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

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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.

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

Explanation:

Breaking the question down into its component parts:

One-half a number : $\to \frac{1}{2} \times ?$ $-> 1/2xx?$

is: $\to \frac{1}{2} \times ? =$ $->1/2xx?=$

one-fourth: $\to \frac{1}{2} \times ? = \frac{1}{4}$ $->1/2xx?=1/4$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let the unknown value be represented by $x$ $x$

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

$\frac{1}{2} \times ? = \frac{1}{4} \to \frac{1}{2} \times x = \frac{1}{4} \to \frac{1}{2} x = \frac{1}{4}$ $1/2xx?=1/4" "->" "1/2xx x=1/4" "->" "1/2x =1/4$

$\frac{1}{2} x = \frac{1}{4} \to \frac{x}{2} = \frac{1}{4}$ $1/2x=1/4" "->" "x/2=1/4$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Determine the value of x$ $color(blue)("Determine the value of "x)$

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

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

This is the same as $x \div 2$ $x-:2$

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

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

$\frac{x}{2} = \frac{1}{4} \to 2 \times \frac{x}{2} = 2 \times \frac{1}{4}$ $color(green)(x/2=1/4" "->" "color(blue)(2)xxx/2=color(blue)(2)xx1/4)$

$.$ $color(white)(.)$
$\frac{2}{2} \times x = \frac{2}{4} \times 1$ $" "color(green)( (color(blue)(2))/2xx x=(color(blue)(2))/4xx1)$

$But \frac{2}{2} = 1 and \frac{2}{4} = \frac{1}{2}$ $color(brown)("But "2/2=1" and "2/4=1/2)$
$.$ $color(white)(.)$

$(1 \times x = \frac{1}{2} \times 1)$ $" "color(green)( (1xx x=1/2xx1)$

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

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

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