One-Step Equations Involving Fractions Worksheets - Free Printable

Let's solve each one-step equation involving fractions step by step.

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1) d – 5/2 = 11

To isolate d, add 5/2 to both sides:

> d = 11 + 5/2

Convert 11 to a fraction with denominator 2:
> 11 = 22/2

So:
> d = 22/2 + 5/2 = 27/2

✔ Answer: d = 27/2

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2) (1/5)r = 8/5

To isolate r, multiply both sides by the reciprocal of 1/5, which is 5:

> r = (8/5) × 5 = 8

✔ Answer: r = 8

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3) 1/3 + p = 8/9

Subtract 1/3 from both sides:

> p = 8/9 – 1/3

Find common denominator (LCM of 9 and 3 is 9):

> 1/3 = 3/9

So:
> p = 8/9 – 3/9 = 5/9

✔ Answer: p = 5/9

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4) 4/5 = c / (6/7)

This means:
> 4/5 = c ÷ (6/7)

Dividing by a fraction is multiplying by its reciprocal:

> 4/5 = c × (7/6)

Now solve for c by multiplying both sides by 6/7:

> c = (4/5) × (6/7) = (4×6)/(5×7) = 24/35

✔ Answer: c = 24/35

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5) –12 = –(3/7)t

Multiply both sides by –1 to make it easier:

> 12 = (3/7)t

Now multiply both sides by 7/3 (reciprocal of 3/7):

> t = 12 × (7/3) = (12/3) × 7 = 4 × 7 = 28

✔ Answer: t = 28

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6) 5/3 = q – 2/3

Add 2/3 to both sides:

> q = 5/3 + 2/3 = 7/3

✔ Answer: q = 7/3

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7) s / (1/9) = 9

This means:
> s ÷ (1/9) = 9

Dividing by 1/9 is same as multiplying by 9:

> s × 9 = 9

Divide both sides by 9:

> s = 9 ÷ 9 = 1

✔ Answer: s = 1

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8) a + 3/4 = 1/2

Subtract 3/4 from both sides:

> a = 1/2 – 3/4

Common denominator is 4:

> 1/2 = 2/4

So:
> a = 2/4 – 3/4 = –1/4

✔ Answer: a = –1/4

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✔ Final Answers:

1) d = 27/2
2) r = 8
3) p = 5/9
4) c = 24/35
5) t = 28
6) q = 7/3
7) s = 1
8) a = –1/4

Let me know if you’d like these written as mixed numbers or decimals too!