Question

Chelsie saves `1/5` of her allowance and spends `2/3` of her allowance at the mall. What fraction of her allowance remains?

Answer 1

`1/5 + 2/3 = (3*1)/(3*5) + (5*2)/(5*3) = 3/15 + 10/15 = 13/15`
`1- 13/15 = 15/15 - 13/15 = 2/15`

Explanation:

First you should add the parts of her allowance that are accounted for. That includes the 1/5 saved and the 2/3 spent. As these have different denominators, you need to change the denominators to that they match.

This can be done by multiplying top and bottom of each fraction by the denominator of the other fraction (for example multiplying the first fraction by 3/3). Note this does not change the value of the fraction, because 3/3 is 1 and multiplying by 1 doesn't change anything. This just gives us a form that has matching denominators, so we can add them more easily.

After the denominators match, you can add the numerators.

This tells us the total amount accounted for. But we want the total amount left . The total amount is 100% or 1. Subtracting the total spent from 1 gives us the amount left.

If the amount left had common factors between the numerator and denominator we would simplify, but the final fraction (2/15) is already as simple as possible.

Answer 2

`2/15`

Explanation:

Add the two fractions and subtract the sum from one.

`1/5 + 2/3 = 3/15 + 10/15`

This is changing both fractions to the common denominator of 15

`3/15 = 10/15 = 13/15`

The numerators can be added as the denominators are the same.

`1 - 13/15 = 15/15 - 13/15`

Changing one to the equivalent fraction with the same denominator.

# 15/15 - 13/15 = 2/15

The numerators can be subtracted as the denominators are the same.