Introduction Introduction # Greater Than and Less Than

INTRO

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.
CALCULATOR

Compare

and

KEY STEPS

## How to Compare Numbers

Compare a

### 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.
LESSON
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!

PRACTICE
Comparing Decimals

## Practice: Greater Than Less Than

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

### Step 1. Line up the decimal points.

LESSON
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!

PRACTICE
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?

LESSON
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!

PRACTICE
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.

CONCLUSION
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