colorful double ten frames that work extra hard to polish children's comparison skills.

Comparing Dominos

Don't miss this never-before math escapism full of learning and practice, in the form of counting and comparing pips on domino tiles. Our domino comparing worksheets are excellent for home and school use.

Comparing Numbers - Balancing Scale

Not sure how well the kindergarten and grade 1 kids make comparisons? Guide them to observe the given pair of numbers and to write them on the appropriate pan of each balance scale.

Cut and Paste Activities

Chock-full of practice in comparing numbers, our cut-and-paste activity worksheets will inspire many a gleeful chuckle in the class! Comparing numbers with crocodile snouts will be a hilarious affair!

Simplifying and Comparing

Elevate the learning experience with this set of worksheets, designed to challenge and inspire kids to simplify the expressions before diving into comparisons.

Circling Numbers

Choose from three modes that impel students to circle the numbers and make the statements true. Demystify the fundamentals of comparing numbers in the company of an array of straightforward questions.

Greater Than, Less Than Worksheets

Take a warm-up trip and prepare young students to open up to the concept of comparison and understand basic inequalities by comparing pictures of objects up to 10 in our winsome practice resources!

(32 Worksheets)

Comparing 2-Digit Numbers Worksheets

Gain access to a host of pdf resources for grade 1, grade 2, and grade 3 to compare numbers using alligator snouts, symbols, and words. They also circle the greatest and smallest numbers.

(43 Worksheets)

Comparing 3-Digit Numbers Worksheets

With our comparing 3-digit numbers worksheets at your disposal, it's super-fun to compare numbers up to 1000 by observing the digits and determine if a number is greater than, less than, or equal to the other.

(38 Worksheets)

Comparing 4-Digit Numbers Worksheets

Children closely observe and study the thousands, hundreds, tens, and ones places of each number in pairs and record the comparison results here as directed. Add a new layer to your comparing-numbers chops!

(34 Worksheets)

Comparing Multi-Digit Numbers Worksheets

Do long numbers cause your child to slip up? A massive relief, our pdf comparing multi-digit numbers worksheets get them comparing numbers that involve up to 8 digits with ease, flair, and imagination.

(21 Worksheets)

Comparing Fractions Worksheets

Watch number lines, shapes, bar and pie models, and more band together so children key into comparing fractions! The answer keys, which facilitate instant self-validation, add to the ease of practice.

(27 Worksheets)

Comparing Decimals Worksheets

Ready to make the daunting task of comparing decimals a playful affair, our pdf comparing worksheets featuring decimals let kids choose from decimal values between tenths and ten thousandths with get-up-and-go.

(66 Worksheets)

Comparing and Ordering Integers Worksheets

An eclectic mix of real-life word problems to kick practice in comparing and ordering integers up a notch! Ideal for 5th grade, 6th grade, and 7th grade students, these printables make your repertoire rich.

(50 Worksheets)

Comparing and Ordering Money Worksheets

Our printable comparing and ordering money worksheets mean that young prodigies develop a soft spot for comparing and counting money using symbols and ordering them in increasing and decreasing formats.

(45 Worksheets)

Related Worksheets

» Ordering Numbers

» More or Less

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Comparing Numbers Hub Page

Welcome to the Math Salamanders' Comparing Numbers hub page.

Here you will find online math help and support to help you compare different numbers, including decimals and fractions.

There are also links to a range of different ordering and comparing number worksheets which will help your child to understand about comparing and ordering different numbers and quantities.

These sheets will complement and hopefully add to your child's knowledge and understanding of place value and the number system.

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Here are the instructions how to enable JavaScript in your web browser .

• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Are you needing to compare numbers to 100, 1000 or 10000?

Trying to compare negative numbers?

Looking to compare fractions or decimals?

This page will help you understand all about comparing numbers and ordering numbers!

• Greater Than Less Than Worksheets Generator
• Compare numbers and amounts to 10
• Compare numbers to 100
• Compare numbers to 1000
• Compare numbers to 4 Digits
• Compare numbers to 6 Digits
• Compare large numbers to 8 Digits
• Compare negative numbers
• Compare decimals
• Compare fractions
• Compare rational numbers

Greater Than Less Than Worksheet Generator

Here is our generator for generating your own greater than less than worksheets.

Our generator will create the following worksheets:

• numbers up to 8 digits
• numbers up to 3dp.
• positive and negative numbers
• Greater Than Less Than Worksheets

Comparing two numbers

When comparing numbers, it is important to know the value of the most significant digit in each of the numbers. This will tell you how large each number is.

The most significant digit is the first non-zero digit the number has.

The number with the largest-valued most significant digit will be the bigger number, unless it is a negative number.

In the number 2318, the most significant digit is '2' which has the value 2000.

In the number 74.39, the most significant digit is '7' which has the value 70.

In the number 0.0825, the most significant digit is '8' which has the value 0.08.

If the two numbers are both positive integers (whole numbers) then looking at the number of digits the number has will show you which is bigger.

We often use the symbols > < and = when comparing numbers.

Using the symbols > < and =

• a > b means a is greater than b ;
• a < b means a is less than b ;
• a = b meas a is equal to (or has the same value as) b .
• 137 > 129 means that 137 is greater than 129
• 65 < 72 means that 65 is less than 72
• 27 = 20+7 means that 27 has the same value as 20+7

Comparing Numbers and Amounts to 10

Our easiest sheets look at comparing numbers up to 10.

At this stage we use words like most, least, biggest, smallest, equal to, greater than and less than.

As well as comparing numbers, we also compare numbers of 'things'.

• Comparing numbers and size
• Comparing Numbers Worksheets to 10

Comparing numbers to 100

When you are comparing numbers up to 100, you need to look at the value of the tens digit (unless the number is 100).

The number with the larger tens digit will be the bigger number, as the tens digit will be the most significant digit.

The only exception is if either of the numbers are negative - in which case, look at the comparing negative number section.

If the numbers have the same tens digit, then look at the ones digit and see which is more.

• 82 > 68 this means 82 is greater than 68
• 49 < 71 this means 49 is less than 71
• 92 > 78 this means 92 is greater than 78

Looking for some practice worksheets to help you compare and order numbers to 100?

• Greater than Less than Worksheets - Comparing to 100
• Ordering Numbers to 100

Comparing numbers up to 3 digits

When you are comparing numbers up to 1000, you need to look at the value of the hundreds digit (unless the number is 1000).

The number with the larger hundreds digit will be the bigger number, as the hundreds digit will be the most significant digit.

