One-Step Equations Involving Fractions Worksheets - Free Printable

Let's solve each of these one-step equations involving fractions step by step.

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1) $ d - \frac{5}{2} = 11 $

To isolate $ d $, add $ \frac{5}{2} $ to both sides:

$$
d = 11 + \frac{5}{2}
$$

Convert 11 to a fraction with denominator 2:

$$
11 = \frac{22}{2}, \quad \text{so} \quad d = \frac{22}{2} + \frac{5}{2} = \frac{27}{2}
$$

✔ Answer: $ d = \frac{27}{2} $

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2) $ \frac{1}{5}r = \frac{8}{5} $

To solve for $ r $, multiply both sides by the reciprocal of $ \frac{1}{5} $, which is 5:

$$
r = \frac{8}{5} \times 5 = 8
$$

✔ Answer: $ r = 8 $

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3) $ \frac{1}{3} + p = \frac{8}{9} $

Subtract $ \frac{1}{3} $ from both sides:

$$
p = \frac{8}{9} - \frac{1}{3}
$$

Convert $ \frac{1}{3} $ to ninths: $ \frac{1}{3} = \frac{3}{9} $

$$
p = \frac{8}{9} - \frac{3}{9} = \frac{5}{9}
$$

✔ Answer: $ p = \frac{5}{9} $

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4) $ \frac{4}{5} = \frac{c}{\left(\frac{6}{7}\right)} $

This means:

$$
\frac{4}{5} = c \div \frac{6}{7} = c \times \frac{7}{6}
$$

Now solve for $ c $:

$$
c = \frac{4}{5} \div \frac{7}{6} = \frac{4}{5} \times \frac{6}{7} = \frac{24}{35}
$$

✔ Answer: $ c = \frac{24}{35} $

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5) $ -12 = -\frac{3}{7}t $

Solve for $ t $ by dividing both sides by $ -\frac{3}{7} $, or multiplying by its reciprocal:

$$
t = -12 \div \left(-\frac{3}{7}\right) = -12 \times \left(-\frac{7}{3}\right)
$$

$$
= 12 \times \frac{7}{3} = \frac{84}{3} = 28
$$

✔ Answer: $ t = 28 $

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6) $ \frac{5}{3} = q - \frac{2}{3} $

Add $ \frac{2}{3} $ to both sides:

$$
q = \frac{5}{3} + \frac{2}{3} = \frac{7}{3}
$$

✔ Answer: $ q = \frac{7}{3} $

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7) $ \frac{s}{\left(-\frac{1}{9}\right)} = 9 $

This means:

$$
s \div \left(-\frac{1}{9}\right) = 9 \quad \Rightarrow \quad s \times (-9) = 9
$$

Now divide both sides by $-9$:

$$
s = \frac{9}{-9} = -1
$$

✔ Answer: $ s = -1 $

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8) $ a + \frac{3}{4} = \frac{1}{2} $

Subtract $ \frac{3}{4} $ from both sides:

$$
a = \frac{1}{2} - \frac{3}{4}
$$

Convert $ \frac{1}{2} $ to fourths: $ \frac{2}{4} $

$$
a = \frac{2}{4} - \frac{3}{4} = -\frac{1}{4}
$$

✔ Answer: $ a = -\frac{1}{4} $

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✔ Final Answers:

1) $ d = \frac{27}{2} $
2) $ r = 8 $
3) $ p = \frac{5}{9} $
4) $ c = \frac{24}{35} $
5) $ t = 28 $
6) $ q = \frac{7}{3} $
7) $ s = -1 $
8) $ a = -\frac{1}{4} $

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