# How do you solve 12/5 = x/6?

Feb 20, 2016

This is the same approach as Simon L but in more detail

$x = 14 \frac{2}{5}$

#### Explanation:

Objective: to end up with $x$ on one side of the equals sign and everything else on the other side.

$\textcolor{b l u e}{\text{Principles behind Simons' short cut method}}$

Simon used the shortcut method. This is based on: if you move something to the other side of the = you reverse 'what it is doing';

So if you had say:$\text{ } x + 3 = 2$ and you wished to move the $+ 3$

When you move the $+ 3$ to the other side it becomes $- 3$

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Suppose you had $x \div 3 = 2$ and you wished to move the $\div 3$ to the others side.

So $x \div 3 = 2 \text{ becomes } x = 2 \times 3$

Another way of writing $x \div 3 \text{ is } \frac{x}{3}$

so $\frac{x}{3} = 2 \text{ becomes } x = 2 \times 3$

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$\textcolor{b l u e}{\text{The first principle method that the short cut method is based on}}$

Given:$\text{ " 12/5" "=" } \frac{x}{6}$

Write as: $\textcolor{b r o w n}{\text{ "12/5" "=" } x \times \frac{1}{6}}$

Multiply both sides by$\text{ } \textcolor{b l u e}{6}$ giving:

$\text{ "color(brown)(12/5 color(blue)(xx6)" "=" } x \times \frac{1}{6} \textcolor{b l u e}{\times 6}$

" "color(brown)((12color(blue)(xx6))/5" "=" "x xx(color(blue)(6))/6)

But $\frac{6}{6} = 1$ giving:

$\text{ "72/5" "=" } x$

$72 \div 5 = 14 \frac{2}{5}$ so we have

$\text{ } \textcolor{red}{x = 14 \frac{2}{5}}$