If the numbers have the same hundreds digit, then look at the tens digit next and see which is more.

If the numbers have the same hundreds and tens digit, then look at the ones digit to find out which is bigger.

• 672 > 594 this means 672 is greater than 594 the 1st number has a higher hundreds digit so it is bigger.
• 386 < 391 this means 386 is less than 391 the hundreds digits are the same, so we look at the tens digit. The 2nd number has the higher tens digit.
• 102 > 97 this means 102 is greater than 97 the 1st number has a hundreds digit, the 2nd number has no hundreds.
• Ordering Numbers up to 3 digits
• Comparing Numbers up to 3 digits Worksheets

Comparing numbers to 10,000

When you are comparing numbers up to 10,000 you need to look at the value of the thousands digit (unless the number is 10,000).

The number with the larger thousands digit will be the bigger number, as the thousands digit will be the most significant digit.

If the numbers have the same thousands digit, then look at the hundreds digit next and see which is more.

If the numbers have the same hundreds digit, then look at the tens digit to find out which is bigger, and so on.

• 4263 > 4193 the thousands digits are the same, but the 1st number has a bigger hundreds digit.
• 7826 < 9014 the 1st number's thousands digits is 7, the 2nd number's is 9.
• 1407 < 1423 the thousands and hundreds digits are the same, but the 2nd number has a higer tens digit.
• Ordering Numbers to 10,000

Comparing numbers up to 6 Digits

There are worksheets and support to help you master the skill of comparing larger numbers up to 6-digits.

There is a selection of ordering and comparing worksheets depending on your skill level.

• Comparing and Ordering Whole Numbers up to 6 Digits

The sheets in this section will help your child to practice and master ordering and comparing numbers with 5 and 6 digits.

There are a range of ordering and comparing worksheets as well as some challenges for more able pupils to test mastery.

• 4th Grade Place Value Ordering 5 & 6 Digits

Comparing numbers up to 8 Digits (ten millions)

The sheets on this page are all about ordering BIG numbers up to 100 million.

There are a range of ordering and comparing worksheets as well as some BIG number challenges for able mathematicians.

• Ordering Large Numbers up to 100 million

Comparing negative numbers

How to compare negative numbers

When you are comparing with negative numbers, everything swaps around and becomes a little more complicated!

With negative numbers, the more negative the number is, the lower its value.

As you go right along the number line, the values are increasing.

As you go left along the number line, the values are decreasing.

This means that any positive number (or even zero) will always be greater than any negative number.

• 0 > -3 this means 0 is greater than -3
• -8 < -5 this means -8 is less than -5
• -27 > -30 this means -27 is greater than -30
• -26 < 2 this means -26 is less than 2
• Ordering Negative Numbers -10 to 10

Comparing decimals

How to Compare Decimals

When you are comparing decimals, you need to look carefully at the value of the most significant digit!

The most significant digit in each decimal below is marked with an arrow.

This means that a decimal like 0.7 is greater than 0.65 because the most significant digit is worth more.

• 1.24 > 0.86 this means 1.24 is greater than 0.86
• 0.35 < 0.5 this means 0.35 is less than 0.5
• 0.7 > 0.586 this means 0.7 is greater than 0.586
• 2.69 < 2.8 this means 2.69 is less than 2.8
• 0.1 > 0.0725 this means 0.1 is greater than 0.0725

Looking for some practice worksheets to help you compare and order decimals?

• Ordering Decimals Worksheets

Comparing fractions

There are 2 different ways to compare fractions: by converting to decimals, and by converting to like denominators.

If you have a calculator, you can use Method 1 which is easiest.

If you do not have a calculator, then you should use Method 2.

How to compare 2 fractions - Method 1

Step 1) Take your two fractions and convert them both into decimals by dividing the numerator by the denominator.

Step 2) Compare the two decimals to see which is bigger.

Which is bigger 3 / 7 or 2 / 5 ?

Step 1) Change both fractions into decimals: 3 / 7 = 3 ÷ 7 ≈ 0.43 2 / 5 = 2 ÷ 5 = 0.4

Step 2) Compare the decimals: 0.43 > 0.4 so 3 / 7 is greater than 2 / 5

The second way to compare 2 fractions - using like denominators.

How to compare 2 fractions - Method 2

Step 1) Take your two fractions and convert them both into equivalent fractions with the same denominator.

Step 2) Compare the two numerators to see which is bigger.

Which is bigger 5 / 6 or 7 / 8 ?

Step 1) Change both fractions into equivalent fractions with the same denominators. We need to multiply the numerator of each fraction by the other fractions denominator. 5 / 6 becomes 5x8 / 6x8 = 40 / 48 7 / 8 becomes 7x6 / 8x6 = 42 / 48

Step 2) Compare the two numerators Now that the denominators are the same, we can compare the 2 numerators. 40 is less than 42 so 5 / 6 is less than 7 / 8

• Equivalent Fractions Worksheets

Comparing Rational Numbers

Comparing rational numbers involves all of the above skills.

Rational numbers include fractions, decimals, negative numbers, and absolute values.

• Ordering and Comparing Rational Numbers

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Comparing Numbers

It is good to know if one number is the same as, smaller than, or bigger than another number:

Learn more about <, >, ≤ and ≥ here .

Less Than and Greater Than

The "less than" sign and "greater than" sign look like a "V" on its side, don't they?

To remember which way around the "<" and ">" signs go, remember this:

• BIG > small
• small < BIG

The "small" end always points to the smaller number, like this:

Greater Than Symbol: BIG > small

"20 is greater than 5"

Try It Yourself !

Practice comparing numbers with:

• Compare Numbers 0 to 10
• Compare Numbers 0 to 100
• Compare Numbers: -10 to +10 (introduces negative numbers)
• Compare Decimal Numbers: 0 to 1 (introduces decimal numbers)
• Compare Decimal Numbers: -1 to +1 (decimal numbers, and negatives too)
• Compare Unit Fractions (introduces simple fractions)
• Compare Fractions (more fractions)

Trending Post : Teaching Fractions with Food

12 Free Comparing Numbers Worksheets for Grade 1

These comparing numbers worksheets for grade 1 will help to visualize and understand the concept of most and least numbers, greater than, less than, or equal to. 1st-grade students will learn to compare numbers and can improve their basic math skills with our free printable comparing numbers worksheets.

12 Fun Comparing Numbers Worksheets for Grade 1

Please download the following comparing number worksheets and practice the exercises on the pages.

