Explainer: Converting and Comparing Capacity: Customary Units

In this explainer, we will learn how to convert and compare customary units of capacity and apply unit conversion to solve real-world problems using fractions, and decimals.

Units are used whenever we measure a physical quantity—a length, an area, a volume, a capacity, a mass, or a temperature. Units allow for comparison between lengths, areas, volumes, capacities, masses, and so on, by providing references.

The volume of an object is often described as the amount of space the volume takes. The capacity of a container indicates how much volume of a substance it can hold (usually a fluid). For instance, a milk bottle may hold 2 pints of milk when it is full, and a car fuel tank may hold 14 gallons of fuel.

The main customary units of capacity are, from least to greatest, as follows: the fluid ounce (fl oz), cup (c), pint (pt), quart (qt), and gallon (gal). They are mutually defined as below.

Definition: Main Customary Units of Capacity

  • 1 cup (c) = 8 fluid ounces (fl oz)
  • 1 pint (pt) = 2 cups (c)
  • 1 quart (qt) = 2 pints (pt)
  • 1 gallon (gal) = 4 quarts (qt)

The equalities between the different units given above will allow us to convert between any of them. For this, we need to realize that the measures of a given capacity in two different units are proportional: the ratio of one to the other is constant. For instance, a measure of a given capacity in ounces will always be 8 times bigger than when it is measured in cups, because one ounce is one-eighth of a cup.

However simple as it may sound, it is easy to get confused when converting between different units. This confusion comes from the fact that when we convert to a bigger unit, the measure becomes smaller, and vice versa. The best way to avoid this kind of confusion is to draw a proportionality double-line diagram.

We are going to see in the following examples how to use this method.

Example 1: Converting Cups into Fluid Ounces

How many fluid ounces are there in 57 c?

Answer

We want to convert 57 cups to fluid ounces. Knowing that 8 fluid ounces make a cup, we can draw the shown double-line diagram.

Each cup corresponds to 8 fluid ounces, so 57 cups corresponds to 57 times as many as one cup, that is, 57 times 8. We find that 57×8=456.

Our answer is that there are 456 fluid ounces in 57 cups.

Example 2: Converting Quarts to Gallons

How many gallons are there in 75 qt?

Answer

We want to convert 75 quarts to gallons. Recall that 4 quarts make a gallon. So, we need to find how many groups of 4 there are in 75 gallons—this number of groups is then the number of gallons.

We find that 75÷4=18, remainder 3. The remainder of 3 quarts is three quarters of four quarts, which make a gallon, that is, three quarters of a gallon. The whole process is illustrated in the double-line diagram.

Our answer is that there are 1834 gallons in 75 quarts.

Example 3: Converting Gallons to Pints

Complete the following: 3,840 pt = gal.

Answer

To convert gallons to pints, we need first to find how many pints make a gallon. Using the triple-line diagram, we find that there are 4 quarts in a gallon and 2 pints in each of the quarts. Hence, there are 8 pints in a gallon.

We need now to find how many groups of 8 pints are in 3,840 pints to convert 3,840 pints to gallons.

We find 3,840÷8=480.

Hence, there are 480 gallons in 3,840 pints.

Example 4: Converting Quarts to Cups in a Word Problem

If Daniel has 8 quarts of watermelon juice to share with his friends, how many of them can have 1 cup of watermelon juice?

Answer

We need to find here how many cups are in 8 quarts. For this, we need to work out how many cups make one quart.

Since 2 pints make a quart and each pint corresponds to 2 cups, we find that there are 4 cups in one quart.

So, in 8 quarts, there are 8 times as many cups as there are in 1 quart; that is, 8×4=32.

Hence, our answer is that 32 people will be able to get 1 cup of watermelon juice.

Example 5: Converting Fluid Ounces to Quarts and Ounces

Complete the following with the maximum number of quarts and the remainder in fluid ounces: 401 fl oz = qt fl oz.

Answer

To express 401 fluid ounces as the maximum whole number of quarts and the remainder in fluid ounces, we need first to know how many fluid ounces make one quart. Using the quadruple-line diagram, we see that there are 32 fluid ounces in one quart.

Now, we need to find how many groups of 32 fluid ounces are in 401 fluid ounces. We find that 401÷32=12,17.remainder

Hence, there are 12 quarts plus 17 fluid ounces in 401 fluid ounces.

Our answer is as follows: 401=1217ozqtoz.

Key Points

  1. The volume of an object is often described as the amount of space the volume takes. The capacity of a container indicates how much volume of a substance it can hold (usually a fluid).
  2. 1 cup (c) = 8 fluid ounces (fl oz).
    1 pint (pt) = 2 cups (c).
    1 quart (qt) = 2 pints (pt).
    1 gallon (gal) = 4 quarts (qt).
  3. The measures of a given capacity in two different units are proportional: the ratio of one to the other is constant. For instance, a measure of a given capacity in ounces will always be 8 times bigger than when it is measured in cups, because one ounce is one-eighth of a cup.

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