Remember back to the lesson on fractions where we learned about multiplicative inverses of fractions.

**Multiplicative Inverse**: Number when multiplied to another number equals \(\mathit{1}\).

When solving equations where our variable is being multiplied by a fraction, we follow the same steps as when it was a whole number, we multiply both sides by the multiplicative inverse.

Solving for a Variable on One Side Part 5-Multiplication and Division with Fractions

Video Source (10:05 mins) | Transcript

The multiplicative inverse is the opposite of the original fraction, but the sign stays the same:

- \( {\dfrac {2} {5}}\) → \( {\dfrac {5} {2}}\)
- \( {-\dfrac {1}{3}}\) → \(−3\)
- \( {\dfrac {7} {8}}\) → \( {\dfrac {8} {7}} \)

## Additional Resources

- Khan Academy: One-step Multiplication Equations (02:22 mins, Transcript)
- Khan Academy: One-step Multiplication & Division Equations: Fractions & Decimals (07:50 mins, Transcript)
- Khan Academy: Linear Equations 1 (07:27 mins, Transcript)

### Practice Problems

**Solve for the variable:**

- \(-7{\text{M}}=-\dfrac{7}{4}\) (Solution
- \(\dfrac{6}{5}{\text{B}}=3\) (Solution
- \(-\dfrac{2}{3}{\text{g}}=-1\) (Video Solution
- \(-\dfrac{2}{7}=-\dfrac{3}{2}{\text{x}}\) (Solution
- \(4{\text{j}}=\dfrac{3}{2}\) (Solution
- \(-\dfrac{3}{5}=\dfrac{3}{2}{\text{D}}\) (Solution
- \(-\dfrac{{\text{J}}}{3}=-\dfrac{7}{6}\) (Video Solution

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