Coloring Numbers

Circling Numbers

Counting and Comparing

Number Lines Activity

Compare Dominos

Compare Using Symbols

Balancing Scale

Cut and Paste Activity

Comparing Polygons

Feeding the Frog

Comparing Cards

Word Problems

Why Comparing Numbers is Important for First Graders

Before learning how to compare numbers easily, let’s find out why comparing numbers is important for your little ones. Comparing numbers is a key skill for first-grade students to build their number sense.

Number sense is the ability of a student to recognize a number, its value, and its relationship with other numbers. It also prepares your little ones to understand the concept of most and least number, the concept of greater than, less than, or equal to.

Additionally, comparing numbers helps grade 1 students to develop their skills for logical thought and problem-solving. It also enhances their fluency in math.

Color Larger and Smaller Numbers from 0-30 Worksheet

In this activity, you have to color the eggs containing larger and smaller numbers.

The first page of the worksheet deals with coloring smaller numbers. Take a look at the eggs in each pair. After comparing the numbers given in both eggs, color the egg with the smaller number. 

On the second page, you again have to color an egg, but this time you will color the eggs with larger numbers.

Circle Larger and Smaller Numbers from 0-100 Worksheet

In the following two worksheets, you just have to identify the star and tree that contain larger and smaller numbers and then circle them.

The first page of the worksheet deals with circling larger numbers. Take a look at the stars in each pair. After comparing the numbers given in both stars, circle the star with the larger number. 

On the second page, you again have to circle some trees, but this time you will circle the trees with smaller numbers.

Counting and Comparing Objects Worksheet

Here, I provide two worksheets. Each worksheet has four pairs of objects. In each pair, you will see fruits, animals, fish, birds, and so on. Your task is to count the fruits, birds, and fish and compare the pairs. At first, you have to count the objects and write them in the gap. Then compare numbers that are larger or smaller and tick the correct position.

Comparing Numbers on Number Lines Worksheet

The rightmost number is always greater than the leftmost number. Because 17 is on the number line to the right of 14, you can see that it is greater than 14 in the number line below. Your task is to identify which number lies on the left and which number lies on the right. And comparing numbers using the symbols greater than and less than.

Compare Numbers Using Various Symbols Worksheet

To improve students’ comparison skills in kindergarten and grade 1, this type of printable worksheet is very necessary. In this section of the worksheet, students can boost their skill in comparing numbers by using symbols like greater than(>), less than(<), or equal to (=) in each box.

Compare Dominos to Find Larger and Smaller Number Worksheet

The traditional domino set is sometimes known as a double-six set because the highest-value piece has six pips on each end and has one unique piece for each possible combination of two ends with zero to six places. Look at the pair of domino titles and place the symbols (greater than or less than) to compare dominoes.

Compare Numbers Using Balancing Scale Worksheet

In this section, you have to observe the given pair of numbers and then write them on each balancing scale’s appropriate pan. Write the larger number on the pan that has more weight and the smaller number on the pan that has less weight.

Comparing Numbers Cut and Paste Worksheet

Cut and paste is an excellent practice in number comparison. The amusing experience of comparing numbers with crocodile snouts will be a hilarious affair. Identify larger and smaller numbers, then just cut the boxes from the PDF and paste them correctly.

Comparing Polygons to Find More and Lesser Sides and Corners Worksheet

This portion of the article is mainly to count the sides and corners of polygons and then compare them with each other. Count the sides and corners of each polygon and write the number down. Then compare the pair of polygons’ sides or corners and mark which has larger or fewer sides and corners.

Feeding the Frog by Comparing Number Worksheet

Here, you have to feed the frog. Just place the snouts on the side which will provide the frog with more food.

Comparing Cards after Adding and Subtracting Worksheet

In this section, I give a pair of cards on each side to compare. On the first worksheet, you have to add two cards on each side and write the value in the box. Then, write – is greater than or is less than from the second pair of cards. On the second worksheet, you have to subtract the value from the first card to the second card, as I did for the first pair, for your clear understanding.

Comparing Numbers Word Problems

Here I present twelve-word problems related to comparing numbers. Read the questions carefully to answer them correctly.

Download Free Worksheet PDF

Download the following combined PDF and enjoy your practice session.

So today, we’ve discussed comparing numbers worksheets for grade 1 using the concepts of coloring, comparing, counting, number lines, cut-paste activity, and word problems. Download our free worksheets and after practicing these worksheets, the students will understand the concept of most and least numbers: greater than, less than, or equal to and get a better understanding of comparing numbers.

I’m Nurun Nahar Chadni. I have completed my B. Arch degree from Rajshahi University of Engineering and Technology (RUET). Now, I’m working at Softeko as a Content Developer and Graphic Designer. My areas of keen interest are creative article writing, art, design, and illustration. I am looking forward to gaining experience as well as improving my technical and design knowledge. I am eager to represent typical math problems here with easy solutions and fun for our little ones.

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Resources tagged with: Comparing and ordering numbers

There are 83 NRICH Mathematical resources connected to Comparing and ordering numbers , you may find related items under Place value and the number system .

Less Is More

Use your knowledge of place value to try to win this game. How will you maximise your score?

Number Lines in Disguise

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Ordering Journeys

How would you put these journey lengths in order?

Carroll Diagrams

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Greater Than or Less Than?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

Round the Two Dice

This activity focuses on rounding to the nearest 10.

Round the Four Dice

This activity involves rounding four-digit numbers to the nearest thousand.

Can You Do it Too?

Try some throwing activities and see whether you can throw something as far as the Olympic hammer or discus throwers.

Now and Then

Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. Compare the results for 2012.

Olympic Starters

Look at some of the results from the Olympic Games in the past. How do you compare if you try some similar activities?

That Number Square

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

Largest Even

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

Dotty Six is a simple dice game that you can adapt in many ways.

Light the Lights

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Dicey Operations

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Nice or Nasty

There are nasty versions of this dice game but we'll start with the nice ones...

Venn Diagrams

How will you complete these interactive Venn diagrams?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Difference Sudoku

Use the differences to find the solution to this Sudoku.

Caterpillars

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Factor-multiple Chains

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Multiplication Square Jigsaw

Can you complete this jigsaw of the multiplication square?

100 Square Jigsaw

Can you complete this jigsaw of the 100 square?

Number Balance

Can you hang weights in the right place to make the the number balance balanced?

Diagonal Sums

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Carrying Cards

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Consecutive Seven

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

Robot Monsters

Use these head, body and leg pieces to make Robot Monsters which are different heights.

The Tall Tower

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.

Would You Rather?

Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?

Highest and Lowest

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Mathland Election

A political commentator summed up an election result. Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.

