# How do you solve 10/12=x/18?

Feb 17, 2017

$x = 15$

#### Explanation:

You an solve this in two ways: proportionality or just rearranging the equation

Rearranging the equation
You can multiply $\frac{10}{12}$ by 18 to leave x to one side.
$\frac{10}{12} \cdot 18 = x$
$x = 15$

Proportionality
You can work out the proportion between 12 and 18, which will be the same for 10 and $x$.
so $\frac{18}{12} = 1 \frac{1}{2}$
Therefore, if we multiply 10 by $1 \frac{1}{2}$ we get the value of $x$ which is $15$

Feb 17, 2017

$x = 15$

#### Explanation:

Using first principles

Multiply both sides by $\textcolor{red}{18}$

$\textcolor{g r e e n}{\frac{10}{12} \textcolor{red}{\times 18} \text{ " =" } \frac{x}{18} \textcolor{red}{\times 18}}$

$\textcolor{g r e e n}{\frac{10}{12} \textcolor{red}{\times 18} \text{ " =" } x \textcolor{red}{\times} \frac{\textcolor{red}{18}}{18}}$

But $\frac{18}{18} = 1$ so $x \times \frac{18}{18} = x \times 1 = x$ giving:

$\frac{10 \times 18}{12} = x$

Write as $\text{ "x=(10xx18)/12" "=" } \frac{2 \times 5 \times 2 \times 3 \times 3}{3 \times 4}$

$x = \frac{2 \times 2}{4} \times \frac{3}{3} \times 5 \times 3 \text{ " =" } 1 \times 1 \times 15$

........................................................................
or if you prefer:

x= "(cancel(2)^1xx5xxcancel(2)^1xx3xxcancel(3)^1)/(cancel(3)^1xxcancel(4)^1) = 5xx3=15