One-Step Equations With Fractions - Kuta Software - Free Printable

Let's solve each of these one-step equations with fractions step by step. These are simple linear equations where you need to isolate the variable using inverse operations.

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1) $ 5\frac{1}{2} + p = 6 $

Convert mixed number to improper fraction:
$ 5\frac{1}{2} = \frac{11}{2} $

So:
$$
\frac{11}{2} + p = 6
$$

Subtract $ \frac{11}{2} $ from both sides:
$$
p = 6 - \frac{11}{2} = \frac{12}{2} - \frac{11}{2} = \frac{1}{2}
$$

✔ Answer: $ p = \frac{1}{2} $

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2) $ m - 1\frac{1}{2} = -\frac{5}{4} $

Convert $ 1\frac{1}{2} = \frac{3}{2} $

So:
$$
m - \frac{3}{2} = -\frac{5}{4}
$$

Add $ \frac{3}{2} $ to both sides:
$$
m = -\frac{5}{4} + \frac{3}{2} = -\frac{5}{4} + \frac{6}{4} = \frac{1}{4}
$$

✔ Answer: $ m = \frac{1}{4} $

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3) $ -\frac{3}{4}b = 2 $

Divide both sides by $ -\frac{3}{4} $, or multiply by its reciprocal:

$$
b = 2 \div \left(-\frac{3}{4}\right) = 2 \times \left(-\frac{4}{3}\right) = -\frac{8}{3}
$$

✔ Answer: $ b = -\frac{8}{3} $ or $ -2\frac{2}{3} $

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4) $ x - 3 = -5\frac{1}{2} $

Convert $ -5\frac{1}{2} = -\frac{11}{2} $

So:
$$
x - 3 = -\frac{11}{2}
$$

Add 3 to both sides:
$$
x = -\frac{11}{2} + 3 = -\frac{11}{2} + \frac{6}{2} = -\frac{5}{2}
$$

✔ Answer: $ x = -\frac{5}{2} $ or $ -2\frac{1}{2} $

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5) $ x - \frac{1}{2} = 1\frac{1}{4} $

Convert $ 1\frac{1}{4} = \frac{5}{4} $

So:
$$
x - \frac{1}{2} = \frac{5}{4}
$$

Add $ \frac{1}{2} $ to both sides:
$$
x = \frac{5}{4} + \frac{1}{2} = \frac{5}{4} + \frac{2}{4} = \frac{7}{4}
$$

✔ Answer: $ x = \frac{7}{4} $ or $ 1\frac{3}{4} $

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6) $ x - 1\frac{1}{4} = -6 $

Convert $ 1\frac{1}{4} = \frac{5}{4} $

So:
$$
x - \frac{5}{4} = -6
$$

Add $ \frac{5}{4} $ to both sides:
$$
x = -6 + \frac{5}{4} = -\frac{24}{4} + \frac{5}{4} = -\frac{19}{4}
$$

✔ Answer: $ x = -\frac{19}{4} $ or $ -4\frac{3}{4} $

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7) $ 2\frac{1}{10}n = 1\frac{1}{6} $

Convert:
- $ 2\frac{1}{10} = \frac{21}{10} $
- $ 1\frac{1}{6} = \frac{7}{6} $

So:
$$
\frac{21}{10}n = \frac{7}{6}
$$

Divide both sides by $ \frac{21}{10} $:
$$
n = \frac{7}{6} \div \frac{21}{10} = \frac{7}{6} \times \frac{10}{21} = \frac{70}{126}
$$

Simplify:
$$
\frac{70}{126} = \frac{10}{18} = \frac{5}{9}
$$

✔ Answer: $ n = \frac{5}{9} $

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8) $ 9\frac{1}{3} = \frac{2}{3}n $

Convert $ 9\frac{1}{3} = \frac{28}{3} $

So:
$$
\frac{28}{3} = \frac{2}{3}n
$$

Divide both sides by $ \frac{2}{3} $:
$$
n = \frac{28}{3} \div \frac{2}{3} = \frac{28}{3} \times \frac{3}{2} = \frac{28}{2} = 14
$$

✔ Answer: $ n = 14 $

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9) $ 5\frac{2}{7} + k = 2\frac{27}{70} $

Convert:
- $ 5\frac{2}{7} = \frac{37}{7} $
- $ 2\frac{27}{70} = \frac{167}{70} $

So:
$$
\frac{37}{7} + k = \frac{167}{70}
$$

Subtract $ \frac{37}{7} $ from both sides:
First, convert $ \frac{37}{7} = \frac{370}{70} $

$$
k = \frac{167}{70} - \frac{370}{70} = \frac{-203}{70}
$$

Simplify:
$$
\frac{-203}{70} = -\frac{29}{10} = -2\frac{9}{10}
$$

✔ Answer: $ k = -\frac{29}{10} $ or $ -2\frac{9}{10} $

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10) $ 2\frac{5}{12} = -3\frac{1}{4} + k $

Convert:
- $ 2\frac{5}{12} = \frac{29}{12} $
- $ -3\frac{1}{4} = -\frac{13}{4} $

So:
$$
\frac{29}{12} = -\frac{13}{4} + k
$$

Add $ \frac{13}{4} $ to both sides:
Convert $ \frac{13}{4} = \frac{39}{12} $

$$
k = \frac{29}{12} + \frac{39}{12} = \frac{68}{12} = \frac{17}{3}
$$

✔ Answer: $ k = \frac{17}{3} $ or $ 5\frac{2}{3} $

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✔ Final Answers:

1) $ p = \frac{1}{2} $
2) $ m = \frac{1}{4} $
3) $ b = -\frac{8}{3} $
4) $ x = -\frac{5}{2} $
5) $ x = \frac{7}{4} $
6) $ x = -\frac{19}{4} $
7) $ n = \frac{5}{9} $
8) $ n = 14 $
9) $ k = -\frac{29}{10} $
10) $ k = \frac{17}{3} $

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