Which Scripts?

There are six numbers written in five different scripts. Can you sort out which is which?

Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?

Birthday Cakes

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Making Sticks

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

Missing Middles

Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of three dominoes?

Buzzy Bee was building a honeycomb. She decorated the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?

A Numbered Route

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Up and Down Donkey

A number card game for 2-6 players.

The Magic Number and the Hepta-tree

Find the exact difference between the largest ball and the smallest ball on the Hepta Tree and then use this to work out the MAGIC NUMBER!

Largest Number

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5x5 array?

Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.

Rachel's Problem

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

From a group of any 4 students in a class of 30, each has exchanged Christmas cards with the other three. Show that some students have exchanged cards with all the other students in the class. How many such students are there?

Fair Exchange

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Comparing Numbers Worksheets 4th Grade

Comparing numbers worksheets 4th grade are a great way to deepen the understanding of number system in the students. Number comparison is all about finding which number is larger, smaller, or equal compared to the other number or numbers.

Benefits of 4th Grade Comparing Numbers Worksheets

The main objective of comparing numbers worksheets for 4th grade is that they not only improve math skills but also problem-solving skills of students. Students can study at their own pace and can solve problems with a gradual increase in difficulty levels. These 4th grade math worksheets are very interactive and contain visual simulations that provide a good understanding of the topic. Comparing numbers worksheets 4th grade come with answer keys that contain detailed stepwise solution of all the questions.

Printable PDF for Grade 4 Comparing Numbers Worksheets

Students can practice at their own pace regularly by downloading Grade 4 math comparing numbers worksheets in PDF format.

• Fourth Grade Math Comparing Numbers Worksheet
• 4th Grade Math Worksheet Comparing Numbers
• Math Worksheet for Grade 4 Comparing Numbers
• 4th Grade Comparing Numbers Worksheet

Explore more topics at Cuemath's Math Worksheets .

Comparing numbers

From a young age, we understand the concept of quantity. There are two baskets in front of you. One has $$3$$ lollipops and the other has $$6$$ lollipops. Which one would 4-year old you choose? Well, obviously the basket with $$6$$ lollipops. Why? Because we compared the numbers $$3$$ and $$6$$ and concluded that $$6$$ is greater than $$3$$.

But how would we compare fractions or decimals? Let’s find out.

What does it mean to compare numbers?

A comparison of numbers is an estimation of whether the given numbers are equal, one number is greater than the other, or one number is less than the other number.

The signs can be combined, meaning that we can see if the numbers are greater than or equal to, or the opposite – less than or equal to, which is denoted by:

Why is comparing numbers so useful?

Comparing numbers is something we do every day. Let’s say, for example, you’re standing in a garden, comparing the heights of two trees. One is $$6$$ ft tall and the other is $$7$$ ft tall, so which symbol do you think should replace the question mark in the following:

How to compare numbers

Now that we know what it means to compare numbers and why it’s so useful, it’s time to see it in action! Let’s walk through a problem together.

Compare the numbers:

Here, we have to determine whether the first number is greater than the second number. Notice that both numbers are positive, so we need to see which number is greater.

The first number consists of three digits and the second one consists of two digits, hence the first number is greater than the second number, which makes this statement true.

Here, we have to determine whether the first number is equal to the second number. Obviously, $$24$$ is not equal to $$23$$, which makes this statement false.

That wasn’t so bad, right? Now that we’ve walked through detailed examples, let’s review the overall process so you can learn how to use it with any problem:

Study summary

• If needed, simplify the numbers on both sides of the equality or inequality.
• Next, compare the numbers.

Do it yourself!

Practicing math concepts like this one is a great way to prepare yourself for the math journey to come! So, when you’re ready, we’ve got some practice problems for you!

• $$\frac{8}{2}=4$$
• $$\frac{9}{4} < 3$$
• $$\sqrt{7} = 7$$
• $$4.25 > \frac{17}{4}$$
• $$\text{True}$$
• $$\text{False}$$

If you’re still struggling with the solving process, that’s totally okay! Stumbling a few times is good for the learning process. If you get too stuck or lost, scan the problem using your Photomath app and we’ll walk you through it!

Here’s a sneak peek of what you’ll see:

Related Topics

• Math Explained: Arithmetic
• Arithmetic Operations

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Decimals to fractions

Simplifying expressions with fractions

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Home / United States / Math Classes / Worksheets / Comparing Numbers Worksheets

Comparing Numbers Worksheets

One of the most fundamental operations and a fundamental building block in mathematics is comparing numbers. Comparing n umbers is a process of comparing two or more numbers and determining if one number is equal to, less than, or larger than the other numbers by using symbols. There are many scenarios in daily life where we make comparisons of numbers, such as estimating costs, distance traveled, number of students in different classes and many other instances. With the help of the BYJU’S Math worksheets, students can understand when and how number comparisons are used in everyday life. ...Read More Read Less

Benefits of Comparing Numbers Worksheets:

Real-life Applications:

Comparing numbers is an important part of building an awareness about numbers in students. ‘Number sense’ is the ability of a student to recognize a number, its value and its relationship with other numbers. There are many uses for comparing numbers in daily life such as measuring ingredients while cooking, counting the distance while traveling from one place to another, or even to know the difference between the scores of multiple tennis matches.

Interactive Worksheets Make Comparing Numbers Interesting :

Math is frequently viewed by students as a challenging topic that makes it tedious for them to tackle several problems at once. Problems on comparing numbers are solved by making it interesting for students through BYJU’S Math online interactive division worksheets.

Precision and Time Management : 

Learning to solve mathematical problems requires the ability to manage your time effectively. Students can improve time management and problem-solving abilities by practicing comparing numbers with these worksheets. Students will be able to narrow down on the topics in which they need additional practice or conceptual comprehension with regular practice.

Builds Logical-Thinking:

BYJU’S Math worksheets encourage students to seek solutions independently by using the worksheets, and this helps them foster logical thinking. These worksheets also allow students to think of solutions and encourage them to strive to come up with solutions and answers on their own, which strengthens their logic.

Learning becomes Fun:

Every worksheet from BYJU'S Math is specifically created to make learning enjoyable for students. These worksheets are carefully designed with engaging questions and puzzles as well as some aesthetically appealing and vibrant images to hold the attention of students.

• Interactive Worksheets
• Printable Worksheets

Choose Math Worksheets by Grade

Choose math worksheets by topic, comparing numbers worksheets explained.

