Customary Units of Capacity Conversion Formulas
Capacity is the amount of liquid that can be filled in a particular container. The units of capacity used in the customary system are quarts, pints, gallons and cups. We can convert one unit to the other by multiplying or dividing by the required number. Conversion of units helps us to express the same value in different units.
Units of Capacity Conversion Formula
Let’s understand the concept visually. If you take a gallon of water and fill it equally into 4 containers, then the quantity of water in each container is a quart. Similarly, if 1 quart is equally poured into two containers, then each of these containers now has 1 pint of water. Finally, 1 pint can be poured equally into two cups.
1 gallon (gal) = 4 quarts (qt)
1 quart (qt) = 2 pints (pt)
1 pint (pt) = 2 cups (c)
To convert from a larger unit to a smaller unit, we need to multiply. Therefore,
1 gallon = 4 quarts = 8 pints = 16 cups
Conversely, to convert from a smaller unit to a larger unit we need to divide. Therefore,
1 cup = \( \frac{1}{2} \) pint = \( \frac{1}{4} \) quart = \( \frac{1}{16} \) gallon
Rapid Recall
Solved Examples
Example 1: Convert 45 gallons into cups.
Solution:
We know that 1 gallon is 4 quarts.
45 gallons = 45 \( \times \) 4 = 180 quarts
1 quart is 2 pints.
180 quarts = 180 \( \times \) 2 = 360 pints
1 pint is 2 cups.
360 pints = 360 \( \times \) 2 = 720 cups
Therefore, 45 gallons is 720 cups.
Example 2: Convert 160 cups of milk into gallons of milk.
Solution:
We know that 1 pint is 2 cups, or, 1 cup is \( \frac{1}{2} \) of a pint.
160 cups = 160 \( \div \) 2 = 80 pints
2 pints is a quart, or, 1 pint is \( \frac{1}{2} \) of a quart.
80 pints = 80 \( \div \) 2 = 40 quarts
4 quarts is a gallon, or, \( \frac{1}{2} \) of a gallon is a quart.
40 quarts = 40 \( \div \) 4 = 10 gallons
Therefore, 160 cups of milk is 10 gallons of milk.
Example 3: Tracy is going to present a very interesting experiment in class tomorrow. For the experiment, she mixes 1 quart of water, 3 pints of oil, and 2 pints of honey. She plans on carrying it in her bottle that can carry 2 quarts. Will she be able to do so?
Solution:
Quantity of water = 1 quart = 2 pints
Quantity of oil = 3 pints
Quantity of honey = 2 pints
Total quantity = 2 + 3 + 2 = 7 pints
Quantity that can be carried in her bottle = 2 quarts = 2 \( \times \) 2 = 4 pints
She needs to carry 7 pints but her bottle can only be filled with 4 pints. Hence she might need another bottle as she won’t be able to carry the mixture of liquids in just one bottle.
Example 4: Jared, Luke, and Matt play a game where they simultaneously pour water into a container. Jared pours 1 cup of water every 4 seconds, Luke pours \( 1\frac{1}{4} \) quarts of water every 30 seconds and Matt pours \( \frac{3}{2} \) pints every 12 seconds. Find the amount of water in the container in 48 seconds.
Solution:
Jared pours 1 cup every 4 seconds.
In 1 second Jared pours = \( \frac{1}{4} \) cup
Luke pours \( 1\frac{1}{4}=\frac{1\times 4+1}{4}=\frac{5}{4} \) quarts every 30 seconds
In 1 second Luke pours \( =\frac{5}{4}\div 30=\frac{1}{24} \) quarts
1 quart = 2 pints
1 pint = 2 cups
Therefore, in 1 second Luke pours \( =\frac{1}{24}\times 2\times 2=\frac{1}{16} \) cup
Similarly,
Matt pours \( \frac{3}{2} \) pint every 12 seconds
In 1 second Matt pours \( =\frac{3}{2}\div 12=\frac{1}{8} \) pint
1 pint = 2 cups
So, in 1 second Matt pours \( =\frac{1}{8}\times 2=\frac{1}{4} \) cup
Total quantity of water poured in 1 second \( =\frac{1}{4}+\frac{1}{6}+\frac{1}{4} \)
\( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\frac{6}{24}+\frac{4}{24}+\frac{6}{24} \)
\( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\frac{16}{24} \) cup.
Quantity of water poured in 48 seconds \( =\frac{16}{24}\times 48 \)
\( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=32 \) cups.
Hence in 48 seconds, the container will have 32 cups of water.
The units of measurement in the customary system of measurement are called customary units. The units include, foot, inches, pound, ton, etc.
The units of measurement in the metric system are called metric units or SI units(International System of Units). The units include meter, kilogram, gram, etc.
The customary units of capacity are as follows: gallons, quarts, pints and cups.
The metric units of capacity include liters(L) and milliliters (mL). 1 liter is 1000 milliliters. Other units can be derived as well, such as kiloliter, dekaliter, hectoliter, and so on.
According to the standard conversion factors, 1 gallon is 16 cups, so the quantity in gallons can be multiplied by 16 to obtain the required answer. Another way to convert gallons to cups, is to first convert gallons to quarts by multiplying by 4, then to pints by multiplying by 2 and then to cups by again multiplying by 2.