# How do you simplify 2 1/10+(1 2/7+ 4 9/10)?

##### 1 Answer
Nov 8, 2016

$= \frac{580}{70}$

#### Explanation:

Simplifying the given expression including mixed numbers is

determined by changing mixed numbers into fractions then

adding the fractions.

Mixed numbers is changed into fractions by:

$\textcolor{red}{a \frac{c}{d} = \frac{a \times d + c}{d}}$

Changing the mixed numbers into fractions:

$2 \frac{1}{10} = \textcolor{red}{\frac{2 \times 10 + 1}{10} = \frac{21}{10}}$

$1 \frac{2}{7} = \textcolor{red}{\frac{1 \times 7 + 2}{7} = \frac{9}{7}}$

$4 \frac{9}{10} = \textcolor{red}{\frac{4 \times 10 + 9}{10} = \frac{49}{10}}$
$\text{ }$

Adding the fractions is determined by computing the common denominator $G . C . D \left(7 , 10\right)$

Common denominator is determined by computing the prime factorization and choosing the greatest common factors.

$10 = 2 \times 5 \times 1$
$7 = 7 \times 1$

Denominator is:
$G . C . D \left(7 , 10\right) = 2 \times 5 \times 7 \times 1 = 70$

$2 \frac{1}{10} + \left(1 \frac{2}{7} + 4 \frac{9}{10}\right)$

$= \textcolor{red}{\frac{21}{10}} + \textcolor{red}{\frac{9}{7}} + \textcolor{red}{\frac{49}{10}}$

$= \frac{21 \times 7}{70} + \frac{9 \times 10}{70} + \frac{49 \times 7}{70}$

$= \frac{147 + 90 + 343}{70}$

$= \frac{580}{70}$