Ray's New Practical Arithmetic · Arts. 151–153 · Unit 12: Decimal Fractions (continued)

71. Decimal compound numbers (measures)

Goal: Your child changes a decimal of one measure to a lower measure by multiplying, to a higher measure by dividing, and finds the value of a decimal "in integers" (for example .3125 bu. = 1 pk. 2 qt.).

⏱ About 35 minutes · 6 steps

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You'll need

  • Paper and pencil, or a slate or small whiteboard

What's in the book

Page 186 starts Decimal Compound Numbers: Art. 151 (to a lower denomination) and Art. 152 (value in integers), each with a worked example. Page 187 has Art. 153 (to a higher denomination) and its problems. Answers are printed.

The lesson, step by step

  1. Warm-up

    Review the old tables the book uses here: 2 pints = 1 quart, 4 quarts = 1 gallon, 8 quarts = 1 peck, 4 pecks = 1 bushel, 3 ft. = 1 yd., 16½ ft. = 1 rod, 160 sq. rd. = 1 acre.

  2. The idea

    Two rules mirror each other:

    A decimal is reduced to a lower denomination by multiplication

    A decimal is reduced to a higher denomination by division

    SayGoing to smaller units, you get more of them, so multiply. Going to bigger units, divide.

  3. Work the book's examples

    Reduce .05 gal. to the decimal of a pint.

    .05 × 4 = .2 qt.; .2 × 2 = .4 pt.

    Find the value of .3125 bu. in integers.

    .3125 × 4 = 1.25 pk. Keep the 1 pk.; .25 × 8 = 2 qt. Answer 1 pk. 2 qt.

    Reduce .64 pt. to the decimal of a gallon.

    .64 ÷ 2 = .32 qt.; .32 ÷ 4 = .08 gal.

  4. Guided practice

    Do one from each article together: .035 pk. to the decimal of a pint (page 186); .75 yd. in integers (page 186).

  5. Independent practice and check

    Your child works the rest of the problems on pages 186–187. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.

  6. Mental-math wrap-up

    Aloud: .5 gal. = ? qt.; .25 bu. = ? pk.; .5 ft. = ? in.; 6 in. = what decimal of a foot?

Tip

Old measures note: the book uses the U.S. measures of its day, plus troy weight (pounds of 12 ounces, used for precious metals). Keep a small table of these on the table while working.

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