Comparing numbers is a method that identifies if one number is equal to, smaller than, or larger than the other numbers. To compare two numbers, we write them using a few symbols. In our daily lives, we make comparisons of numbers, such as the temperature, the cost of things used on a regular basis, our height and weight, etc. A number with more digits is greater than a number with fewer digits, this is the foundation of comparing numbers. Numbers can be arranged in either ascending or descending order. The comparison of two numbers is done using the symbols, ‘>’ and ‘=’. Students learn how to deal with numbers and apply it to real-world scenarios by solving questions in the BYJU’S Math comparing numbers worksheets. The best way to avoid numbers confusing young minds is to make them work and solve a variety of problems in these worksheets. To keep students motivated, these arithmetic worksheets combine enjoyment with learning from which they can effectively internalize the concepts and enhance their capacity for problem solving. The BYJU’S Math worksheets are well structured, and it ensures that students quickly grasp the subject. According to the order of introduction of concepts from grades 1 to 4, the problems in each worksheet are based on the following comparing numbers methods and properties:

• Identifying which group has more objects by using pictures but not numbers.
• Counting the objects and circling the correct symbol (>, <, =)
• Circling the number which is greater or lesser.
• Comparing the numbers and write in the correct symbol (>, <, =)
• Comparing and ordering the numbers from least to greatest.
• Comparing and ordering 5 numbers least to greatest (0-100)
• Comparing numbers as less than, greater than, or equal to (<, >, =) from 0-100
• Compare numbers up to 100 or 1,000

Click on the links below if you want to refresh your knowledge of comparing numbers as a concept.

• Comparison of Numbers
• Greater than Symbol
• Greater than and Less than Symbol
• Less than Symbol
• Concepts of Counting using more or less numbers 

Interactive and Printable Comparing Numbers Worksheets

Students now have the option of solving worksheets online by clicking on interactive comparing numbers worksheets. They can also click on the printable worksheets to download the PDF version of comparing numbers worksheets and solve problems at their convenience. Worksheets are aligned with the common core concepts to help supplement the concepts learnt in the classroom. So whether a student is learning the basics of division or is at an advanced level of performing division operations, BYJU’s Math worksheets can help give them the confidence to succeed.

How many levels does each worksheet have?

The prerequisites and difficulty level for the topic are taken into consideration when creating worksheets. Each worksheet has the word ‘ easy’ , ‘ medium ’, or ‘ hard ’, depending on how difficult the problems are in that worksheet. It is suggested that a student starts with the easy level worksheets before moving on to the medium and hard levels.

Is there any fee to pay in order to use BYJU’S Math worksheets?

No, there isn’t. All BYJU’S Math interactive worksheets are absolutely free.

Why is it important to learn how to compare numbers?

The comparing numbers worksheets is a building block for any student aiming to master advanced topics in math. It is useful in a number of everyday situations like comparing a certain quantity to other  quantities.

What does a ‘greater than’ symbol look like?

In math, the greater than symbol is represented by‘ > ’.

What does a ‘lesser than’ symbol look like?

In math, the greater than symbol is represented by‘ < ’.

How can a student know the results of the worksheets once they submit their answers?

After the successful submission of worksheets, the student can instantly see how much they scored on a certain worksheet along with the respective answer key.

How can I access and print worksheets?

BYJU’S Math offers worksheets of various math concepts that are available in PDF format. A student or parent can easily open and print them using any free PDF tool.

Are these worksheets accessible both offline and online?

Both offline and online worksheets are available. Interactive worksheets are offered for the student who chooses the online mode. Students can download the PDF for offline worksheets, print it, and start answering the questions.

Helping with Math

Comparing Numbers

Comparison of Numbers is the process of defining similarities between two numbers and identifying the number greater than, smaller than, or equal to the other number. In Mathematics, there are several basic comparison rules. These are greater than (>), less than (<), and equal (=).

For young learners to be able to compare numbers, they must have a thorough understanding of the numbers and their meanings. Hands-on learning can be crucial for achieving this understanding, which includes the use of manipulatives and other devices.

Take two numbers a and b

• a > b means a is greater than b;
• a < b means a is less than b;
• a = b means a is equal to (or has the same value as)b.

To illustrate, if you asked a student which is more, 3 or 4, the student must understand that the word “three” stands for the symbol 3. This also applies to number 4. But once a student has grasped this fundamental knowledge, they can begin to study number comparison.

Why is comparing numbers important?

The ability to compare numbers plays an important role in building students’ number sense.  Students with number sense are able to recognize a number, its value, and its relation to other numbers. The evaluation of numbers allows for the development of this last component.

In order to compare numbers, it is necessary for students to understand what the numbers are and the value they have. The understanding can be basic, and it can involve manipulatives and other hands-on aids.

How to Compare Numbers?

These are the following ways of comparing numbers :

• Using counting
• Using number line

Using ordering

Using Counting

There is no question that a number with more digits is usually higher than one with fewer digits.

When any numbers have the same number of digits, once we come across unequal digits, we compare them based on the leftmost digit.

Using Number Line

When comparing two numbers, you can use a number line to determine which number is greater. Usually, the number on the right is greater than the number on the left. As you can see from the illustration below, 4 is greater than 2 since it is to the right of 2.

The arrangement of objects, numbers, etc in ascending or descending order of their values after comparison is called ordering.

Reference: https://hindisutra.com/wp-content/uploads/2020/06/Ascending-Order-Descending-Order-in-hindi.jpg

Representation

The process of comparison is the way we determine whether different objects have similar properties to each other. In Mathematics, this is the primary concept for describing whether two numbers are equal, or if one is greater or smaller than the other.

When comparing numbers, there are three special symbols used. The basic symbols used in the comparison of numbers are given below:

• Greater than (>)
• Less than (<)
• Equals to (=)

Less than (<) is true if the left value is lower than the right value, otherwise, it is false.

When the left value is larger than the right value, greater than (>) returns true, otherwise, the return will be false.

Less than or equal to (<=) returns true if the value on the left is less than or equal to the value on the right, otherwise, it returns false.

In the case that the left-hand value exceeds or equals the right-hand value, greater than or equal to (>=) returns true, otherwise it returns false.

If the left value is equal to the right value, then equal to (=) returns true, otherwise it returns false.

Greater than

Lesser than

The above symbols can be used to compare two numbers of any type, such as natural numbers , whole numbers , integers, decimal numbers, etc. Thus the comparison of numbers is the process by which one compares and explores the differences between two numbers.

Rules for Comparison of Numbers

There are certain mathematical rules that help us to compare numbers. Listed below are a few of them:

• Numbers with a different number of digits
• Numbers with the same number of digits
• Numbers with more digits are always greater among the given, and numbers with fewer digits are always smaller.

