Grade 8 Distributive Property Worksheets 2024 - Free Printable

Let's go through this Distributive Property Worksheet step by step.

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Part 1: Can you simplify using the distributive property?

The distributive property states:

> $ a(b + c) = ab + ac $

It applies when a number or variable is multiplied by a sum or difference inside parentheses. It does not apply to expressions involving only addition, subtraction, or division without multiplication across terms.

We'll evaluate each expression.

#### Left Column:

| Expression | Distrib. Prop.? (Yes/No) | Reason |
|--------------------|--------------------------|--------|
| $ 3(4 + y) $ | Yes | Multiplication over addition → distribute 3 to both 4 and y |
| $ 7(x ÷ 2) $ | No | This is not a sum/difference in parentheses; it's just division. Distributive property doesn't apply here. You can write it as $ \frac{7x}{2} $, but that’s simplification, not distribution. |
| $ (z + 6) - 7 $ | No | No multiplication involved. Just subtraction of constants. |
| $ (c - 2) \cdot 6 $ | Yes | Multiplication over subtraction → distribute 6 to both c and -2 |

#### Right Column:

| Expression | Distrib. Prop.? (Yes/No) | Reason |
|----------------------|--------------------------|--------|
| $ c - 2 \cdot 6 $ | No | Order of operations: multiplication first. So $ 2 \cdot 6 = 12 $, then $ c - 12 $. No distribution needed or possible. |
| $ 5(5 - 5h) $ | Yes | Multiply 5 by both 5 and -5h |
| $ 9(a + k + g) $ | Yes | Multiply 9 by each term inside parentheses |
| $ 9 + (a + k + g) $ | No | Addition outside the parentheses — no multiplication involved. Cannot use distributive property. |

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✔ Part 1 Answers:

| Expression | Distrib. Prop.? |
|--------------------|-----------------|
| $ 3(4 + y) $ | Yes |
| $ 7(x ÷ 2) $ | No |
| $ (z + 6) - 7 $ | No |
| $ (c - 2) \cdot 6 $ | Yes |
| $ c - 2 \cdot 6 $ | No |
| $ 5(5 - 5h) $ | Yes |
| $ 9(a + k + g) $ | Yes |
| $ 9 + (a + k + g) $ | No |

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Part 2: Simplify using the distributive property

We now simplify each expression.

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a. $ 9(3 + 4) $
= $ 9 \cdot 3 + 9 \cdot 4 $
= $ 27 + 36 $
= 63

✔ Answer: 63

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b. $ (6 - 2) \cdot 3 $
First simplify inside: $ 6 - 2 = 4 $, then $ 4 \cdot 3 = 12 $
But if we use distributive property:
= $ 6 \cdot 3 - 2 \cdot 3 $
= $ 18 - 6 $
= 12

✔ Answer: 12

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c. $ 7 \cdot (6 + 5 - 8) $
Simplify inside: $ 6 + 5 - 8 = 3 $, so $ 7 \cdot 3 = 21 $
Or distribute:
= $ 7 \cdot 6 + 7 \cdot 5 - 7 \cdot 8 $
= $ 42 + 35 - 56 $
= $ 77 - 56 = 21 $

✔ Answer: 21

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d. $ (7 + y) \cdot 2 $
= $ 7 \cdot 2 + y \cdot 2 $
= $ 14 + 2y $

✔ Answer: $ 14 + 2y $

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e. $ 4(5 + 3g) $
= $ 4 \cdot 5 + 4 \cdot 3g $
= $ 20 + 12g $

✔ Answer: $ 20 + 12g $

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f. $ 6(4 - w) $
= $ 6 \cdot 4 - 6 \cdot w $
= $ 24 - 6w $

✔ Answer: $ 24 - 6w $

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g. $ (3f - 6) \cdot 9 $
= $ 3f \cdot 9 - 6 \cdot 9 $
= $ 27f - 54 $

✔ Answer: $ 27f - 54 $

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h. $ (9 + 8a - 4r) \cdot 4 $
= $ 9 \cdot 4 + 8a \cdot 4 - 4r \cdot 4 $
= $ 36 + 32a - 16r $

✔ Answer: $ 36 + 32a - 16r $

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i. $ 7 \cdot (3 - 12v) $
= $ 7 \cdot 3 - 7 \cdot 12v $
= $ 21 - 84v $

✔ Answer: $ 21 - 84v $

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Now, fractions and decimals:

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j. $ 4.6(3x + 2) $
= $ 4.6 \cdot 3x + 4.6 \cdot 2 $
= $ 13.8x + 9.2 $

✔ Answer: $ 13.8x + 9.2 $

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k. $ \frac{1}{2}(10 - 14h) $
= $ \frac{1}{2} \cdot 10 - \frac{1}{2} \cdot 14h $
= $ 5 - 7h $

✔ Answer: $ 5 - 7h $

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l. $ \frac{1}{3}\left(\frac{1}{2}n + \frac{3}{4}\right) $
Distribute $ \frac{1}{3} $ to each term:

= $ \frac{1}{3} \cdot \frac{1}{2}n + \frac{1}{3} \cdot \frac{3}{4} $
= $ \frac{1}{6}n + \frac{3}{12} $
= $ \frac{1}{6}n + \frac{1}{4} $

✔ Answer: $ \frac{1}{6}n + \frac{1}{4} $

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✔ Final Answers for Part 2:

| Expression | Simplified Form |
|------------------------------|-------------------------------|
| a. $ 9(3 + 4) $ | 63 |
| b. $ (6 - 2) \cdot 3 $ | 12 |
| c. $ 7 \cdot (6 + 5 - 8) $ | 21 |
| d. $ (7 + y) \cdot 2 $ | $ 14 + 2y $ |
| e. $ 4(5 + 3g) $ | $ 20 + 12g $ |
| f. $ 6(4 - w) $ | $ 24 - 6w $ |
| g. $ (3f - 6) \cdot 9 $ | $ 27f - 54 $ |
| h. $ (9 + 8a - 4r) \cdot 4 $| $ 36 + 32a - 16r $ |
| i. $ 7 \cdot (3 - 12v) $ | $ 21 - 84v $ |
| j. $ 4.6(3x + 2) $ | $ 13.8x + 9.2 $ |
| k. $ \frac{1}{2}(10 - 14h) $| $ 5 - 7h $ |
| l. $ \frac{1}{3}\left(\frac{1}{2}n + \frac{3}{4}\right) $ | $ \frac{1}{6}n + \frac{1}{4} $ |

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📌 Summary:

- The distributive property applies only when a number is being multiplied by a sum or difference in parentheses.
- Always multiply the outer term by each term inside the parentheses.
- Be careful with signs and order of operations.
- Fractions and decimals follow the same rules.

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