How to Convert, Compare, Add, and Subtract Mixed Customary Units?

How to convert, compare, add, and subtract mixed customary units, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

Mixed customary units combine a larger unit with a smaller one — for example, 3 feet 7 inches or 2 pounds 11 ounces. Working with these measurements means knowing the basic conversion facts, then applying them to compare values, or to add and subtract measurements in real-world problems. This lesson gives you the key facts and a clear method for every operation.

What Are Mixed Customary Units?

A mixed customary measurement expresses a quantity using two different units of the same type, such as 2 feet 5 inches (length) or 1 gallon 3 quarts (capacity). To work with them mathematically, you need the standard conversion facts:

Key Customary Conversion Facts

Length

• 1 foot \(\color{blue}{(\text{ ft }) = 12}\) inches (in)
• 1 yard \(\color{blue}{(\text{ yd }) = 3}\) \(\color{blue}{\text{ feet } = 36}\) inches
• 1 mile \(\color{blue}{(\text{ mi }) = 5}\),280 feet

Weight

• 1 pound \(\color{blue}{(\text{ lb }) = 16}\) ounces (oz)
• 1 \(\color{blue}{\text{ ton } = 2}\),000 pounds

Capacity

• 1 cup \(\color{blue}{(c) = 8}\) fluid ounces (fl oz)
• 1 pint \(\color{blue}{(\text{ pt }) = 2}\) cups
• 1 quart \(\color{blue}{(\text{ qt }) = 2}\) \(\color{blue}{\text{ pints } = 4}\) cups
• 1 gallon \(\color{blue}{(\text{ gal }) = 4}\) quarts

How to Convert Mixed Customary Units

Converting to a smaller unit (multiply)

Multiply the larger-unit part by the conversion factor, then add the smaller-unit part.

• 2 ft 5 in to inches: \(\color{blue}{2 \times 12 + 5 = 24 + 5}\) = 29 in
• 3 lb 6 oz to ounces: \(\color{blue}{3 \times 16 + 6 = 48 + 6}\) = 54 oz

Converting to a larger unit (divide)

Divide the total smaller units; the quotient is the larger part and the remainder is the smaller part.

• 43 in to feet and inches: \(\color{blue}{43 \div 12 = 3}\) remainder 7 → 3 ft 7 in
• 50 oz to pounds and ounces: \(\color{blue}{50 \div 16 = 3}\) remainder 2 → 3 lb 2 oz

Step-by-Step Summary

1. Convert: decide direction (smaller or larger), multiply or divide by the conversion factor.
2. Compare: convert both to the same unit, then compare numerically.
3. Add: add units column by column (larger units, then smaller); rename/carry if the smaller unit total exceeds the conversion factor.
4. Subtract: subtract column by column; borrow from the larger unit if needed.

Watch: Customary Conversions with Mixed Numbers (Video Lesson)

This video walks through customary conversions involving mixed numbers step by step:

Worked Examples

Example 1 (Convert): Convert 2.5 feet to inches.

\(\color{blue}{2.5 \times 12}\) = 30 inches

Example 2 (Add): Add 4 ft 9 \(\color{blue}{\text{ in } + 2}\) ft 8 in.

\(\color{blue}{9 + 8 = 17}\) in; 17 \(\color{blue}{\text{ in } = 1}\) ft 5 in (since 17 > 12)
\(\color{blue}{4 + 2 + 1 = 7}\) ft; answer = 7 ft 5 in

Example 3 (Subtract): Subtract 5 lb 6 \(\color{blue}{\text{ oz } – 2}\) lb 11 oz.

6 oz < 11 oz, so borrow 1 lb: 5 lb 6 \(\color{blue}{\text{ oz } = 4}\) lb 22 oz (since \(\color{blue}{16 + 6 = 22}\)).
\(\color{blue}{22 – 11 = 11}\) oz; \(\color{blue}{4 – 2 = 2}\) lb; answer = 2 lb 11 oz

Example 4 (Compare): Which is greater: 3 qt 1 pt or 7 pt?