Example: Of the four numbers given 9999, 55, 2, 333, 9999 is the greatest number since it has four digits. The smallest number is 2, which has only one digit.

Based on the given rule, the following conclusions can be drawn:

• A two-digit number is always greater than a one-digit number
• A three-digit number is always greater than a two-digit number
• A four-digit number is always greater than a three-digit number
• A five-digit number is always greater than a four-digit number, and so on.

Numbers With the Same Number of Digits

When comparing numbers with the same digits, we start from the extreme leftmost digit. Thus, the number with the greatest extreme leftmost digit is the greater number.

Example 1: Compare the numbers 632 and 529.

Based on a comparison of the left-most digits of two numbers, 6 is greater than 5 in this case.

Therefore, 632 is greater than 529. When the left-most digits of the numbers are equal, we compare the next digit rightward, and so on.

Example 2: Compare the numbers 572 and 518.

In the given example above, the number of digits is the same, and the leftmost digit (5) is the same. The next step is to compare the numbers towards the right, such as (7) and (1).

Therefore, 572 is the greater number.

Greater Than Type Operator

Taking two numbers and comparing them according to their absolute values allows us to determine which number is greater.

Example: In the numbers 3 and 2, we know that 3 is greater than 2.

We can use one special symbol (>) for “Greater than”, and it is called a greater than sign. So, the above relation can be represented as 3 > 2.

Let us consider the example:

A greater than sign signifies that 3 is greater than 2, which is represented mathematically by the greater than sign. Therefore, there are two points on the left side and only one point on the right side of the greater than sign.

The wide-open side of the sign is always facing towards the larger number, and the narrow endpoint is facing towards the smaller number.

Here are some examples:

• 1001>1000

Less Than Type Operator

By comparing two numbers, based on their absolute value , we can determine which number is smaller.

Example: In the numbers 3 and 2, we know that 2 is smaller than 3.

We use the symbol (<) for “Less than”, and it is called a less-than sign. So, the above relation can be represented as 2 < 3.

In this case, 2 is smaller than 3, which is symbolized by the less-than sign in mathematics. On the right side, there are two points, and on the left, there is only one point.

The wide-open side of the sign always faces towards the greater number, and the narrow endpoint faces towards the smaller number.

• 111<1111
• 5500<50000
• 9999<10001

Tricks For Comparison of Numbers

As we know, for comparing the greater and smaller numbers, we have some mathematical symbols. Even though the greater than and less than signs have clear meanings, they can be difficult to remember. With the exception of the “does not equal” sign, they all resemble one another. Then how are you going to remember them? Here are a few simple tricks.

• Alligator Method

To memorize the greater than and less than signs, imagine them as little alligators (or crocodiles), with the numbers on either side representing fish. Alligators hunt for the fish with the larger number, so whichever direction their mouths are open they are searching for the bigger fish.

Reference: https://blog.prepscholar.com/hs-fs/hubfs/body_alligator.png?width=900&name=body_alligator.png

In the example, we see the numbers 4 and 3, the alligator’s mouth places towards the left (4). So mathematically, we can show it as 4 > 3.

References: https://blog.prepscholar.com/hs-fs/hubfs/body_alligator2.png?width=900&name=body_alligator2.png

This also works the other way around. In this case, the alligator’s mouth faces right, as does the less-than sign.

In the example, we see the numbers 5 and 8, the alligator’s mouth places towards the right (8). So mathematically, we can show it as 5 < 8.

In this method, “less than” is represented by the symbol that most resembles the letter L — it is the symbol used to denote “less than.”

The < sign looks more like an L than the > sign, so < means “less than.” Since > doesn’t look like an L, it cannot be denoted by “less than.”

Comparison of Integers

Numbers that contain both positive and negative digits, as well as zero, are called integers. The values on the number line increase as we move to the right, and decrease as we move to the left, as already shown in the illustration above.

Reference: https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/integer-number-line-1621880568.png

We know that zero is in the middle of the number line. Positive numbers are to the right of the zero, and negative numbers are to the left of the zero.

The number at the extreme right of the number line is the greatest, and the number at the extreme left is the smallest.

Below are some conclusions which are drawn from the integers on a number line:

• A positive number is always greater than a negative number.
• The value of any negative integer is less than that of any positive integer.
• As compared to all negative integers, zero is the greater number.
• Zero is the least number among all positive integers.

Comparison of Decimal Numbers

A decimal number has both a whole number part and a decimal part. Decimal numbers with a greater whole part, therefore, have more value.

Example: When comparing 2.34 and 1.23, 2.34 is the larger number since it has a greater whole number part (2>1).

In another way, we must compare the most significant decimal numbers in order to compare the given decimal numbers. A decimal’s most significant digit is the first digit other than zero. Consider the following examples:

The most significant digit has the value 7 → 7.273

The most significant digit has the value 20 → 26.85

The most significant digit has the value 0.4 → 0.49

The most significant digit has the value 0.08 → 0.083

Therefore, a decimal like 0.7 is greater than 0.65, since the most significant digit is worth more  (7>6).

Comparisons of Fractions

Step 1) Take the two fractions and convert them into decimals by dividing the numerator by the denominator.

Step 2) Compare both the decimals to see which is bigger.

Which is bigger, 3/7 or 2/5?

1) Change both fractions into decimals:

3/7 = 3 ÷ 7 = 0.43

2/5 = 2 ÷ 5 = 0.4

2) Compare the decimals:

0.43 > 0.4

Therefore, 3/7 is greater than ⅖.

Comparison with Ratios

Ratios let you compare quantities, but they do not tell you their actual values by themselves.

Comparing quantities via a ratio is different from subtracting amounts to find the difference because a ratio refers to how much one quantity is for a given amount of the other quantity.

There are two steps to be remembered while comparing ratios.

The first step is to make the consequent of both ratios equal by finding the Least Common Multiple (LCM). As soon as you have determined the LCM, divide it by both the consequent of the ratio. Finally, multiply the antecedent and consequent of the two ratios with the quotient obtained before.

Next, compare the 1st number i.e. the antecedent of both the ratios with each other. Once step 1 is done, then we move forward to step 2 to find out the comparison between the two ratios.

Example: Compare the ratios of the given quantities 2:6 and 5:4. Which of the ratios is greater?

