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Multiply. Simplify your answer. $\newline$ $\frac{13w^2x}{18x^2} \times 10wx$

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Multiply and divide rational expressions

Full solution

Q. Multiply. Simplify your answer.

\newline

\frac{13w^2x}{18x^2} \times 10wx

Factor out common terms: Write down the multiplication problem and factor out any common terms if possible. $\newline$ We have $(\frac{13w^2x}{18x^2}) \times (10wx)$ . First, we can factor out the common terms in the numerators and denominators.
Cancel out x terms: Cancel out the common x terms from the numerator and denominator. The $x$ in the numerator of the first fraction and one $x$ from the $x^2$ in the denominator of the first fraction cancel out, leaving us with $(\frac{13w^2}{18x}) \times (10wx)$ .
Cancel out w terms: Cancel out the common w terms from the numerator and denominator. $\newline$ The $w$ in the numerator of the second fraction and one $w$ from the $w^2$ in the numerator of the first fraction cancel out, leaving us with $(\frac{13w}{18x}) \times (10x)$ .
Multiply numerators and denominators: Multiply the remaining terms in the numerators and denominators. $\newline$ Now we multiply the numerators together and the denominators together: $(13w \times 10x) / (18x)$ .
Simplify numerator multiplication: Simplify the multiplication of the numerators. Multiplying the numerators gives us $130wx^2$ .
Simplify denominator multiplication: Simplify the multiplication of the denominators. $\newline$ Since there is only one term in the denominator, it remains $18x$ .
Cancel out x terms: Cancel out the common x terms from the numerator and denominator. The $x$ in the numerator and the $x$ in the denominator cancel out, leaving us with $\frac{130w}{18}$ .
Simplify fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor if possible. $\newline$ The greatest common divisor of $130$ and $18$ is $2$ . Dividing both by $2$ gives us $\frac{65w}{9}$ .

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