How do you solve: #2/3# of a number is 22?

2 Answers
Aug 11, 2017

See a solution process below:

Explanation:

In this type of problem when dealing with a fraction, the term "of" means to multiply.

Let's call the "number" we are looking for: #n#

We can write this problem as follows and solve for #n#;

#2/3 xx n = 22#

#color(red)(3)/color(blue)(2) xx 2/3 xx n = color(red)(3)/color(blue)(2) xx 22#

#cancel(color(red)(3))/cancel(color(blue)(2)) xx color(blue)(cancel(color(black)(2)))/color(red)(cancel(color(black)(3))) xx n = color(red)(3)/cancel(color(blue)(2)) xx color(blue)(cancel(color(black)(22)))11#

#n = 33#

#2/3# of #color(red)(33)# is 22.

Aug 11, 2017

#33#

Explanation:

We can reason through this question by understanding what the fraction means.

#2/3# means 'two-thirds'

If two-thirds of a number is #22#

Then one-third of the the number is #22div 2 = 11#

Three-thirds will be the number itself: #3 xx 11 = 33#

This can also be simplified by:

'increase #22# in the ratio #3:2#'

#22 xx 3/2 = 33#