# How do you solve 7r \div 7= 21\div 7?

Mar 27, 2017

$r = 3$

#### Explanation:

First multiply both sides by $7$ and cancel
$7 r \textcolor{red}{\cancel{\textcolor{b l a c k}{\div 7}}} \textcolor{red}{\cancel{\textcolor{b l a c k}{\times 7}}} = 21 \textcolor{red}{\cancel{\textcolor{b l a c k}{\div 7}}} \textcolor{red}{\cancel{\textcolor{b l a c k}{\times 7}}}$
$7 r = 21$

Next divide both sides by $7$ and cancel

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} r}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}} = \frac{21}{7}$
$r = \frac{21}{7}$

Simplify
$r = \frac{3 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}}$
$r = 3$

Mar 28, 2017

$r = 3$

#### Explanation:

The divisions can be written in fraction form:

$\frac{7 r}{7} = \frac{21}{7} \text{ } \leftarrow$simplify each side.

$\frac{\cancel{7} r}{\cancel{7}} = \frac{21}{7}$

$r = 3$

Mar 29, 2017

$\frac{7 r}{7} = \frac{21}{7}$
$r = 3$
Verification:
$\frac{7 \left(3\right)}{7} = \frac{21}{7}$
$\frac{21}{7} = \frac{21}{7}$
$3 = 3$