Question

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

Answer 1

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.

Answer 2

`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`