# What is 3 1/3 + 4 + 2/5?

Mar 11, 2018

$\frac{116}{15}$

#### Explanation:

We should change the mixed number to just a fraction to make things a little easier:
$3 \frac{1}{3} = 3 + \frac{1}{3} = \frac{3 \cdot 3}{3} + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3}$

We then see that we have denominators of 3, 5 (and secretly a 1 under the 4), but we need them to be equal.

We know that the first number that both 3 and 5 can divide is 15, so we want all of the numbers to become 15. We do this by multiplying in fractions like 3/3 and 5/5 (which don't change the value of the fractions)

$\frac{10}{3} + \frac{4}{1} + \frac{2}{5} = \frac{10}{3} \cdot \frac{5}{5} + \frac{4}{1} \cdot \frac{15}{15} + \frac{2}{5} \cdot \frac{3}{3}$

$= \frac{50}{15} + \frac{60}{15} + \frac{6}{15} = \frac{50 + 60 + 6}{15} = \frac{116}{15}$

We can't simplify this at all because 116 = $2 \cdot 58 = {2}^{2} \cdot 29$ which doesn't have any factors of 3 or 5.

Mar 11, 2018

$3 \frac{1}{3} + 4 + \frac{2}{5} = \frac{116}{15} \mathmr{and} 7 \frac{11}{15}$

#### Explanation:

First to add fractions they all need to be over the same denominator.
To find a denominator you find the LCM in this case it is 15.
The lowest common multiple is the lowest number that both original numbers (in this case 5 and 3) go into.

The second step is to make sure the fractions are over this denominator. To make sure all the fractions are over 15 we need to multiply them. $\frac{1}{3}$ is multiplied by 5 to create $\frac{5}{15}$.
$\frac{2}{5}$ is multiplied by 3 to create $\frac{6}{15}$.

Now we input these fractions into the original sum.
$3 \frac{5}{15} + 4 + \frac{6}{15}$

Now it is simple addition, 3+4 = 7 and 5 + 6 = 11 so your final total is $7 \frac{11}{15}$