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

1 Answer
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=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#

#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#