Ray's New Higher Arithmetic · Art. 142 · Unit 8: Common Fractions
35. Multiplying fractions
Goal: Your student multiplies a fraction by a whole number, a whole number by a fraction, and a fraction by a fraction, using cancellation.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Multiplication of fractions in three cases, the rule (numerators together, denominators together), remarks on mixed numbers, worked examples (6 × 3/4, 8 × 3/5), and two sets of examples including cloth and tape prices. Answers are printed.
The lesson, step by step
Warm-up
Mental: 3 × 1/4; half of 3/4; 2/3 of 9.
The idea
Read:
Multiplication of Fractions is finding the product when either or when each of the factors is a fractional number.
The book shows that all three cases come to one rule:
Multiply the numerators together for the numerator of the product, and the denominators for the denominator of the product.
Work the book's examples
6 × 3/4 = 18/4 = 4½. 8 × 3/5: one fifth of 8 is 8/5, so three fifths is 24/5 = 4⅘.
Mixed numbers
Read:
In finding the product of two mixed numbers, it is generally best to reduce them to improper fractions
Work 2½ × 3⅓ = 5/2 × 10/3 = 50/6 = 8⅓. Cancel before multiplying when you can.
Independent practice
Your student works the examples for practice, including the cloth and tape problems near the end.
Check
Answers are printed.
Wrap-up
Ask: Why is 3/4 × 2/3 smaller than both? (Taking part of a part.)
Tip
The scan's small printed fractions are often hard to read. Keep the paper book or a clear copy of the page open when your student works the examples.