One-Step Equations Involving Fractions Worksheets - Free Printable

Let’s solve each equation one by one. We’ll isolate the variable (get it alone on one side) using inverse operations — that means if something is added, we subtract; if multiplied, we divide, and so on.

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1)
Equation:
> \( d - \frac{5}{2} = 11 \)

To get \( d \) alone, add \( \frac{5}{2} \) to both sides:

\( d = 11 + \frac{5}{2} \)

Convert 11 to a fraction with denominator 2:
\( 11 = \frac{22}{2} \)

So:
\( d = \frac{22}{2} + \frac{5}{2} = \frac{27}{2} \)

✔ Final answer for #1: \( \boxed{\frac{27}{2}} \)

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2)
Equation:
> \( \frac{1}{5}r = -\frac{8}{5} \)

Multiply both sides by 5 to cancel the denominator:

\( r = -\frac{8}{5} \times 5 = -8 \)

✔ Final answer for #2: \( \boxed{-8} \)

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3)
Equation:
> \( \frac{1}{3} + p = -\frac{8}{9} \)

Subtract \( \frac{1}{3} \) from both sides:

\( p = -\frac{8}{9} - \frac{1}{3} \)

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

So:
\( p = -\frac{8}{9} - \frac{3}{9} = -\frac{11}{9} \)

✔ Final answer for #3: \( \boxed{-\frac{11}{9}} \)

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4)
Equation:
> \( \frac{4}{5} = \frac{c}{\left(\frac{6}{7}\right)} \)

This means: \( \frac{4}{5} = c \div \frac{6}{7} \), which is same as \( \frac{4}{5} = c \times \frac{7}{6} \)

So to solve for \( c \), multiply both sides by reciprocal of \( \frac{7}{6} \), which is \( \frac{6}{7} \):

Wait — actually, let's rewrite clearly:

If \( \frac{4}{5} = \frac{c}{\frac{6}{7}} \), then multiplying both sides by \( \frac{6}{7} \) gives:

\( c = \frac{4}{5} \times \frac{6}{7} = \frac{24}{35} \)

✔ Final answer for #4: \( \boxed{\frac{24}{35}} \)

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5)
Equation:
> \( -12 = -\frac{3}{7}t \)

Divide both sides by \( -\frac{3}{7} \), or multiply by its reciprocal \( -\frac{7}{3} \):

\( t = -12 \times \left(-\frac{7}{3}\right) = \frac{84}{3} = 28 \)

✔ Final answer for #5: \( \boxed{28} \)

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6)
Equation:
> \( \frac{5}{3} = q - \frac{2}{3} \)

Add \( \frac{2}{3} \) to both sides:

\( q = \frac{5}{3} + \frac{2}{3} = \frac{7}{3} \)

✔ Final answer for #6: \( \boxed{\frac{7}{3}} \)

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7)
Equation:
> \( \frac{s}{\left(-\frac{11}{9}\right)} = 9 \)

This means: \( s \div \left(-\frac{11}{9}\right) = 9 \), so multiply both sides by \( -\frac{11}{9} \):

\( s = 9 \times \left(-\frac{11}{9}\right) = -11 \)

✔ Final answer for #7: \( \boxed{-11} \)

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8)
Equation:
> \( a + \frac{3}{4} = \frac{1}{2} \)

Subtract \( \frac{3}{4} \) from both sides:

\( a = \frac{1}{2} - \frac{3}{4} \)

Convert \( \frac{1}{2} \) to fourths: \( \frac{1}{2} = \frac{2}{4} \)

So:
\( a = \frac{2}{4} - \frac{3}{4} = -\frac{1}{4} \)

✔ Final answer for #8: \( \boxed{-\frac{1}{4}} \)

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Final Answer:
1) \( \frac{27}{2} \)
2) \( -8 \)
3) \( -\frac{11}{9} \)
4) \( \frac{24}{35} \)
5) \( 28 \)
6) \( \frac{7}{3} \)
7) \( -11 \)
8) \( -\frac{1}{4} \)