# How do you simplify 5/7 - 2/3?

Aug 4, 2016

$\frac{1}{21}$

#### Explanation:

$\textcolor{b l u e}{\text{Two very important facts}}$

$\textcolor{b r o w n}{\text{Fact 1}}$
You can not $\underline{\text{directly}}$ add or subtract counts in fractions unless their 'size' indicators are the same.

$\left(\text{count")/("size indicator")->("numerator")/("denominator}\right)$

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$\textcolor{b r o w n}{\text{Fact 2}}$
Multiplying by 1 does not change the intrinsic value of something.

Multiply by 1 in some different form does not change the intrinsic value but $\underline{\text{does change the way it looks}}$.

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$\textcolor{b l u e}{\text{Answering your question}}$

color(brown)((5/7xx1)-(2/3xx1))color(blue)(" "->" "(5/7xx3/3)-(2/3xx7/7)

$= \frac{5 \times 3}{7 \times 3} - \frac{2 \times 7}{3 \times 7}$

$= \frac{15}{21} - \frac{14}{21}$

$\frac{15 - 14}{21} = \frac{1}{21}$