Customary unit conversions involving fractions and mixed numbers

Students convert between customary units when the answer is not always a whole number, then simplify.

• Length: 36 inches = 1 yard
• Weight: 16 ounces = 1 pound
• Capacity: 2 pints = 1 quart, 4 cups = 1 quart

The worked answers multiply by a unit fact written as a fraction, for example 18 inches × 1 yard / 36 inches. This is ratio reasoning to convert measurement units, standard 6.RP.A.3.d, building on the conversions of 5.MD.A.1.

Print both pages and keep the answer page aside. Before the first problem, write the three unit facts above on a sticky note so your child does not have to remember them.

• Decide first: is the new unit bigger or smaller? A bigger unit means fewer of them, so divide; a smaller unit means more of them, so multiply.
• Write the conversion as a fraction and cancel the units.
• Simplify the result and write it as a proper fraction, a whole number or a mixed number.

• Multiplying when they should divide: 18 inches becomes 648 yards instead of 1/2 yard. Ask whether the answer should be bigger or smaller.
• Wrong unit fact: using 12 instead of 36 inches in a yard, or 8 instead of 16 ounces in a pound.
• Unsimplified answers: 18/36 left as it is instead of 1/2.

When these four problems feel easy, move to converting and comparing metric units, then try the temperature sheets in the series.