Ray's New Elementary Algebra · Arts. 133–136 · Unit 3: Chapter III: Algebraic fractions

20. Common and least common denominators

Goal: Your student rewrites fractions with a common denominator, and with the least common denominator.

⏱ About 40 minutes · 7 steps

Open it at the Internet Archive ↗

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 IV: the rule for a common denominator (multiply each fraction by all the other denominators), then the least common denominator using the L.C.M., and how to write an entire quantity or a fraction over a given denominator. Answers are printed.

The lesson, step by step

  1. Warm-up

    Ask: Add 1/4 and 1/6 the way you learned in arithmetic. What denominator did you use?

  2. A common denominator

    Read Art. 133 and the rule:

    Multiply both terms of each fraction by the product of all the denominators except its own.

    Example 1: a/b and c/d become ad/bd and bc/bd.

  3. The least common denominator

    Read Art. 134 and the rule:

    1. Find the least common multiple of all the denominators; this will be the common denominator.

    2. Divide the least common multiple by the first of the given denominators, and multiply the quotient by the first of the given numerators; the product will be the first of the required numerators.

    Work the book's example: m/b, n/bc and r/cd have L.C.M. bcd, giving mcd/bcd, nd/bcd and br/bcd.

  4. Guided practice

    Your student does exercises 3 and 4 of Art. 133 and exercise 2 of Art. 134 while you watch, reducing each fraction first.

  5. Given denominators

    Read Arts. 135 and 136.

    Divide the given denominator by the denominator of the fraction, and multiply both terms by the quotient.

    Example: reduce x to a fraction with denominator 4 (4x/4).

  6. Independent practice

    The remaining exercises of Arts. 133 to 136, checked against the printed answers.

  7. Wrap-up

    Ask: Why is the least common denominator better than just multiplying all the denominators?

Tip

Have your student say the L.C.M. aloud before writing any numerators. Most mistakes come from rushing past it.

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 ↗.

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