One-Step Equations Involving Fractions Worksheets - Free Printable

Problem: Solve each one-step equation involving fractions.

We will solve each equation step by step.

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

To isolate \( d \), add \( \frac{5}{2} \) to both sides of the equation:
\[
d - \frac{5}{2} + \frac{5}{2} = 11 + \frac{5}{2}
\]
\[
d = 11 + \frac{5}{2}
\]

Convert 11 to a fraction with a denominator of 2:
\[
11 = \frac{22}{2}
\]
\[
d = \frac{22}{2} + \frac{5}{2} = \frac{27}{2}
\]

So, the solution is:
\[
\boxed{\frac{27}{2}}
\]

---

#### 2) \( \frac{1}{5}r = -\frac{8}{5} \)

To isolate \( r \), multiply both sides of the equation by 5:
\[
5 \cdot \frac{1}{5}r = 5 \cdot \left(-\frac{8}{5}\right)
\]
\[
r = -8
\]

So, the solution is:
\[
\boxed{-8}
\]

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

To isolate \( p \), subtract \( \frac{1}{3} \) from both sides of the equation:
\[
p = -\frac{8}{9} - \frac{1}{3}
\]

Convert \( \frac{1}{3} \) to a fraction with a denominator of 9:
\[
\frac{1}{3} = \frac{3}{9}
\]
\[
p = -\frac{8}{9} - \frac{3}{9} = -\frac{11}{9}
\]

So, the solution is:
\[
\boxed{-\frac{11}{9}}
\]

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#### 4) \( -\frac{4}{5} = \frac{c}{-\frac{6}{7}} \)

To isolate \( c \), multiply both sides of the equation by \( -\frac{6}{7} \):
\[
c = -\frac{4}{5} \cdot \left(-\frac{6}{7}\right)
\]

Multiply the numerators and denominators:
\[
c = \frac{4 \cdot 6}{5 \cdot 7} = \frac{24}{35}
\]

So, the solution is:
\[
\boxed{\frac{24}{35}}
\]

---

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

To isolate \( t \), divide both sides of the equation by \( -\frac{3}{7} \). Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
t = -12 \div \left(-\frac{3}{7}\right) = -12 \cdot \left(-\frac{7}{3}\right)
\]

Multiply the numbers:
\[
t = \frac{12 \cdot 7}{3} = \frac{84}{3} = 28
\]

So, the solution is:
\[
\boxed{28}
\]

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

To isolate \( q \), add \( \frac{2}{3} \) to both sides of the equation:
\[
q = \frac{5}{3} + \frac{2}{3}
\]

Add the fractions:
\[
q = \frac{5 + 2}{3} = \frac{7}{3}
\]

So, the solution is:
\[
\boxed{\frac{7}{3}}
\]

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

To isolate \( s \), multiply both sides of the equation by \( \frac{1}{9} \):
\[
s = 9 \cdot \frac{1}{9}
\]

Simplify:
\[
s = 1
\]

So, the solution is:
\[
\boxed{1}
\]

---

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

To isolate \( a \), subtract \( \frac{3}{4} \) from both sides of the equation:
\[
a = \frac{1}{2} - \frac{3}{4}
\]

Convert \( \frac{1}{2} \) to a fraction with a denominator of 4:
\[
\frac{1}{2} = \frac{2}{4}
\]
\[
a = \frac{2}{4} - \frac{3}{4} = -\frac{1}{4}
\]

So, the solution is:
\[
\boxed{-\frac{1}{4}}
\]

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Final Answers:

\[
\boxed{\frac{27}{2}, -8, -\frac{11}{9}, \frac{24}{35}, 28, \frac{7}{3}, 1, -\frac{1}{4}}
\]