# How do you add 12\frac { 5} { 6} + 87\frac { 3} { 5} + 34\frac { 3} { 10}?

Mar 20, 2018

$\frac{4042}{30} = \frac{2021}{15} = 134.73$

#### Explanation:

When adding or subtracting fractions, we always need a COMMON DENOMINATOR. However, when dealing with mixed numbers, it is easier to first convert them to IMPROPER FRACTIONS.

If you do not know how to convert a mixed number to an improper fraction, follow the steps below:
1. Multiply denominator by whole number.
2. Add the product and numerator.
3. Put the sum over the original denominator.

This will give us a different looking problem:
$\frac{77}{6} + \frac{438}{5} + \frac{343}{10}$

Now we need to give them all a common denominator by finding the least common multiple (LCM) of all three denominators (6, 5, and 10). This number is 30, so multiply the numerator and denominator of each fraction by the number that will make the denominator 30.
$\left(\frac{5}{5}\right) \frac{77}{6} + \left(\frac{6}{6}\right) \frac{438}{5} + \left(\frac{3}{3}\right) \frac{343}{10}$
We can do this because $\frac{5}{5} , \frac{6}{6} ,$ and $\frac{3}{3}$ are equal to $1$, and anything multiplied by $1$ is itself. We are just changing the look of the number, not the value.

$\frac{385}{30} + \frac{2628}{30} + \frac{1029}{30}$

Now that they have the same denominator, we can add them.
$\frac{385 + 2628 + 1029}{30} = \frac{4042}{30}$

Simplify or write in decimal form (whatever your teacher wants).
$\frac{4042}{30} = \frac{2021}{15}$
$\frac{4042}{30} = 134.73$

Mar 20, 2018

$\frac{4042}{30} = \frac{2021}{15} = 134.73$

#### Explanation:

When adding or subtracting fractions, we always need a COMMON DENOMINATOR. However, when dealing with mixed numbers, it is easier to first convert them to IMPROPER FRACTIONS.

If you do not know how to convert a mixed number to an improper fraction, follow the steps below:
1. Multiply denominator by whole number.
2. Add the product and numerator.
3. Put the sum over the original denominator.

This will give us a different looking problem:
$\frac{77}{6} + \frac{438}{5} + \frac{343}{10}$

Now we need to give them all a common denominator by finding the least common multiple (LCM) of all three denominators (6, 5, and 10). This number is 30, so multiply the numerator and denominator of each fraction by the number that will make the denominator 30.
$\left(\frac{5}{5}\right) \frac{77}{6} + \left(\frac{6}{6}\right) \frac{438}{5} + \left(\frac{3}{3}\right) \frac{343}{10}$
We can do this because $\frac{5}{5} , \frac{6}{6} ,$ and $\frac{3}{3}$ are equal to $1$, and anything multiplied by $1$ is itself. We are just changing the look of the number, not the value.

$\frac{385}{30} + \frac{2628}{30} + \frac{1029}{30}$

Now that they have the same denominator, we can add them.
$\frac{385 + 2628 + 1029}{30} = \frac{4042}{30}$

Simplify or write in decimal form (whatever your teacher wants).
$\frac{4042}{30} = \frac{2021}{15}$
$\frac{4042}{30} = 134.73$