 Hong Kong
Stage 1 - Stage 3

# Integers and their opposites

Lesson

In this lesson we're going to use the number line to find the opposite of a number. Let's first review how we can read values of number lines.

## Representing values on a number line

The number line can be used to show both positive and negative numbers. The numbers don't always have to increase by $1$1's but they do have to have a common scale.

For example this line goes up in $3$3's: Sometimes you need to identify the scale used based on just a few markings.

Let's have a look at an example.

#### Example 1

Deduce the place on the number line indicated by the $A$A. Think: First we have to determine the scale. We can see that between $0$0 and $4$4 there is just one mark, indicating that the scale is going up by $2$2's.

Do: The $A$A is the next mark after $4$4, so the $A$A is at point $4+2=6$4+2=6

Once we know the scale we can identify and mark on the line other points of interest, and also deduce locations on the line.

## Numbers and their opposites

Two numbers are opposites if they are the same distance from $0$0, but on opposite sides (i.e. one is negative and one is positive). The numbers $6$6 and $-6$6 are the same distance from $0$0, so they are opposites.

This applet lets you visualise the idea of opposites. Slide the red point and see its opposite move.

#### Example 2

Deduce the place on the number line indicated by the $A$A. Think: We can immediately notice that $A$A and $4$4 are the same distance from $0$0, but $A$A is on the negative side. This means that the value of $A$A is the opposite of $4$4.

Do: The opposite of $4$4 is $-4$4, so $A$A represents the number $-4$4.

#### Example 3

Mark on the number line the opposites of the values marked. Think: The opposite of $-1$1 is $1$1 and the opposite of $3$3 is $-3$3. So, we need to mark on the number line $1$1 and $-3$3. To be able to identify equal distances from the point $0$0, we need to locate $0$0 first.

Do: The scale is going up by $1$1's, so the $0$0 can be found. Once the $0$0 is found, we can mark the opposites easily. #### Worked Examples

##### Question 1

Consider the number marked on the number line.

1. State the number that has been marked.

2. Numbers are opposite one another if they are the same distance from $0$0, and on opposite sides of $0$0. What number is the opposite of $4$4?

##### question 2

Numbers are opposite one another if they are the same distance from $0$0 and on opposite sides of $0$0. On the number line, mark the number $7$7 and the number that is the opposite of $7$7.

##### question 3

Numbers are opposite to one another if they are the same distance from $0$0, and on opposite sides of $0$0.

1. On the number line, mark the opposite of the number $8$8.

2. On the number line, now mark the opposite of $-8$8.