Find the LCM of both the consequents in the ratios, namely 6 and 4. LCM of 6 and 4 is 12

Once the LCM is determined, divide it with both the numbers i.e. 12 ÷ 6 = 2 and 12 ÷ 4 = 3

Therefore, (2 x 2 ): (6 x 2) = 4 and 12  (5 x 3) : (4 x 3) = 15 and 12

Since 15 > 4, the ratio 5:4 is greater than 2:6

Compare problems in number and measurement

Compare problems involve comparisons (differences). Number comparisons are between disjoint sets (groups of objects), whereas measurements are between quantities (for example, lengths).

• Comparing sets: Number

There are 18 teachers and 25 students.

How many more students are there than teachers?

This problem involves two separate groups (teachers and students), it does not involve action (the groups are not joining or splitting), and it concerns “how many more” (a comparison).

A comparison problem can be modeled using two bars:

Using the model, we can see that there are two possible ways to find a solution:

25 – 18 = ? which is 7

18 + ? = 25 which is

• Comparing quantities: Measurement

To make comparisons, measurements can be used. Take this pencil for instance. The length is different.

This problem is structurally identical to the student and teacher problem, as can be seen from the visual models. The difference can be found in two ways:

• Subtracting one length from the other when measuring each pencil
• Comparing the two lengths of the pencils by lining them up at one end.

What Are the Benefits Of Comparing And Ordering?

Comparing and ordering have the following benefits and achievements:

• It allows children to classify objects according to their size, shape, weight, and value.
• It develops children’s logical reasoning skills and aptitude.
• They are able to understand the daily challenges they face when choosing items during shopping.
• Their decision-making is strengthened as a result.
• It allows qualitative sorting among kids.
• Children develop a strong numerical sense which helps them build strong mathematical concepts.

Examples of Comparison

Example 1: Find the least four-digit number and the greatest three-digit number. Show the greater number by using the Mathematical symbol.

We know that the least four-digit number is 1000.

999 is the greatest three-digit number.

We know, numbers with more digits are greater.

Therefore, 1000 is the greater number.

Mathematically, it can be written as follows:

So, 1000>999.

Example 2: Put the correct sign of comparison:

988 > 987

Example 3: Compare 71.92  and 71.9. Find the greater and least number among them.

Numbers 71.92 and 71.90 contain the same whole number (71).

In both cases, the decimal number at the tenths place (9) is the same.

Comparing, the hundredth place digit 2 is greater than 0.

Therefore, 71.92 is greater than 71.9.

71.92 > 71.9

71.92 is the greater number, and 71.9 is the least number.

Example 4: Chris has 3kg of apples, and Nathan has 5kg of oranges. Compare their weights and find out who has a large number/ quantity of fruits?

Given, Chris has 3 kg of apples, and Nathan has 5 kg of oranges.

Comparing their weights, we can say that 5 is larger than 3.

5kg > 3kg

Hence, Nathan has more fruits.

In Mathematics, the compare function is used to determine which number is greater, or lesser, or equal to another. It is an essential concept that early learners must understand to move into advanced study of the subject.

• https://blog.prepscholar.com/greater-than-sign-less-than-sign
• https://www.cuemath.com/numbers/comparing-and-ordering/

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Comparing and Ordering Numbers: Definition with Examples

What are comparing and ordering numbers, what is ordering numbers, comparing and ordering real numbers using a number line, solved examples on comparing and ordering, practice problems on comparing and ordering, frequently asked questions on comparing and ordering.

Have you ever compared your height and your friend’s height to decide who is taller? Or has the teacher ever asked your class to stand in increasing order of height? 

This type of situation can be answered by comparing and ordering numbers. “Comparing” in math is the process in which we observe similar properties of different persons or objects or things. Ordering a list of numbers means stating the numbers from the least to the greatest or from the greatest to the least. Before we learn how to compare and order numbers, let us first introduce the meaning of comparing numbers.

Comparing Numbers Meaning

Comparing in math refers to viewing something in relation to another. So, what is comparing numbers? Comparing numbers in math is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to its values. 

The definition of comparison in math is all about identifying a quantity greater, smaller, or equal in relation with the given number.

Related Worksheets

Symbols for Comparing Numbers

The symbols used for comparing numbers are $\gt,\; \lt,$ or $=$.

• $“\gt”$ means “greater than”
• $“\lt”$ means “less than”
• $“=”$ means “equal to”

We also use the following symbols for comparing two quantities.

means “less than or equal to”

means “greater than or equal to”

Example: Let’s understand this visually using vertical bars composed of blocks. Each small block is of the same size. We can compare the numbers by comparing the heights of the bars.

On comparing two numbers, we can find out by how much a number is greater or smaller. 

• In the first example, $7 \gt 3$ since the green bar is taller than the pink bar. We can also say that 7 is more or greater than 3 by $7 \;−\; 3 = 4$.
• In the second part, $3 \lt 6$ since the red bar is shorter than the yellow bar.  We can also say that 3 is less or smaller than 6 by $6 \;−\; 3 = 3$.

Steps for Comparing Numbers

Step 1: Compare the number of digits. The number with the more digits, is greater. Note that 0 placed at the beginning of a number is insignificant.

Example: $358 \lt 9104$

Step 2: If the number of digits are the same, we start by comparing the highest place values.

Example: In the following example, $312521 \lt 312712$ since $5 \lt 7$ at the hundreds place.

Ordering a list of numbers means arranging the numbers from least to greatest or greatest to least. In other words, we can say that ordering numbers means arranging numbers either in increasing order or decreasing order.

• Ascending order

Arrangement of numbers in increasing order, from the smallest to the greatest, is called ascending order.

For example $2 \lt 4 \lt 6 \lt 8 \lt 10$

• Descending order

Arrangement of numbers in decreasing order, from the greatest to smallest, is called descending order.

For example, $10 \gt 8 \gt 6 \gt 4 \gt 2$ 

On a number line, the numbers increase as we go from left to right. Thus, the number on the right is always greater than the number on the left. Thus, any two real numbers can be compared based on their position on the number line.

Example: Compare – 9 and 8 on the number line. 

-9 lies on the left side of 8.

Thus, -9 < 8.

We can order the integers in increasing order as shown below

$…\; \lt -9 \lt -8 \lt -7 \lt -6 \lt …\lt -2 \lt -1 \lt 0 \lt 1 \lt 2 \lt 3 \lt 4 \lt …$

Similarly, $0.5 \lt 1.4$ since 0.5 lies on the left side of 1.4.

Comparing Rational Numbers

Comparing two or more rational numbers is similar to comparing fractions. We just need to keep in mind that:

• All negative rational numbers are smaller than 0.
• All positive rational numbers are greater than 0.
• All positive rational numbers are greater than all negative rational numbers.

