How to Convert, Compare, Add, and Subtract Mixed Customary Units?
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
- Convert: decide direction (smaller or larger), multiply or divide by the conversion factor.
- Compare: convert both to the same unit, then compare numerically.
- Add: add units column by column (larger units, then smaller); rename/carry if the smaller unit total exceeds the conversion factor.
- 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
- Convert 3 yd 2 ft to feet.
- Add: 6 ft 8 \(\color{blue}{\text{ in } + 5}\) ft 7 in.
- Subtract: 8 lb 4 \(\color{blue}{\text{ oz } – 3}\) lb 10 oz.
- Which is greater: 2 gal 3 qt or 11 qt?
- Convert 78 in to feet and inches.
- Add: 2 gal 3 \(\color{blue}{\text{ qt } + 1}\) gal 2 qt.
Answers
- \(\color{blue}{3 \times 3 + 2}\) = 11 ft
- \(\color{blue}{8 + 7 = 15}\) \(\color{blue}{\text{ in } = 1}\) ft 3 in; \(\color{blue}{6 + 5 + 1 = 12}\) ft; 12 ft 3 in
- 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
- 2 gal 3 \(\color{blue}{\text{ qt } = 2 \times 4 + 3 = 11}\) qt; 11 \(\color{blue}{\text{ qt } = 11}\) qt; equal
- \(\color{blue}{78 \div 12 = 6}\) r 6; 6 ft 6 in
- \(\color{blue}{3 + 2 = 5}\) \(\color{blue}{\text{ qt } = 1}\) gal 1 qt; \(\color{blue}{2 + 1 + 1 = 4}\) gal; 4 gal 1 qt
Frequently Asked Questions
What does “renaming” mean when adding customary units?
Renaming (also called carrying or regrouping) means converting extra smaller units into the next larger unit. For example, 15 inches becomes 1 foot 3 inches because \(\color{blue}{15 \div 12 = 1}\) remainder 3.
How do I subtract when the smaller unit is not enough?
Borrow 1 of the larger unit and convert it to smaller units. For example, if you have 3 ft 2 in and need to subtract 9 in, rewrite as 2 ft 14 in (borrowing 1 \(\color{blue}{\text{ ft } = 12}\) in), then subtract: \(\color{blue}{14 – 9 = 5}\), giving 2 ft 5 in.
Why do I need to know customary units for the GED?
The GED Math test includes real-world measurement problems that use both customary (U.S.) and metric units. Being comfortable converting and operating with both systems helps you tackle a broad range of applied math problems.
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