Positive & Negative Rational Number Operations — Practice
Negative numbers are directions, not just "less than nothing". Subtraction is adding the opposite, and sign rules come from patterns you can see.
What these questions cover
These questions use 3 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
Problem 1
Compute -7 + 4.
Worked answer
-3
-7 + 4 = -3
Problem 2
Compute 5 + (-12).
Worked answer
-7
Start at 5, walk 12 left
5 - 12 = -7
Problem 3
Compute 3 - (-8).
Worked answer
11
3 - (-8) = 3 + 8
= 11
Problem 4
Compute (-6) × 7.
Worked answer
-42
6 × 7 = 42
Different signs, so -42.
Problem 5
Compute (-48) ÷ (-6).
Worked answer
8
48 ÷ 6 = 8
Same signs, so +8.
Problem 6
Compute -9 - (-4) + (-6).
Worked answer
-11
-9 + 4 + (-6)
-9 + 4 = -5
-5 + (-6) = -11
Problem 7
Compute (-3)2.
Worked answer
9
(-3)(-3) = 9
Same signs, positive.
Problem 8
Compute -32.
Worked answer
-9
-32 = -(32) = -(9) = -9
The minus sign waits outside the exponent.
Problem 9
Compute (-2)(-3)(-5).
Worked answer
-30
2 × 3 × 5 = 30
Three negatives — an odd count — so the answer is -30.
Problem 10
Compute -23 × 94.
Worked answer
-3/2
One negative, so the answer is negative
23 × 94 = 1812 = 32
Answer: -32
Problem 11
Compute -35 ÷ (-910).
Worked answer
2/3
Same signs, so the answer is positive
35 × 109 = 3045 = 23
Problem 12
The temperature is -4°C at dawn and rises 11° by noon, then falls 6° by night. What is the night temperature?
Worked answer
1
-4 + 11 = 7
7 - 6 = 1
It is 1°C at night.
Problem 13
Compute -23 + (-4)2 - (-5).
Worked answer
13
-23 = -(8) = -8 — no parentheses, so the sign stays outside
(-4)2 = 16 — two negatives, positive
-(-5) = +5
-8 + 16 + 5 = 13
Problem 14
Compute -24 + 9-3 - 7.
Worked answer
-2
Top: -24 + 9 = -15
-15-3 = 5 — same signs, positive
5 - 7 = -2
Problem 15
A submarine at -180 m rises at 15 m per minute. What is its depth after 7 minutes?
Worked answer
-75
It rises 15 × 7 = 105 m
-180 + 105 = -75
It is 75 m below the surface.
Problem 16
What is the value of (-1)99 + (-1)100?
Worked answer
0
(-1)99 = -1 — odd count of negatives
(-1)100 = 1 — even count
-1 + 1 = 0