# Compare directed numbers

Lesson

An inequality exists when one amount does not equal the other. In other words, one side of an expression is greater than the other. You can think of this like a set of unbalanced scales, where one side is heavier than the other.

## Inequality Symbols

So far we have compared the relative size of numbers using a number line - the further to the right a number is the larger it is. In maths, we have special symbols to indicate that one quantity is bigger or smaller than another. Let's run through them now.

### "Greater than"

The symbol   >   is used to tell us that the number on the left is greater than the number on the right.

For example, $3>2$3>2.

### "Less than"

The symbol   <   is used to tell us that the number on the left is less than the number on the right.

For example, $2<3$2<3.

Remember!

$>$> means "is greater than"

$<$< means "is less than"

The inequality symbol always points to the smaller number.

#### Example 1

Write a mathematical statement for:

• "Two is greater than one": $2>1$2>1
• "Three is greater than negative four": $3>-4$3>4
• "Minus seven is less than minus two": $-7<-4$7<4

#### Example 2

What does each inequality statement expression?

 $-2>-5$−2>−5 $-2$−2 is greater than $-5$−5 $5>0$5>0 $5$5 is greater than $0$0 $-15<-6$−15<−6 $-15$−15 is less than $-6$−6 $-10<3$−10<3 $-10$−10 is less than $3$3

Let's look at some examples where we use an inequality statement to compare two numbers.

#### Examples

##### Question 1

Write an inequality comparing the numbers $2$2 and $-9$9

Think: The number $2$2 is greater than the number $-9$9. So we want to write an inequality that says "$2$2 is greater than $-9$9".

Do: We can do this in two ways:

1) We can use the "$>$>" symbol to state $2>-9$2>9. This is read as "$2$2 is greater than $-9$9".

2) We can use the "$<$<" symbol to state $-9<2$9<2. This is read as "$-9$9 is less than $2$2".

##### QUESTION 2

Sharon has made $\$86$$86 selling ice creams. Patricia has made \125$$125 selling lemonade.

Choose the correct number statement below that represents the relationship between Sharon and Patricia's earnings.

A) $125\le86$12586     B) $86>125$86>125     C) $86<125$86<125     D) $86\ge125$86125

Think: What do each of these inequalities mean?

Do:

A) means $125$125 is less than or equal to $86$86 - this is not true.

B) means $86$86 is greater than $125$125 - this is not true.

C) means $86$86 is less than $125$125 - this is true

D) means $86$86 is greater than or equal to $125$125 - this is not true.

$125$125 is a larger number than $86$86. In other words, $86$86 is less than $125$125. This means C) $86<125$86<125 is true.

##### Question 3

Tobias has $778$778 songs on his mobile phone. Marge has $525$525 songs on her tablet.

Construct an inequality directly comparing these quantities.

##### Question 4

Ray's account balance is $-\$10$$10. Mohamad's account balance is -\13$$13.

Choose the correct number statement below that represents the relationship between Ray and Mohamad's savings.

A) $-13\ge-10$1310     B) $-10>-13$10>13     C) $-13>-10$13>10     D) $-10\le-13$1013

##### Question 5

Ray is designing a dress pattern using $\frac{3}{5}$35 of a metre of blue fabric and $1$1 metre of  orange fabric.

Construct an inequality directly comparing the amount of blue and orange fabric used.

Think: Which is the bigger number? What side of the inequality sign do we write the bigger number on?

Do: There are two ways we can write this relationship. We can write $\frac{3}{5}<1$35<1 or $1>\frac{3}{5}$1>35.