Add Subtract Multiply Divide Rational Numbers Review - Free Printable

Sure! Let’s solve each problem step by step. The worksheet is titled “Add, Subtract, Multiply, Divide Rational Numbers,” and you’re asked to evaluate expressions without calculators.

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## Part 1: Evaluate each expression (Addition/Subtraction)

1) (-7) + (-4) + 7

→ Add the negatives first: -7 + (-4) = -11
→ Then add 7: -11 + 7 = -4

✔ Answer: -4

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2) (-4) + 8 - (-2)

→ Subtracting a negative is adding: -(-2) = +2
→ So: -4 + 8 + 2 = 4 + 2 = 6

✔ Answer: 6

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3) (-1) - (-4) - (-3)

→ Subtracting negatives becomes addition:
→ -1 + 4 + 3 = 3 + 3 = 6

✔ Answer: 6

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4) (-1) - 4 + 6

→ Left to right: -1 - 4 = -5
→ -5 + 6 = 1

✔ Answer: 1

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## Part 2: Find each product (Multiplication)

5) 7 × (-6) × 6

→ First: 7 × (-6) = -42
→ Then: -42 × 6 = -252

✔ Answer: -252

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6) -10 × (-9) × (-1)

→ Multiply two negatives first: (-10) × (-9) = 90
→ Then: 90 × (-1) = -90

✔ Answer: -90

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7) -7 × 6 × (-8)

→ First: -7 × 6 = -42
→ Then: -42 × (-8) = +336 (negative × negative = positive)

✔ Answer: 336

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8) -3 × (-2) × (-6)

→ First: -3 × (-2) = 6
→ Then: 6 × (-6) = -36

✔ Answer: -36

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9) -5/3 × (-3/4)

→ Multiply numerators: (-5) × (-3) = 15
→ Multiply denominators: 3 × 4 = 12
→ Result: 15/12 → simplify by dividing numerator and denominator by 3 → 5/4

✔ Answer: 5/4

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10) -7/4 × 1/2

→ Multiply numerators: -7 × 1 = -7
→ Multiply denominators: 4 × 2 = 8
→ Result: -7/8

✔ Answer: -7/8

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## Part 3: Find each quotient (Division)

11) 7 ÷ (-1)

→ Positive divided by negative = negative → -7

✔ Answer: -7

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12) 6 ÷ 3

→ Simple division: 2

✔ Answer: 2

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13) -6 ÷ 6

→ Negative divided by positive = negative → -1

✔ Answer: -1

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14) -45 ÷ 9

→ Negative divided by positive = negative → -5

✔ Answer: -5

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15) (-3/4) ÷ (5/8)

→ Dividing fractions: multiply by reciprocal
→ (-3/4) × (8/5)
→ Multiply numerators: -3 × 8 = -24
→ Multiply denominators: 4 × 5 = 20
→ Result: -24/20 → simplify by dividing by 4 → -6/5

✔ Answer: -6/5

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16) (-1/5) ÷ (-6/5)

→ Dividing fractions: multiply by reciprocal
→ (-1/5) × (5/-6) → Wait — actually, reciprocal of -6/5 is -5/6? Let's be careful:

Actually:
Reciprocal of -6/5 is -5/6? No — reciprocal means flip numerator and denominator, so reciprocal of -6/5 is -5/6? Actually, no:

Wait — let's do it properly:

Dividing:
(-1/5) ÷ (-6/5) = (-1/5) × (5/-6) ??

No — reciprocal of -6/5 is -5/6? Actually, yes — because flipping -6/5 gives -5/6.

But better to think:
(-1/5) × (5/-6) → but that’s incorrect.

Correct:
Reciprocal of -6/5 is -5/6? Actually, no — reciprocal of a/b is b/a, regardless of sign.

So reciprocal of -6/5 is -5/6? Let’s check:
(-6/5) × (-5/6) = (+30/30) = 1 → yes, correct.

So:
(-1/5) × (-5/6) = ?

Multiply:
Numerators: (-1) × (-5) = 5
Denominators: 5 × 6 = 30
→ 5/30 = 1/6

✔ Answer: 1/6

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## ✔ Final Answers Summary:

Part 1:
1) -4
2) 6
3) 6
4) 1

Part 2:
5) -252
6) -90
7) 336
8) -36
9) 5/4
10) -7/8

Part 3:
11) -7
12) 2
13) -1
14) -5
15) -6/5
16) 1/6

Let me know if you’d like to see any step explained in more detail!