Ray's New Practical Arithmetic · Arts. 102–105 · Unit 10: Fractions

54. Reduction of fractions, Cases I–III

Goal: Your child changes whole numbers and mixed numbers to improper fractions and improper fractions back to whole or mixed numbers.

⏱ About 35 minutes · 7 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 fractions, Case I (an integer to an improper fraction), Case II (a mixed number to an improper fraction), and Case III (an improper fraction to a whole or mixed number), each with a rule and problems.

The lesson, step by step

  1. Warm-up

    Mental: halves in 3 apples? (6.) Thirds in 2 apples? (6.) Fourths in 3 dollars? (12.)

  2. The idea

    Read:

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

    Case I:

    To reduce an integer to an improper fraction, having a given denominator.

    Multiply the integer by the given denominator; under the product write the denominator.

  3. Case II

    Work the book's example: In 3½ apples, how many halves? 3 apples are 6 halves, and 1 half more makes 7 halves.

    6 halves and 1 half are 7 halves.

    SayMultiply the whole number by the denominator and add the numerator.

  4. Case III

    Read:

    To reduce an improper fraction to an integer or mixed number.

    Divide the numerator by the denominator; the quotient will be the integer or the mixed number.

    Example: 9/4 of a dollar: 9 ÷ 4 = 2, with 1 fourth over: 2¼ dollars.

  5. Guided practice

    Together, from the Case I list:

    Reduce 4 to sevenths.

    Then two from Case II and two from Case III.

  6. Independent practice

    Your child does about eight problems from each case.

  7. Check and wrap-up

    Answers are printed beside the problems. Mental: 2½ = how many halves? 11/3 = what mixed number?

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