Question

How do you solve `13 2/9 - 7 1/3` and simplify the answer?

Answer 1

Convert to improper fractions, make the denominator common, subtract, then convert to the asked fraction form (perhaps a mixed fraction) to obtain `5 8/9`.

Explanation:

Before starting, I would turn any subtraction into negative addition to reduce ambiguity and reduce the possibility of errors:

`= 13 2/9 + (- (7 1/3))`

Now, let's convert each to improper fractions. Mixed fractions really are a sum of a whole number and a proper fraction:

`= (13 + 2/9) + (- (7 + 1/3))`

I'll take the whole number, `13`, from `13 2/9`, and make it a fraction with a denominator of `9`. To do that, first divide `13` by `1` (which shouldn't change anything):

`13 = 13/1`

Then multiply by `1` (doesn't change anything either):

`= 13/1 * 1`

Still not changing anything, we can turn that `1` into a number divided by itself. Choose `9`:

`= 13/1 * 9/9`

And multiply:

`= (13 * 9)/(1 * 9) = 117/9`

Now add them together:

`13 + 2/9 = 117/9 + 2/9 = 119/9`

Alright, that's our first improper fraction, now we have:

`= (13 + 2/9) + (- (7 + 1/3)) = 119/9 + (- (7 + 1/3))`

Time to tackle the second! However, we need to make sure both fractions end up having common denominators. So let's make both `7` and `1/3` have a denominator of `9` (without changing the value!) by the same method:

`7 + 1/3`

`= (7/1) + (1/3)`

`= (7/1 * 1) + (1/3 * 1)`

`= (7/1 * 9/9) + (1/3 * 3/3)`

`= 63/9 + 3/9 = 66/9`

Putting this back into our problem:

`119/9 + (- (7 + 1/3)) = 119/9 + (-(66/9)) = 119/9 - 66/9`

Now solve:

`119/9 - 66/9 = 53/9`

I assume you need a mixed fraction... Well, split `53` into a multiple of `9` and another number... maybe `45` and `8`?

`53/9 = 45/9 + 8/9`

Then divide `45/9`:

`= 5 + 8/9 = 5 8/9`