Multiply and simplify: 10/x * 12/(5x^2)
Understand the Problem
The question asks to multiply and simplify two given fractions. The fractions contain numerical constants and the variable x. We will multiply the numerators and denominators, then simplify by canceling out common factors.
Answer
$\frac{24}{x^3}$
Answer for screen readers
$\frac{24}{x^3}$
Steps to Solve
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Multiply the numerators and denominators Multiply the numerators $10$ and $12$, and multiply the denominators $x$ and $5x^2$: $$ \frac{10}{x} \cdot \frac{12}{5x^2} = \frac{10 \cdot 12}{x \cdot 5x^2} = \frac{120}{5x^3} $$
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Simplify the fraction Divide the numerator and the denominator by their greatest common factor. The greatest common factor of $120$ and $5$ is $5$.
$$ \frac{120}{5x^3} = \frac{120 \div 5}{5x^3 \div 5} = \frac{24}{x^3} $$
$\frac{24}{x^3}$
More Information
The simplified form of $\frac{10}{x} \cdot \frac{12}{5x^2}$ is $\frac{24}{x^3}$.
Tips
A common mistake is not simplifying the fraction completely. For example, stopping at $\frac{120}{5x^3}$ instead of reducing it to $\frac{24}{x^3}$. Another common mistake is incorrectly multiplying the variables in the denominator. Remember that $x \cdot x^2 = x^{1+2} = x^3$.
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