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