Ray's New Elementary Algebra · Arts. 73–78 · Unit 1: Chapter I: Fundamental rules

9. Dividing monomials, and a polynomial by a monomial

Goal: Your student divides one monomial by another (divide the numbers, subtract the exponents, use the rule of signs) and divides each term of a polynomial by a monomial.

⏱ About 40 minutes · 8 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

Division defined, the rule for dividing monomials with its rule of signs, the cases where exact division is impossible, and dividing a polynomial by a monomial. Answers are printed.

The lesson, step by step

  1. Warm-up

    Ask: 3a times what makes 12a²? (4a.) Say: Division undoes multiplication; that is the whole idea of today.

  2. Division defined

    Read Arts. 73 and 74.

    Division, in Algebra, is the process of finding how many times one algebraic quantity is contained in another.

    Do the first oral questions together:

    How many times is a contained in 6a?

    Is 2 contained in 4a?

    (6 times; 2a times.)

  3. The rule for monomials

    Read Art. 75.

    Like signs give plus, and unlike signs give minus.

    Divide the coefficient of the dividend by that of the divisor

    SayThen subtract the exponent of each letter in the divisor from its exponent in the dividend. a⁵ ÷ a² = a³, because a³ × a² = a⁵.

  4. Guided practice

    Cover the answers. Your student works these while you watch:

    13. Divide —18a²x by —6ax.

    Then −12a³b by 4ab (−3a²). Check each by multiplying back.

  5. When it can't be done exactly

    Read Art. 76. Ask: Can 3a be divided exactly by b? (No; we can only write 3a/b.)

  6. Polynomial by monomial

    Read Art. 78.

    Divide each term of the dividend by the divisor, according to the rule for the division of monomials.

    Work together:

    1. Divide 6x+12y by 3

    3. Divide 21a+35b by —7. . . .

    (2x + 4y; −3a − 5b.)

  7. Independent practice

    Art. 74 and 75 exercises 1 to 18 and Art. 78 exercises 1 to 8 (the optional ones too, if time allows). Check each against the printed answer, and check two by multiplying back.

  8. Wrap-up

    Your student explains why a² ÷ a² is 1 and a² ÷ a is a.

Tip

Multiplying back (quotient × divisor = dividend) is the best check in this lesson. Make it automatic.

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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