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Given an equation of the form $a/b=c$, how do you move $a$, the numerator, over to the other side so that you get $b =c?$ (where $?$ denotes my ignorance of what the right side should look like).

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3 Answers 3

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$$\begin{align*} a/b &= c\\ a &= bc\\ b &= a/c \end{align*}$$

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I know this has been answered but here is it worded. You multiply the denominator out by multiplying both sides so: a/b = c becomes a/bb = cb. As you are multiplying the fraction by the denominator the denominator and the multiplier cancel out and you are left with a = bc. You cannot get rid of a letter but if you wanted b on one side then you would simply move c, to do this you factorise so its a = b(c). You then divide both sides by c, so then a/c = (b(c))/c. Then the c on the numerator and denominator cancel out so you will be left with a/c = b or rearrange to b = a/c.

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$$ \begin{align} \frac{a}{b} & = c \\ \\ b \cdot \frac{a}{b} & = c \cdot b \\ \require{cancel} \\ \cancel{b} \cdot \frac{a}{\cancel{b}} & = c \cdot b \\ \\ a & = cb \\ \\ \frac{a}{c} & = \frac{cb}{c} \\ \\ \frac{a}{c} & = \frac{\cancel{c}b}{\cancel{c}} \\ \\ \frac{a}{c} & = b \end{align} $$

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