Adjacent signs
Just Give Me a Sign
In some questions that involve negative numbers, you'll see that two operators, or mathematical signs, might be written together.
There are some rules to follow to make sure you always use the right operation:
- A negative sign and a positive sign [$+$+($-$−) or $-$−($+$+)] becomes a negative [$-]$−]
- Two negatives [$-$−($-$−)] become a positive [$+]$+]
Examples
question 1
Evaluate: $4-\left(-5\right)$4−(−5)
Think: Two negative signs become a positive.
Do:
| $4-\left(-5\right)$4−(−5) | $=$= | $4+5$4+5 |
| $=$= | $9$9 |
question 2
Evaluate: $-9+\left(-6\right)$−9+(−6)
Think: A positive and a negative sign together become a negative.
Do:
| $-9+\left(-6\right)$−9+(−6) | $=$= | $-9-6$−9−6 |
| $=$= | $-15$−15 |
question 3
Evaluate: $4+\left(-10\right)$4+(−10)
Think: A positive and a negative sign together become a negative.
Do:
| $4+\left(-10\right)$4+(−10) | $=$= | $4-10$4−10 |
| $=$= | $-6$−6 |
The two negative signs have to be right next to each other.
$-4-8$−4−8 means "$-4$−4 minus $8$8." This does not become a positive.
$-4-\left(-8\right)$−4−(−8) means "$-4$−4 minus $-8$−8" This becomes "$-4$−4 plus $8$8." In this case, the operators changed.
The same rules apply, even when there are more than $2$2 numbers.
Examples
question 4
Evaluate: $18+\left(-7\right)-\left(-12\right)$18+(−7)−(−12)
Think: A positive and a negative sign together become a negative and two negative signs together become a positive.
Do:
| $18+\left(-7\right)-\left(-12\right)$18+(−7)−(−12) | $=$= | $18-7+12$18−7+12 |
| $=$= | $23$23 |
QUeSTION 5
Evaluate: $-7-\left(-2\right)-\left(-6\right)$−7−(−2)−(−6)
QUESTION 6
Evaluate: $9+\left(-8\right)$9+(−8)
QUESTION 7
Evaluate: $-14-\left(-16\right)$−14−(−16)