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Introduction

QUICK LINKS


Introduction

Greater Than and Less Than

INTRO
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Remembering which inequality sign or symbol to use in a number comparison can be difficult, but we have an easy memory trick that can help!

See how the inequality symbol has a wide end and a narrow end?

The wide end opens to the greater value, and the narrow end points to the lesser value. If we describe the image below from left to right, it reads as all the Spider People are greater (or bigger) than just one Spider-Ham.

If we flip things around, we can still read it left to right, but now it reads as one Spider-Ham is less (or smaller) than all the Spider People.

We can apply the same concept to comparing numbers. The wide end of the sign should always open to the greater number.
When we’re comparing numbers, we compare place values from left to right. The number that has the first place value with a bigger digit is farther from 0 on the number line.

The number farthest to the right on the number line is the greater number.

Remember that numbers farther to the right are greater by imagining a phone's signal bars - the bars get bigger and greater in strength as we go further to the right.

This also means that any positive number is greater than any negative number πŸ’‘.

Why is a bigger negative number less than a smaller negative number? πŸ€”

Remember, numbers get greater as we move to the right on the number line.

For negative numbers, you can think of β€œgreater than” as meaning β€œwhich number is less negative (or more positive).”

Since is farther to the right than , is greater than .

Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about how to compare numbers, fractions, and decimals and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

CALCULATOR
β€”

Greater Than and Less Than Calculator

Compare

and

KEY STEPS
β€”

How to Compare Numbers

Compare a
No steps here! Any positive number is greater than any negative number πŸ˜‰.

Step 1. Line up the decimal points.

Step 2. Compare digits from left to right.

  • If they’re the same, move to the next digit.
  • If they’re different, the bigger digit belongs to the number that is farther from 0.

Step 3. Imagine the two decimals on a number line.

The number farthest to the right is the greater number.

Step 4. Use the correct inequality sign.

The wide end of the sign should always open to the greater number.

Step 1. Check the denominators.

If they're the same, skip to Step 3. Otherwise, continue to Step 2.

Step 2. Make the denominators the same.

Multiply the numerator and denominator of fraction 1 by the denominator of fraction 2.
Multiply the numerator and denominator of fraction 2 by the denominator of fraction 1.

Step 3. Compare the digits of the numerators from left to right.

  • If they’re the same, move to the next digit.
  • If they’re different, the bigger digit belongs to the numerator of the fraction that is farther from 0.

Step 4. Imagine the two decimals on a number line.

The number farthest to the right is the greater number.

Step 5. Use the correct inequality sign.

The wide end of the sign should always open to the greater number.

Step 1. Convert the decimal to a fraction.

Just place the decimal over .

Step 2. Check the denominators.

If they're the same, skip to Step 3. Otherwise, continue to Step 2.

Step 3. Make the denominators the same.

Multiply the numerator and denominator of fraction 1 by the denominator of fraction 2.
Multiply the numerator and denominator of fraction 2 by the denominator of fraction 1.

Step 4. Compare the digits of the numerators from left to right.

  • If they’re the same, move to the next digit.
  • If they’re different, the bigger digit belongs to the numerator of the fraction that is farther from 0.

Step 5. Imagine the two decimals on a number line.

The number farthest to the right is the greater number.

Step 6. Use the correct inequality sign.

The wide end of the sign should always open to the greater number.
LESSON
β€” Comparing Decimals

Comparing Decimals

Compare two numbers that are :

The first thing we have to do when we’re comparing decimals is line up decimal points.

Once the decimal points are lined up, we can compare the digits of each number from left to right.

The number that has the first place value with a bigger digit is the number that is farther away from 0.

When the two numbers are positive, then the number with the bigger digit is farther from 0 and farther to the right. This makes it greater than the other number.
Once we know which number is greater, we can use the correct inequality symbol. Remember, the wide end of the sign should always open to the greater number.

Let’s walk through some step-by-step examples of comparing decimals!

EXAMPLE 1

Which number is greater: or ?

EXAMPLE 2

Which number is greater: or ?

EXAMPLE 3

Which number is greater: or ?
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to explore what we do to compare two fractions.
PRACTICE
β€” Comparing Decimals

Practice: Greater Than Less Than

Question 1 of 10: Use the correct inequality sign between
.

Step 1. Line up the decimal points.

Step 2. Compare place values from left to right.

  • If they’re the same, move to the next place value.
  • If they’re different, the bigger digit belongs to the number farther from 0.
Select the first column with differing digits:
The number farthest from 0 is

Step 3. Imagine the numbers on a number line.

