Skill: Solve equations with fractional coefficients informally

Explanation and Free Practice Resources

An equation with a fractional coefficient represents a multiplicative relationship in which a fraction of an unknown quantity equals a known amount, such as $\frac{3}{4}x=9$ . The learner reasons with inverse operations—finding the whole quantity represented by the fractional part or multiplying by the reciprocal—while preserving equality and checking the solution by substitution; the focus is on simple positive rational coefficients and solutions, not generalized symbolic equations or formal denominator-clearing techniques.

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Detailed Explanation: Solve equations with fractional coefficients informally

A fractional coefficient tells you that a fraction of the unknown number equals a known amount.

For example:

\frac{3}{4}x=9

This means three-fourths of $x$ is 9. We want to find the whole number, $x$ .

Use the inverse operation. Since $x$ is multiplied by $\frac{3}{4}$ , multiply both sides by its reciprocal, $\frac{4}{3}$ :

\frac{4}{3}\cdot\frac{3}{4}x=9\cdot\frac{4}{3}

On the left, $\frac{4}{3}\cdot\frac{3}{4}=1$ , so only $x$ remains:

x=9\cdot\frac{4}{3}

Calculate:

x=12

Check the solution by substituting $12$ for $x$ in the original equation:

\frac{3}{4}(12)=9

Since $\frac{3}{4}$ of $12$ is $9$ , the solution is correct.

\boxed{x=12}

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