# How do you solve the equation n times 500=5000?

Oct 22, 2016

$n = 10$

#### Explanation:

We have the equation.

$n \times 500 = 5000 \Rightarrow 500 n = 5000$

To solve for n, divide both sides by 500.

$\frac{\cancel{500} n}{\cancel{500}} = \frac{5000}{500}$

$\Rightarrow n = 10 \text{ is the solution}$

Oct 22, 2016

n=10

#### Explanation:

$\textcolor{b l u e}{\text{Using shortcut method}}$

Move the 500 to the other side of the = and change it to divide

$n = \frac{5000}{500}$

$n = \frac{{\cancel{5000}}^{10}}{{\cancel{500}}^{1}} \leftarrow \text{ canceling out}$

$n = 10$

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$\textcolor{b l u e}{\text{Using first principles method}}$

Divide both sides by 500

$\frac{n \times 500}{500} = \frac{5000}{500}$

But $10 \times 500 = 5000$ so we have

$\frac{n \times 500}{500} = \frac{10 \times 500}{500}$

This is the same as

$n \times \frac{500}{500} = 10 \times \frac{500}{500}$

But $\frac{500}{500} = 1$

$n \times 1 = 10 \times 1$

$n = 10$