As we know that rational numbers include whole numbers, integers, fractional, and decimal numbers in it, hence comparing two or more rational numbers can be categorized as

Comparing Whole Numbers

Comparing integers, comparing fractions, comparing decimals.

Let’s discuss steps for comparing numbers for each category one by one.

There are some steps through which we can compare two or more whole numbers:

Step 1: We should compare the number of digits. If there are more digits, it means the number is greater. For example $15 \gt 9,\; 125 \gt 32$, etc.

Step 2: If the number of digits is the same in both numbers, then we should compare the highest place values or the digit to the extreme left of the numbers. For example, $65 \gt 57,\; 243 \gt 127$, etc.

Step 3: If the digits at the highest place value are the same, we should compare the digits in the next digits to the right or the second highest place value. For example $76 \gt 72,\; 358 \gt 348$, etc.

Step 4: We keep comparing digits with the same place value until we find digits that are different. The number with the greater face value is the greater number. $109 \gt 102,\; 557 \gt 552$ etc.

• Comparing two positive integers is the same as comparing whole numbers except comparing with a negative integer.
• A positive integer is always greater or more than a negative integer. 

For example $5 \gt \;−\;5,\; 80 \gt \;−\; 80$, etc.

For comparing two negative numbers, we say that the greater number with a negative sign is the smallest of two negative integers.

For example $−\;80 \lt \;−\;75,\; −\;15 \lt \;−\;5$, etc.

• Negative integers are less than 0 and positive integers are greater than 0.

For example $−\;5 \lt 0, \;−\;12 \lt 0,\; 8 \gt 0$, etc.

When two or more fractions share the same denominator, the fractions are called “like fractions.” When two or more fractions have different denominators, they are called “unlike fractions.”

Comparing Like Fractions

To compare two or more like fractions, we just have to compare the numerators.

In the above figure, since $7 \gt 5$, hence $78\gt58$.

Comparing Unlike Fractions

To compare two or more unlike fractions, we can use different methods.

• Cross Multiplication Method

We multiply the numerator of the first fraction by the denominator of the second fraction and write the answer.

For example, we have to compare $\frac{5}{8}$ and $\frac{6}{11}$.

So, we multiply 5 and 11 together and 8 and 6 together, and we get

$5 \times 11 = 55$ and $6 \times 8 = 48$

After that, we can compare them like two whole numbers.

$55 \gt 48$

Finally, we replace the numbers with fractions. 

$\frac{5}{8} \gt \frac{6}{11}$

• Making the Denominators the Same 

In this method, we first find the LCM of both denominators. 

Let us take the above example, i.e., compare $\frac{5}{8}$ and $\frac{6}{11}$.

LCM $(8,\; 11) = 88$

To make the denominator the same, multiply the numerator and denominator by a relevant number. 

$\frac{5 \times 11}{8 \times 11} = \frac{55}{88}$ and $\frac{6\times8}{11\times8} = \frac{48}{88}$

After the denominators become the same, we compare the numerator. 

$55 > 48$

Finally, we replace the numbers with fractions.

$\frac{55}{88} \gt \frac{48}{88} \Rightarrow \frac{5}{8}\gt\frac{6}{11}$

We can compare two or more decimals by using the following steps:

Step 1: Firstly, compare the whole number part (i.e., compare the digits before the decimal). If they are different, you can compare the numbers as you would for any whole number. If they are the same, then follow the next step.

Step 2: Compare the tenth place. If they are different, then compare the numbers as you would for whole numbers. If they match, then move on to the next digit.

Step 3: Compare the hundredths place. If they are different, then compare those digits as you would for whole numbers. If they match, then move on to the next digit.

Example: Compare 23.56 and 23.289.

The numbers before the decimal are the same. So, we move to the next step, i.e., comparing the tenth place. Since $5 \gt 3,\; 23.56 \gt 23.289$.

In this article, we have discussed the meaning and symbols of comparing numbers, the method of comparing numbers, ordering, ascending and descending order as well as some important facts, and problems based on comparing and ordering numbers.

• Compare the numbers 425 and 412.

Given numbers 425 and 412.

Since the number of digits is the same in both numbers and the first digit is also the same, i.e., 4. But the digit at tens places 2 > 1.

Therefore, $425 \gt 412$

Hence, 425 is greater than 412.

• Which number is smaller out of $−612$ and $−625$ ?

Therefore, $−625 \lt −612$

Hence, $−625$ is smaller than $−612$.

• Compare $\frac{3}{5}$ and $\frac{5}{9}$ .

We have to compare $\frac{3}{5}$ and $\frac{5}{9}$.

Using the cross multiplication method,

$\frac{3}{5} = \frac{3 \times 9}{5 \times 9} = \frac{27}{45}$

$\frac{5}{9} = \frac{5 \times 5}{9 \times 5} = \frac{25}{45}$

Here, $27 \gt 25$

So, $\frac{27}{45} \gt \frac{25}{45}$

Finally, we replace the numbers with fractions $\frac{3}{5} \gt \frac{5}{9}$ .

• Compare the numbers 5, 0, 10, and $−15$ . Also, arrange them in ascending order.

Given a list of numbers $5, 0, 10,$ and $−15$.

Since a positive integer is always greater than a negative integer, $−15$ is smaller than all of the given numbers.

Also, negative integers are less than 0 and positive integers are greater than 0.

Hence, $−15 \lt 0 \lt 5 \lt 10$ (ascending order).

• Which is greater: 3.025 or 3.003?

Since the ones and tenth place of both the numbers are the same. So, we will see the hundredth place. Since $2 \gt 0$.

Hence, $3.025 \gt 3.003$.

Attend this quiz & Test your knowledge.

Which of the following is not a sign of comparing two numbers?

Which of the following is greater than $−5$, choose the correct sign for blank space: $\frac{13}{19}$ ——— $\frac{17}{19}$., ordering of a list of numbers in increasing order is called _________ order..

Why is comparing numbers important in our daily lives?

We compare numbers in our daily lives. For example, for comparing weights, for comparing the prices of everyday items, comparing the height of two or more people, etc.

How is comparing numbers different from ordering numbers?

Comparing numbers is a method of identifying greater, smaller, or equal numbers. Ordering numbers means arranging them in an ascending or descending order.

What is a quick way of comparing numbers?

The easiest way to compare numbers is by marking the numbers on a number line.

What are the different ways to compare numbers?

We can use different approaches to compare numbers, such as comparing numbers on a number line, by counting the number of digits, using place values of the numbers, etc.

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