Module 1 · Numbers and number sets · Lesson 3 of 39
Opposites and absolute value
Use the number line to find a number's opposite and its distance from 0.
In this lesson · about 10 minutes
- Find the opposite of a positive or negative number
- Find the absolute value of a number
- Explain both ideas with a number line
On a number line, 0 sits in the middle. Numbers to the right are positive and numbers to the left are negative. The numbers 1 and −1 are the same distance from 0, on opposite sides.
Opposites
Two numbers are opposites when they are the same distance from 0 on opposite sides: 3 and −3, or −10 and 10. To find the opposite, change the sign. The opposite of a negative number is positive: −(−10) = 10, because the two negative signs cancel. 0 is its own opposite.
Absolute value
The absolute value of a number is its distance from 0. We write it with bars: |−3| = 3, because −3 is 3 units from 0. Distances are never negative, so absolute value turns every number into a positive number (and 0 into 0).
| Number | Opposite | Absolute value |
|---|---|---|
| 2 | −2 | 2 |
| −5 | 5 | 5 |
| 0 | 0 | 0 |
Try it · interactive
Explore the number line
Start at a number and move. Try starting at 4 and subtracting 8: where do you land, and how far is it from 0?
−3 + 5 = 2
Move 5 to the right.
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Key terms
Say the meaning to yourself, then tap a card to check.
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