BB.5 Convert and compare customary units of volume
What is volume?
Volume is the amount of space a container or object takes up. In the United States, we measure volume using customary units. The main customary units of volume are the fluid ounce, cup, pint, quart, and gallon. These units are used for liquids such as water, milk, juice, and oil.
- A small spoon of medicine might be measured in fluid ounces.
- A recipe might call for one cup of milk.
- A large bottle of soda might hold two quarts.
- A bucket of paint might contain one gallon.
Volume is different from weight. Weight tells how heavy something is. Volume tells how much space it fills.
Customary units of volume
The customary system of volume uses these units from smallest to largest: fluid ounce (fl oz), cup (c), pint (pt), quart (qt), and gallon (gal). Each unit is related to the others by a fixed number. Learning these relationships is the key to converting between units.
- 1 cup = 8 fluid ounces
- 1 pint = 2 cups
- 1 quart = 2 pints
- 1 gallon = 4 quarts
These relationships are exact. You can use them to change any measurement from one unit to another.
How to convert between customary units of volume
Converting means changing a measurement from one unit to another without changing the actual amount. To convert, you multiply or divide by the relationship between the units. If you are changing a larger unit to a smaller unit, you multiply. If you are changing a smaller unit to a larger unit, you divide.
- Convert 3 cups to fluid ounces. 1 cup = 8 fluid ounces. 3 × 8 = 24. So, 3 cups = 24 fluid ounces.
- Convert 10 pints to quarts. 1 quart = 2 pints. 10 ÷ 2 = 5. So, 10 pints = 5 quarts.
Always check your answer. If you multiply when you should divide, your answer will be much too large or too small.
Using multiplication to convert larger units to smaller units
When you convert from a larger unit to a smaller unit, you multiply. This is because it takes many small units to make one large unit. For example, it takes 4 quarts to make 1 gallon, so 1 gallon is equal to 4 quarts. To find how many quarts are in 3 gallons, you multiply 3 by 4.
- 2 gallons = ___ quarts. 1 gallon = 4 quarts. 2 × 4 = 8. So, 2 gallons = 8 quarts.
- 5 quarts = ___ pints. 1 quart = 2 pints. 5 × 2 = 10. So, 5 quarts = 10 pints.
- 4 pints = ___ cups. 1 pint = 2 cups. 4 × 2 = 8. So, 4 pints = 8 cups.
- 7 cups = ___ fluid ounces. 1 cup = 8 fluid ounces. 7 × 8 = 56. So, 7 cups = 56 fluid ounces.
Multiplying always gives a larger number when you convert from a larger unit to a smaller unit. This makes sense because you are counting with smaller pieces.
Using division to convert smaller units to larger units
When you convert from a smaller unit to a larger unit, you divide. This is because you are grouping smaller units together to make one larger unit. For example, it takes 8 fluid ounces to make 1 cup, so 16 fluid ounces is equal to 2 cups. To find how many cups are in 24 fluid ounces, you divide 24 by 8.
- 16 cups = ___ pints. 1 pint = 2 cups. 16 ÷ 2 = 8. So, 16 cups = 8 pints.
- 12 quarts = ___ gallons. 1 gallon = 4 quarts. 12 ÷ 4 = 3. So, 12 quarts = 3 gallons.
- 20 pints = ___ quarts. 1 quart = 2 pints. 20 ÷ 2 = 10. So, 20 pints = 10 quarts.
- 40 fluid ounces = ___ cups. 1 cup = 8 fluid ounces. 40 ÷ 8 = 5. So, 40 fluid ounces = 5 cups.
Dividing always gives a smaller number when you convert from a smaller unit to a larger unit. This makes sense because you are counting with larger pieces.
Converting between units that are not directly related
Sometimes you need to convert between units that do not have a direct relationship, such as fluid ounces and pints. In these cases, you can convert in two steps. First, change the starting unit to a unit that is related to both, such as cups. Then change that unit to the unit you want.
- Convert 32 fluid ounces to pints. Step 1: 32 fluid ounces ÷ 8 = 4 cups. Step 2: 4 cups ÷ 2 = 2 pints. So, 32 fluid ounces = 2 pints.
- Convert 3 gallons to pints. Step 1: 3 gallons × 4 = 12 quarts. Step 2: 12 quarts × 2 = 24 pints. So, 3 gallons = 24 pints.
You can also use a single multiplication or division if you know the combined relationship. For example, 1 gallon = 8 pints, so 3 gallons = 24 pints.
Comparing customary units of volume
To compare two measurements, they must be in the same unit. If they are in different units, convert one or both measurements first. Then compare the numbers using the symbols > (greater than), < (less than), or = (equal to).
