Question

How do you add `\frac { 53} { 80} + \frac { 9} { 16}`?

Answer 1

`49/40`, `1 9/40`.

Explanation:

`53/80+9/16`

find a common multiple, in this case `80`, and multiply both parts of each fraction to have the same denominator as the other.

`9/16 = (9 * 5)/(16*5) = 45/80`

`53/80 = 53/80`

the expression is now `53/80 + 45/80`

`53 + 45 = 98`

`53/80 + 45/80 = 98/80`

this can be simplified to `49/40`, and as a mixed number, `1 9/40`.

Answer 2

Find a common denominator for 80 and 16 and the answer will be `1""9/40`

Explanation:

Whenever you prepare to add fractions, you must first find a common denominator for all the fractions. This means the number on the bottom must be the same.

There are a few ways this can be done, but the quickest way is to check whether one denominator can be divided evenly by the other, as is the case here.

Because `80 -: 16 = 5`, you now need to multiply numerator and denominator of the second fraction `9/16` by 5. If you don't multiply both the 9 and the 16, you change the value of the fraction!

Once you do this, the problem becomes

`53/80+45/80`

Now, keep the denominator as 80, but add the two numerators together to get `98/80`, which is the answer.

However, because the numerator is greater than the denominator, you should write this as a "mixed fraction" and simplify it if possible

`98/80 = 80/80 + 18/80 = 1 + 9/40`

Here I divided both 18 and 80 by 2 to get the simpler fraction.

Write this as `1""9/40` and you are done.