0
The number that is farthest to the right is the greater number, so the greater number is.

Step 4. Use the correct inequality sign.

The wide end of the sign should always open to the greater number
Awesome job!

LESSON
β€” Comparing Fractions

Comparing Fractions

Compare two numbers that are :

The first thing we have to do when we’re comparing fractions is check the denominators.

For example, to compare and , we first need to make the denominators the same.

We can get to a common denominator by multiplying the numerator and denominator of fraction 1 by the denominator of fraction 2:

And multiplying the numerator and denominator of fraction 2 by the denominator of fraction 1:

Once the denominators are the same, we can compare the digits of the numerators from left to right.

The numerator that has the first place value with a bigger digit will belong to the number that is farther away from . In this case, is farther away from .

Once we know which number is greater, we can use the correct inequality symbol. Remember, the wide end of the sign should always open to the greater number.

Comparing Fractions with Common Denominators

If both fractions are positive and have a common denominator, the fraction with the larger numerator is greater than the other fraction.

If both fractions are negative and have a common denominator, the fraction with the larger numerator is less than the other fraction.

Comparing Fractions with Common Numerators

If both fractions are positive and have a common numerator, the fraction with the smaller denominator is greater than the other fraction.

If both fractions are negative and have a common numerator, the fraction with the smaller denominator is less than the other fraction.

Let’s walk through some step-by-step examples of comparing fractions!

EXAMPLE 1

Which number is greater: or ?

EXAMPLE 2

Which number is greater: or ?

EXAMPLE 3

Which number is greater: or ?
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to explore what we do to compare a fraction and a decimal.
PRACTICE
β€” Comparing Fractions

Practice: Greater Than Less Than

Question 1 of 10: Use the correct inequality sign between
.

Step 1. Check the denominators.

Are the denominators the same or different?

Step 2. Make the denominators the same.

Multiply the numerator and denominator of fraction 1 by the denominator of fraction 2.
Multiply the numerator and denominator of fraction 2 by the denominator of fraction 1.


Step 3. Compare the digits of the numerators from left to right..

Select the first column with differing digits:
The numerator with the bigger digit belongs to the fraction that is farther from 0.
The number farthest from 0 is

Step 4. Imagine the numbers on a number line.

0
The number that is farthest to the right is the greater number, so the greater number is

Step 5. Use the correct inequality sign..

The wide end of the sign should always open to the greater number
Awesome job!

LESSON
β€” Comparing Decimals to Fractions

Comparing a Decimal and Fraction

Compare two numbers that are :

It’s easiest to compare numbers when they’re both fractions or both decimals, which is why the first step to comparing decimals and fractions is to turn the decimal into a fraction.

For example, to compare and , we need to first convert the decimal to a fraction. We can do this by just putting it over .

Then check the denominators,

And if needed, find a common denominator:

Then we compare the numerators from left to right.

The numerator that has the first place value with a bigger digit will belong to the number that is farther away from . In this case, is farther away from .

Once we know which number is greater, we can use the correct inequality symbol. Remember, the wide end of the sign should always open to the greater number.

Let’s walk through some step-by-step examples of comparing a decimal and a fraction!

EXAMPLE 1

Which number is greater: or ?

EXAMPLE 2

Which number is greater: or ?

EXAMPLE 3

Which number is greater: or ?
Awesome! If you’d like to practice additional problems comparing decimals and fractions, expand the
Practice
below before closing out this lesson! ⚑
PRACTICE
β€” Comparing Decimals to Fractions

Practice: Greater Than Less Than

Question 1 of 10: Use the correct inequality sign between
.

Step 1. Convert the decimal into a fraction.

Just put the decimal value over 1.

Step 2. Check the denominators.

Are the denominators the same or different?

Step 3. Make the denominators the same.

Multiply the numerator and denominator of fraction 1 by the denominator of fraction 2.
Multiply the numerator and denominator of fraction 2 by the denominator of fraction 1.


Step 4. Compare the digits of the numerators from left to right..

Select the first column with differing digits:
The numerator with the bigger digit belongs to the fraction that is farther from 0.
The number farthest from 0 is

Step 5. Imagine the numbers on a number line.

0
The number that is farthest to the right is the greater number, so the greater number is

Step 6. Use the correct inequality sign.

The wide end of the sign should always open to the greater number.
Awesome job!

CONCLUSION
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Incredible job, look at you go! Thanks for checking out this lesson β˜ΊοΈπŸ™. Where to next?
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