# One-half of a number is one-fourth. How do you find the number?

Nov 26, 2016

Rather than just do the calculation I have given a lot of guidance as to how to go about the process.

$x = \frac{1}{2}$

#### Explanation:

Breaking the question down into its component parts:

One-half a number : -> 1/2xx?

is: ->1/2xx?=

one-fourth: ->1/2xx?=1/4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let the unknown value be represented by $x$

$\textcolor{b l u e}{\text{Building it up to how it is written in algebra:}}$

1/2xx?=1/4" "->" "1/2xx x=1/4" "->" "1/2x =1/4

$\frac{1}{2} x = \frac{1}{4} \text{ "->" } \frac{x}{2} = \frac{1}{4}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Determine the value of } x}$

Given:$\text{ } \frac{x}{2} = \frac{1}{4}$

To get $x$ on its own we need to 'get rid' of the 2 in $\frac{x}{2}$

This is the same as $x \div 2$

For multiply or divide change the value into 1 to get rid of it. It then turns up on the other side of the =

$\textcolor{b r o w n}{\text{Multiply both sides by } \textcolor{b l u e}{2}}$

$\textcolor{g r e e n}{\frac{x}{2} = \frac{1}{4} \text{ "->" } \textcolor{b l u e}{2} \times \frac{x}{2} = \textcolor{b l u e}{2} \times \frac{1}{4}}$

$\textcolor{w h i t e}{.}$
$\text{ } \textcolor{g r e e n}{\frac{\textcolor{b l u e}{2}}{2} \times x = \frac{\textcolor{b l u e}{2}}{4} \times 1}$

$\textcolor{b r o w n}{\text{But "2/2=1" and } \frac{2}{4} = \frac{1}{2}}$
$\textcolor{w h i t e}{.}$

" "color(green)( (1xx x=1/2xx1)

$\text{ } x = \frac{1}{2}$