How do you solve $\frac{10}{k} = \frac{8}{4}$ $10/k=8/4$ ?

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How do you solve $\frac{10}{k} = \frac{8}{4}$ $10/k=8/4$ ?

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Answer 1 · 2016-09-03T18:58:50

$k = 5$ $k=5$

Explanation:

We have one fraction equal to another. In this situation we can $cross-multiply$ $color(blue)"cross-multiply"$ to solve.

$\Rightarrow \frac{10}{k} = \frac{8}{4}$ $rArrcolor(blue)(10)/color(red)(k)=color(red)(8)/color(blue)(4)$

Now cross-multiply(X) the values on either end of an 'imaginary' cross and equate them. That is multiply the $blue$ $color(blue)"blue"$ values together and the $red$ $color(red)"red"$ values together and equate them.

$\Rightarrow 8 k = (10 \times 4) \Rightarrow 8 k = 40$ $rArrcolor(red)(8k)=(color(blue)(10)xxcolor(blue)(4))rArr8k=40$

now divide both sides by 8 to solve for k.

$rArr(cancel(8)^1 k)/cancel(8)^1=(cancel(40)^5)/cancel(8)^1rArrk=5$

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