Question

What is the answer to 4/5+9/11

Answer 1

Hi there!
When adding fractions we ALWAYS need to make sure the that denominators are the SAME .We need to find a common denominator so that the two fractions are on the same terms. In the end, the denominator stays the same. Let's start:
We are given 2 fractions to add:

`(4)/(5) + (9)/(11)`

We need to find a LEAST common denominator, start by listing the factors of 5 and 11 since both of these numbers are in the denominator.

Factors of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
Factors of 11: 11, 22, 33, 44, 55

As we see above, 55 is our LCD (least common denominator)

We can change the denominator of both fractions to 55 since this is our LCD:

`(4)/(55) + (9)/(55)`

However, if the denominator changes, the numerator changes as well. We use the following formula to find the numerators:
(Common Denominator ÷ Denominator) x Numerator = NumeratorLets start by finding the numerator for the first fraction:
4/55
(55 (common denominator) ÷ 5 (original denominator) × 4 (numerator) = 44The first fraction becomes:
`(44)/(55)`
Now let's do the second:9/55(55(common denominator) ÷ 11(original denominator))×9(numerator) = 45Now we have:
`(45)/(55)`Now we have two fractions to add:
`(44)/(55) + (45)/(55)`Only add the numerators, the denominators stay the SAME !
44+45=89Final answer:
`(89)/(55)`If you have further questions on this problem, please do not hesitate to comment below! :) Have a nice day!