Ray's New Higher Arithmetic · Arts. 157–159 · Unit 9: Decimal Fractions

40. Changing decimals and common fractions

Goal: Your student changes decimals to common fractions in lowest terms, and common fractions to decimals.

⏱ About 35 minutes · 8 steps

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You'll need

  • The book
  • A slate, small whiteboard or scrap paper
  • A notebook and pencil

What's in the book

Reduction of decimals: Case I, a decimal to a common fraction (examples .24 and .12½), and Case II, a common fraction to a decimal (7/8 = .875), with a note on fractions that never end, and examples with printed answers.

The lesson, step by step

  1. Warm-up

    Mental: .5 as a fraction; 1/4 as a decimal.

  2. The idea

    Read:

    Reduction of decimals is changing their form without altering their value.

  3. Decimal to fraction

    Read:

    Write the decimal as a common fraction; then reduce the fraction to its lowest terms.

    Work the book's examples: .24 = 24/100 = 6/25. And .12½ = 12½/100 = 25/200 = 1/8.

  4. Fraction to decimal

    Read:

    Annex ciphers to the numerator and divide it by the denominator.

    Then point off as many decimal places in the quotient as there are ciphers annexed.

    Work 7/8: 7.000 ÷ 8 = .875.

  5. When it never ends

    The book notes that a fraction in lowest terms whose denominator has a prime factor other than 2 or 5

    can not be reduced exactly to a decimal.

    Try 1/3 and 1/6 and watch the figures repeat. (Circulating decimals come in a later chapter.)

  6. Independent practice

    Your student works the examples under both cases.

  7. Check

    Answers are printed; some are hard to read in the scan, so check fraction-to-decimal answers by dividing again.

  8. Wrap-up

    Ask: Will 3/40 make an ending decimal? (Yes: 40 = 2 × 2 × 2 × 5. It is .075.)

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