Ray's New Elementary Algebra · Arts. 139–140 · Unit 3: Chapter III: Algebraic fractions
22. Multiplying fractions
Goal: Your student multiplies fractions by entire quantities and by fractions, canceling common factors first.
You'll need
- The book, open to the page
- Pencil and plenty of paper (or a whiteboard)
- A card to cover printed answers
What's in the book
Case VI: a fraction times an entire quantity (two ways), exercises 1 to 11, then a fraction times a fraction, with remarks on canceling and exercises 1 to 11. Answers are printed.
The lesson, step by step
Warm-up
Ask: What is 2/3 of 6? What is 3/4 × 2/5?
Times an entire quantity
Read Art. 139.
Multiply the numerator by the entire quantity, and write the product over the denominator.
And the shortcut:
we should always divide the denominator of the fraction by the entire quantity, when it can be done without a remainder.
Guided practice
Your student does exercises 1 and 2 of Art. 139. Read the Remark after exercise 9: a fraction times its own denominator gives the numerator.
Fraction times fraction
Read Art. 140.
Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Read Remark 3 and the two worked examples of canceling before multiplying. In the second, a² − b² is factored so that a + b cancels.
Guided practice
Exercises 1 and 2 of Art. 140, with your student canceling first and multiplying only what is left.
Independent practice
The remaining exercises of Arts. 139 and 140, checked against the printed answers.
Wrap-up
Ask: Why is it easier to cancel before multiplying than after?
Tip
Factor every numerator and denominator completely before canceling. Writing the factors out is not wasted time.
Answers to the book's problems
The book prints the answer after each exercise.
Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in the Key ↗.