How many quarts equals five gallons, and how many liters equals five gallons?

May 5, 2016

$\text{ 5 US gallons"~~18.925 " litres}$
$\text{ 5 US gallons = 20 quarts}$

Explanation:

The name 'quart' sounds like quarter $\to \frac{1}{4}$

From this you can see the link between 4 quarts = 1 gallon
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$\textcolor{b l u e}{\text{Solving for quarts in 5 gallons}}$

$\textcolor{b r o w n}{\text{showing every step}}$

Using ratios $\left(\text{quarts")/("gallons") -> ("4 quarts")/("1 gallon}\right)$

But we need 5 gallons.

Then $\frac{4}{1} = \frac{\text{quarts count}}{5}$

Multiply both sides by 5

$\frac{4}{1} \times 5 = \frac{\text{quarts count}}{5} \times 5$

Write as $4 \times 5 = \text{quarts count} \times \frac{5}{5}$

But $\frac{5}{5} = 1$

$4 \times 5 = \text{quarts count} \times 1$

$20 = \text{quarts count}$

$\textcolor{b l u e}{\text{So 20 quarts make 5 gallons.}}$

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$\textcolor{b l u e}{\text{Solving for litres in 5 US Gallons}}$

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Understood that 3.785411784 litres = 1 US Gallon
Use litre conversion as 3.785

As a ratio

$\frac{3.785 \text{ litres")/(1" US gallon") = ("litres count}}{5}$

$\textcolor{b l u e}{\text{litres count"~~5(3.785)~~18.925 " litres ~~ 5 US gallons}}$