# Question #8e30a

Feb 28, 2017

$\frac{9}{6125}$

#### Explanation:

$\textcolor{b l u e}{\text{Dealing with a lot of those zeros}}$

What follows is where the shortcut of cancelling comes from.

$72000 \to 72 \times 1000$

$4900000 \to 4900 \times 1000$

$\frac{72 \times 1000}{4900 \times 1000} \text{ "=" } \frac{72}{4900} \times \frac{1000}{1000}$

But $\frac{1000}{1000} = 1$ and anything multiplied by 1 does not change its value.

$\frac{72}{4900} \times \frac{1000}{1000} \text{ "=" "72/4900xx1" "=" } \frac{72}{4900}$
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$\textcolor{b l u e}{\text{Dealing with what is left}}$

$\frac{72}{4900} \text{ "=" } \frac{72 \div 8}{49000 \div 8} = \frac{9}{6125}$
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$\textcolor{b l u e}{\text{This is one way to find a common factor - there are other methods}}$

Observe that the highest $\underline{\text{common}}$ factor is $2 \times 2 \times 2 = 8$