In Grade 6 you met opposites: $3$ and $-3$ are the same distance from $0$, on opposite sides. This lesson is about what happens when you add them. It is the key to adding any signed numbers.
Key idea
A number plus its opposite is zero: $a + (-a) = 0$. A $+1$ and a $-1$ together make a zero pair.
Why it works
Adding a positive number moves you right on the number line; adding a negative number moves you left. Start at $0$, move 5 right, then 5 left: you are back at $0$. With money it is the same: earn \$5, spend \$5, and you have the same amount as before.
Worked examples
Worked example: A number and its opposite
Find $-8 + 8$.
- $-8$ and $8$ are opposites.
- Opposites add to $0$.
Answer: $0$
Worked example: Spotting a zero pair
Find $6 + (-9) + (-6)$.
- $6$ and $-6$ are opposites, so together they make $0$.
- What is left is $-9$.
Answer: $-9$
Worked example: Counters
A bag holds 7 positive counters and 4 negative counters. What number does it show?
- Match each negative counter with a positive one: 4 zero pairs, worth $0$.
- 3 positive counters are left over, so the bag shows $3$.
Answer: $3$
This is why the number of counters can change while the value stays the same: adding a zero pair (one $+1$ and one $-1$) adds nothing.