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How do you multiply and simplify $\frac{12}{5 x} \times \frac{x^{3}}{12 x}$ $\frac { 12} { 5x } \times \frac { x ^ { 3} } { 12x }$ ?

1 Answer

Mar 4, 2017

$\frac{x}{5}$ $x/5$

Explanation:

Multiply the top and bottom together, so

$\frac{12}{5 x} \times \frac{x^{3}}{12 x} = \frac{12 \times x^{3}}{5 x \times 12 x} = \frac{12 x^{3}}{60 x^{2}}$ $12/(5x)xxx^3/(12x) = (12xxx^3)/(5x xx 12x) = (12x^3)/(60x^2)$

Now we have effectively two fractions, one with numbers and one with $x$ $x$ 's:

$\frac{12 x^{3}}{60 x^{2}} = \frac{12}{60} \times \frac{x^{3}}{x^{2}}$ $(12x^3)/(60x^2) = 12/60 xx x^3/x^2$

The $\frac{12}{60}$ $12/60$ fraction simplifies to $\frac{1}{5}$ $1/5$ because

$12/60 = (12*1)/(12*5) = (cancel(12)*1)/(cancel(12)*5) = 1/5$

and the $x^3/x^2$ fraction, by rules of indices, subtracts the powers, so

$x^3/x^2=x^(3-2)=x^1=x$

The whole thing, then, becomes

$x * 1/5 = x/5$

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