Customary Unit Conversions Involving Mixed Numbers and Fractions

Customary unit conversions get trickier when the measurements involve mixed numbers (like 3¼ feet) or fractions (like ½ pound). The process is the same as whole-number conversions, but you multiply or divide with fractions instead of whole numbers. Mastering this skill saves time on the GED test and in everyday life.

What Are Customary Unit Conversions with Fractions?

When a measurement is expressed as a mixed number or fraction, you still multiply to convert to a smaller unit and divide (or use the reciprocal) to convert to a larger unit. The conversion factors are the same as always; only the arithmetic involves fractions.

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Key Conversion Factors (Review)

Length

• 1 \(\color{blue}{\text{ ft } = 12}\) in  •  1 \(\color{blue}{\text{ yd } = 3}\) ft  •  1 \(\color{blue}{\text{ mi } = 5}\),280 ft

Weight

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

Capacity

• 1 \(\color{blue}{c = 8}\) fl oz  •  1 \(\color{blue}{\text{ pt } = 2}\) c  •  1 \(\color{blue}{\text{ qt } = 2}\) pt  •  1 \(\color{blue}{\text{ gal } = 4}\) qt

Rules for Converting with Fractions and Mixed Numbers

To convert to a smaller unit: multiply

Multiply the mixed number or fraction by the conversion factor.

• 3¼ ft to inches: 3¼ × \(\color{blue}{12 = (\frac{13}{4}) \times 12 = \frac{156}{4}}\) = 39 in
• ¾ lb to ounces: ¾ × \(\color{blue}{16 = \frac{12}{4} \times 1}\) = 12 oz

To convert to a larger unit: divide (or multiply by the reciprocal)

• 9 in to feet: \(\color{blue}{9 \div 12 = \frac{9}{12}}\) = ¾ ft
• 10 oz to pounds: \(\color{blue}{10 \div 16 = \frac{10}{16}}\) = \(\color{blue}{\frac{5}{8}}\) lb

Step-by-Step Summary

1. Identify the conversion factor (e.g., 1 \(\color{blue}{\text{ ft } = 12}\) in).
2. Convert any mixed number to an improper fraction (a \(\color{blue}{\frac{b}{c}}\) → \(\color{blue}{\frac{(\text{ ac } + b)}{c}}\)).
3. To get a smaller unit: multiply by the conversion factor.
4. To get a larger unit: divide by the conversion factor (multiply by its reciprocal).
5. Simplify the result; convert back to a mixed number if needed.

Watch: Customary Conversions with Mixed Numbers (Video Lesson)

This video provides a quick, memorable method for converting customary units when mixed numbers are involved:

Worked Examples

Example 1: Convert 2½ gallons to quarts.

2½ × \(\color{blue}{4 = (\frac{5}{2}) \times 4 = \frac{20}{2}}\) = 10 qt

Example 2: Convert 3¼ yards to feet.

3¼ × \(\color{blue}{3 = (\frac{13}{4}) \times 3 = \frac{39}{4} = 9}\)¾ ft = 9 ft 9 in

Example 3: Convert 18 oz to pounds (as a fraction).

\(\color{blue}{18 \div 16 = \frac{18}{16} = \frac{9}{8}}\) = 1⅛ lb

Example 4: A board is 5½ ft long. How many inches is that?

5½ × \(\color{blue}{12 = (\frac{11}{2}) \times 12 = \frac{132}{2}}\) = 66 in

More Practice: Unit Conversion Review (Video)

Khan Academy covers unit conversion in this clear Pre-Algebra lesson:

Exercises

1. Convert 4½ feet to inches.
2. Convert 2¾ pounds to ounces.
3. Convert 30 in to feet (as a fraction or mixed number).
4. Convert 3½ gallons to quarts.
5. A bag weighs 2¼ lb. How many ounces is that?
6. Convert 20 oz to pounds as a mixed number.

Answers

1. \(\color{blue}{(\frac{9}{2}) \times 12 = \frac{108}{2}}\) = 54 in
2. \(\color{blue}{(\frac{11}{4}) \times 16 = \frac{176}{4}}\) = 44 oz
3. \(\color{blue}{30 \div 12 = \frac{30}{12} = \frac{5}{2}}\) = 2½ ft
4. \(\color{blue}{(\frac{7}{2}) \times 4 = \frac{28}{2}}\) = 14 qt
5. \(\color{blue}{(\frac{9}{4}) \times 16 = \frac{144}{4}}\) = 36 oz
6. \(\color{blue}{20 \div 16 = \frac{5}{4}}\) = 1¼ lb

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Frequently Asked Questions

Do I need to convert a mixed number before multiplying?

Yes. Convert the mixed number to an improper fraction first (multiply the whole number by the denominator, add the numerator, keep the same denominator), then multiply by the conversion factor. This prevents arithmetic errors.

How do I convert a fraction of a unit back to mixed customary form?

For example, ¾ ft: ¾ × \(\color{blue}{12 = 9}\) in, so ¾ \(\color{blue}{\text{ ft } = 9}\) in. For 2¼ ft: the whole feet stay as feet; multiply just the fraction part by 12: ¼ × \(\color{blue}{12 = 3}\) in, giving 2 ft 3 in.

Are these conversions the same for both the customary and metric systems?

The process (multiply to go smaller, divide to go larger) is the same, but the conversion factors differ. Metric uses powers of 10, which makes arithmetic easier. Customary uses factors like 12, 16, and 4, which require more care with fractions.

Related Topics

• Converting, Comparing, Adding and Subtracting Mixed Customary Units
• Using Properties to Convert Traditional and Metric Units
• Multiplying Mixed Numbers
• Dividing Mixed Numbers
• Word Problems Involving Volume of Cubes and Rectangular Prisms