# How do you simplify the sum of 3/5 + 2/7?

Apr 4, 2016

$\frac{31}{35}$

#### Explanation:

You can not directly add or subtract the top numbers of fractions unless the bottom numbers are all the same.

Both 5 and 7 will divide into 35 because $5 \times 7 = 35$
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Multiply $\frac{3}{5}$ by 1 but in the form of $\textcolor{g r e e n}{1 = \frac{7}{7}}$ giving

$\text{ } \frac{3}{5} \textcolor{g r e e n}{\times \frac{7}{7}} = \frac{21}{35}$
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Multiply $\frac{2}{7}$ by 1 but in the form of $\textcolor{b r o w n}{1 = \frac{5}{5}}$ giving

$\text{ } \frac{2}{7} \textcolor{b r o w n}{\times \frac{5}{5}} = \frac{10}{35}$
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color(blue)("Putting it all together"

$\text{ "3/5+2/7 " is the same as } \frac{21}{35} + \frac{10}{35}$

The correct way to write this is:

$\text{ "3/5+2/7" " -=" } \frac{21}{35} + \frac{10}{35}$

$\text{ } = \frac{31}{35}$