Integers and their opposites
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.
State the number that has been marked.
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.
On the number line, mark the opposite of the number $8$8.
On the number line, now mark the opposite of $-8$−8.