# How do you define a variable and write an expression for each phrase: the number of gallons in 21 quarts?

Jul 22, 2017

$5 \frac{1}{4}$ gallons

#### Explanation:

The way to remember this relationship is to make a mental link between the word 'quart' and the word 'quarter'.

A quarter is $\frac{1}{4}$ and there are 4 quarts in 1 gallon.

One way to do the conversion is to consider it as a ratio. So we can write:

Let the unknown count of gallons be $x$

$\left(\text{count of gallons")/("count of quarts}\right) \to \frac{1}{4} = \frac{x}{21}$

Multiply both sides by $\textcolor{red}{21}$

$\textcolor{g r e e n}{\frac{1}{4} = x \times \frac{1}{21} \text{ "->" } \frac{1}{4} \textcolor{red}{\times 21} = x \times \frac{1}{21} \textcolor{red}{\times 21}}$

$\text{ } \textcolor{g r e e n}{\frac{1 \textcolor{red}{\times 21}}{4} = x \times \frac{\textcolor{red}{21}}{21}}$

But $\frac{21}{21} = 1$

$\text{ } \frac{21}{4} = x \times 1$

$x = 5 \frac{1}{4}$ gallons