Question

What is `10 2/3- 5 9/10`?

Answer 1

`143/30`

or

`4 23/30`

Explanation:

First, we need to convert these mixed numbers to improper fractions. To convert a mixed number to an improper fraction you multiply the integer portion by the correct form of `1` and then add it to the fraction portion:

`((10 xx 3/3) + 2/3) - ((5 xx 10/10) + 9/10)`

`(30/3 + 2/3) - (50/10 + 9/10)`

`(30 + 2)/3 - (50 + 9)/10`

`32/3 - 59/10`

Next, to add or subtract fractions they need to be over common denominators, in this case `30`. We need to multiple each fraction by the appropriate form of `1` to make the denominator `30`:

`(10/10 xx 32/3) - (3/3 xx 59/10)`

`(10 xx 32)/(10 xx 3) - (3 xx 59)/(3 xx 10)`

`320/30 - 177/30`

`(320 - 177)/30`

`143/30`

or

`143 -: 30 = 4` with a remainder of `23 =`

`4 + 23/30 = 4 23/30`