- Compare 3 quarts and 5 pints. Convert 3 quarts to pints: 3 × 2 = 6 pints. 6 pints > 5 pints. So, 3 quarts > 5 pints.
- Compare 2 gallons and 8 quarts. Convert 2 gallons to quarts: 2 × 4 = 8 quarts. 8 quarts = 8 quarts. So, 2 gallons = 8 quarts.
- Compare 4 cups and 40 fluid ounces. Convert 4 cups to fluid ounces: 4 × 8 = 32 fluid ounces. 32 fluid ounces < 40 fluid ounces. So, 4 cups < 40 fluid ounces.
Always convert before you compare. Never compare numbers in different units directly, because the numbers alone do not tell the whole story.
Real-world problems with customary units of volume
In everyday life, you often need to convert and compare volumes. For example, you might need to know if a pitcher holds enough lemonade for a party, or if a recipe calls for more milk than you have. Solving these problems requires careful reading and correct conversion.
- A recipe needs 3 cups of milk. You have 1 pint of milk. Do you have enough? 1 pint = 2 cups. 2 cups < 3 cups. So, you do not have enough milk.
- A water cooler holds 5 gallons. How many quart bottles can you fill? 5 gallons × 4 = 20 quarts. So, you can fill 20 quart bottles.
- A soup pot holds 6 quarts. A smaller pot holds 10 pints. Which pot holds more? 6 quarts × 2 = 12 pints. 12 pints > 10 pints. So, the soup pot holds more.
When solving real-world problems, always write down the units. This helps you keep track of what you are converting and why.
Using a conversion table
A conversion table is a helpful tool that lists the relationships between units. You can use it to check your work or to find a relationship you have forgotten. The table below shows the customary units of volume from smallest to largest.
- 1 cup = 8 fluid ounces
- 1 pint = 2 cups = 16 fluid ounces
- 1 quart = 2 pints = 4 cups = 32 fluid ounces
- 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces
You can make your own conversion table on a piece of paper. Keep it handy when you practice converting and comparing volumes.
Common mistakes to avoid
Students sometimes make mistakes when converting or comparing volumes. One common mistake is multiplying when they should divide, or dividing when they should multiply. Another mistake is comparing numbers without converting to the same unit. A third mistake is forgetting the unit labels in the answer.
- Mistake: 4 quarts = 8 gallons (multiplied instead of divided). Correction: 4 quarts ÷ 4 = 1 gallon.
- Mistake: 2 cups > 20 fluid ounces (compared without converting). Correction: 2 cups = 16 fluid ounces, so 2 cups < 20 fluid ounces.
- Mistake: 3 pints = 6 (forgot the unit). Correction: 3 pints = 6 cups.
Always ask yourself: Am I going from a larger unit to a smaller unit, or from a smaller unit to a larger unit? This will help you choose the correct operation.
Practice with mixed units
Sometimes a measurement includes more than one unit, such as 2 gallons and 3 quarts. To convert or compare mixed units, you can change the larger unit to the smaller unit and then add. This gives you a single measurement in one unit.
- Convert 2 gallons 3 quarts to quarts. 2 gallons = 8 quarts. 8 quarts + 3 quarts = 11 quarts. So, 2 gallons 3 quarts = 11 quarts.
- Convert 1 quart 2 cups to cups. 1 quart = 4 cups. 4 cups + 2 cups = 6 cups. So, 1 quart 2 cups = 6 cups.
- Compare 1 gallon 2 quarts and 6 quarts. 1 gallon 2 quarts = 6 quarts. 6 quarts = 6 quarts. So, they are equal.
When you convert mixed units, always convert the largest unit first. Then add the remaining units.
Why converting and comparing volume matters
Converting and comparing customary units of volume is an important skill for everyday life. It helps you cook, shop, measure medicine, and complete science experiments. It also builds a strong foundation for understanding the metric system and other measurement systems in later grades.
- Cooking: A recipe might call for 2 quarts of broth, but you only have a 1-gallon container. You need to know if it will fit.
- Shopping: A store sells juice in 64-fluid-ounce bottles. You want to know how many cups that is.
- Science: A science experiment requires 500 milliliters, but you only have a cup measure. You need to convert.
Mastering customary units now will help you later when you learn about the metric system. The same ideas of multiplying and dividing apply.
Common Core alignment: CCSS.MATH.CONTENT.4.MD.A.1 – Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
Notes for teachers
All content is 100% free, student-safe, aligned with CCSS.MATH.CONTENT.4.MD.A.1. Use it for whole-class instruction, independent practice, or homework.