Distributive Property with Fractions - 2 step worksheet | Live ... - Free Printable

Let’s solve each equation step by step. We’ll isolate x by undoing the operations around it — first multiply both sides to get rid of the fraction, then subtract or add to get x alone.

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1) ⅓(x + 4) = 12

Multiply both sides by 3:
x + 4 = 36
Subtract 4:
x = 32

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2) ¼(2 - x) = 6

Multiply both sides by 4:
2 - x = 24
Subtract 2:
-x = 22
Multiply by -1:
x = -22

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3) ½(x + 10) = 20

Multiply both sides by 2:
x + 10 = 40
Subtract 10:
x = 30

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4) ⅛(x + 1) = 4

Multiply both sides by 8:
x + 1 = 32
Subtract 1:
x = 31

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5) ⅕(x - 10) = 10

Multiply both sides by 5:
x - 10 = 50
Add 10:
x = 60

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6) ½(x + 5) = 4

Multiply both sides by 2:
x + 5 = 8
Subtract 5:
x = 3

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7) ⅓(x - 12) = 4

Multiply both sides by 3:
x - 12 = 12
Add 12:
x = 24

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8) ⅙(x + 5) = 3

Multiply both sides by 6:
x + 5 = 18
Subtract 5:
x = 13

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9) ¹/₇(x - 2) = 2

Multiply both sides by 7:
x - 2 = 14
Add 2:
x = 16

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10) ¼(x + 3) = 8

Multiply both sides by 4:
x + 3 = 32
Subtract 3:
x = 29

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11) ¼(x + 7) = 5

Multiply both sides by 4:
x + 7 = 20
Subtract 7:
x = 13

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12) ⅕(x - 11) = 3

Multiply both sides by 5:
x - 11 = 15
Add 11:
x = 26

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Final Answer:
1) x = 32
2) x = -22
3) x = 30
4) x = 31
5) x = 60
6) x = 3
7) x = 24
8) x = 13
9) x = 16
10) x = 29
11) x = 13
12) x = 26