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: 
$\frac{4}{5} + \frac{9}{11}$

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:
$\frac{4}{55} + \frac{9}{55}$

However, if the denominator changes, the numerator changes as well. We use the following formula to find the numerators: 

(Common Denominator ÷ Denominator) x Numerator =  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: 

$\frac{44}{55}$

Now let's do the second:

9/55

(55(common denominator) ÷ 11(original denominator))×9(numerator) = 45

Now we have: 

$\frac{45}{55}$

Now we have two fractions to add: 

$\frac{44}{55} + \frac{45}{55}$

Only add the numerators, the denominators stay the SAME !

44+45=89

Final answer: $\frac{89}{55}$

If you have further questions on this problem, please do not hesitate to comment below! :) Have a nice day!