Question

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

Answer 1

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

`x=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`
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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`