# How do you add 10\frac { 3} { 4}+ \quad 10\frac { 1} { 3}?

Mar 14, 2017

$\frac{253}{12}$

#### Explanation:

Convert the numbers into mixed fractions. The first $10$ should be written as $\frac{40}{4}$ and the other $10$ should be written as $\frac{30}{3}$ so we can add the numerators together:

$\frac{40 + 3}{4} + \frac{30 + 1}{3} = \frac{43}{4} + \frac{31}{3}$

Now we have another problem. The denominators don't match so we can't simply add them. Worry not. We can use common denominators. Multiply the first fraction by $\frac{3}{3}$ and the second fraction by $\frac{4}{4}$

$\frac{43 \times 3}{4 \times 3} + \frac{31 \times 4}{3 \times 4} = \frac{129}{12} + \frac{124}{12}$

Now we have common denominators so we can just add the numerators:

$\frac{129 + 124}{12} = \frac{253}{12}$

Mar 14, 2017

$21 \frac{1}{12}$

#### Explanation:

$10 \frac{3}{4} + 10 \frac{1}{2}$

$\therefore = \frac{43}{4} + \frac{31}{3}$

L.C.D. of 4 and 3$= 12$

$\therefore = \frac{129 + 124}{12}$

$\therefore = \frac{253}{12}$

$\therefore = 21 \frac{1}{12}$