3 qt 1 \(\color{blue}{\text{ pt } = 3 \times 2 + 1 = 7}\) pt; 7 \(\color{blue}{\text{ pt } = 7}\) pt. They are equal.

More Practice: Unit Conversions (Video)

Khan Academy explains unit conversion within the metric and customary systems:

Exercises

1. Convert 3 yd 2 ft to feet.
2. Add: 6 ft 8 \(\color{blue}{\text{ in } + 5}\) ft 7 in.
3. Subtract: 8 lb 4 \(\color{blue}{\text{ oz } – 3}\) lb 10 oz.
4. Which is greater: 2 gal 3 qt or 11 qt?
5. Convert 78 in to feet and inches.
6. Add: 2 gal 3 \(\color{blue}{\text{ qt } + 1}\) gal 2 qt.

Answers

1. \(\color{blue}{3 \times 3 + 2}\) = 11 ft
2. \(\color{blue}{8 + 7 = 15}\) \(\color{blue}{\text{ in } = 1}\) ft 3 in; \(\color{blue}{6 + 5 + 1 = 12}\) ft; 12 ft 3 in
3. Borrow: 8 lb 4 \(\color{blue}{\text{ oz } = 7}\) lb 20 oz; \(\color{blue}{20 – 10 = 10}\) oz; \(\color{blue}{7 – 3 = 4}\) lb; 4 lb 10 oz
4. 2 gal 3 \(\color{blue}{\text{ qt } = 2 \times 4 + 3 = 11}\) qt; 11 \(\color{blue}{\text{ qt } = 11}\) qt; equal
5. \(\color{blue}{78 \div 12 = 6}\) r 6; 6 ft 6 in
6. \(\color{blue}{3 + 2 = 5}\) \(\color{blue}{\text{ qt } = 1}\) gal 1 qt; \(\color{blue}{2 + 1 + 1 = 4}\) gal; 4 gal 1 qt

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Frequently Asked Questions

What are mixed units?

Mixed units describe one measurement using two sizes of the same kind of unit, such as 5 feet 4 inches, 3 pounds 9 ounces, or 2 gallons 1 quart. The larger unit counts the full groups and the smaller unit counts what is left over. To compare or calculate with them, you usually convert the whole amount into the smaller unit first.

How do you convert mixed customary units?

Multiply the larger unit by its conversion factor and add the smaller part. For example, 4 ft 7 in = 4 × 12 + 7 = 55 inches. To go back, divide: 55 ÷ 12 = 4 remainder 7, so 4 ft 7 in. The same method works for weight (1 lb = 16 oz) and capacity (1 gal = 4 qt).

How do you add and subtract mixed customary units?

Line up like units, add or subtract each column, and then regroup. For 2 lb 11 oz + 1 lb 9 oz, you get 3 lb 20 oz, and since 20 oz = 1 lb 4 oz, the answer is 4 lb 4 oz. When subtracting, borrow one larger unit if needed: 5 ft 2 in − 1 ft 8 in becomes 4 ft 14 in − 1 ft 8 in = 3 ft 6 in.

How do you convert customary units of length?

Use the length facts: 12 inches = 1 foot, 3 feet = 1 yard, 36 inches = 1 yard and 5,280 feet = 1 mile. Multiply when changing to a smaller unit and divide when changing to a larger one. For example, 4 yards = 4 × 3 = 12 feet, and 90 inches = 90 ÷ 12 = 7.5 feet, or 7 feet 6 inches.

How do you convert customary units of capacity?

Use the chain 1 gallon = 4 quarts, 1 quart = 2 pints, 1 pint = 2 cups and 1 cup = 8 fluid ounces. To change 3 quarts to cups, multiply 3 × 2 × 2 = 12 cups. To change 20 cups to quarts, divide by 4 to get 5 quarts. Writing the chain at the top of your paper keeps you from skipping a step.

Related Topics

• Customary Unit Conversions Involving Mixed Numbers and Fractions
• Using Properties to Convert Traditional and Metric Units
• Word Problems Involving Volume of Cubes and Rectangular Prisms
• Compare the Temperatures Above and Below Zero
• Rectangular Prisms