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

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Answer 1 · 2016-11-26T13:59:04

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

$x=1/2$

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 $x$

$color(blue)("Building it up to how it is written in algebra:")$

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

$1/2x=1/4" "->" "x/2=1/4$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("Determine the value of "x)$

Given: $" " x/2=1/4$

To get $x$ on its own we need to 'get rid' of the 2 in $x/2$

This is the same as $x-:2$

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

$color(brown)("Multiply both sides by "color(blue)(2))$

$color(green)(x/2=1/4" "->" "color(blue)(2)xxx/2=color(blue)(2)xx1/4)$

$color(white)(.)$
$" "color(green)( (color(blue)(2))/2xx x=(color(blue)(2))/4xx1)$

$color(brown)("But "2/2=1" and "2/4=1/2)$
$color(white)(.)$

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

$" "x=1/2$