6.3.1 Dividing by Monomials

Algebra 16.3.1 Dividing by Monomials

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Warm Up

In this unit, remember to double click on mathematical expressions/equations to enlarge, if needed.

Look at the division expression $- 54 a^{6} b^{3} \div 9 a^{4} b^{2}$ .

Rewrite the division expression as a fraction.

Compare your answer:

Fraction form: $\frac{- 54 a^{6} b^{3}}{9 a^{4} b^{2}}$

Since we have a monomial divided by a monomial, we can rewrite the fraction as a product of several fractions where the factors in the numerator and denominator “match.”

Compare your answer:

$\frac{- 54}{9} \cdot \frac{a^{6}}{a^{4}} \cdot \frac{b^{3}}{b^{2}}$

Now we can simplify the fraction multiplication and use the Quotient Property to divide.

Compare your answer:

$\frac{- 54}{9} \cdot \frac{a^{6}}{a^{4}} \cdot \frac{b^{3}}{b^{2}} = - 6 \cdot a^{2} \cdot b$ So $- 54 a^{6} b^{3} \div 9 a^{4} b^{2} = - 6 a^{2} b$ .

For 4 - 6, divide a polynomial by a monomial. Divide each term of the polynomial by the monomial.

Find the quotient: $(18 x^{3} y - 36 x y^{2}) \div (- 3 x y)$ .

Compare your answer:

Step 1 - Rewrite as a fraction.

$\frac{18 x^{3} y - 36 x y^{2}}{- 3 x y}$

Step 2 - Divide each term by the divisor.

$\frac{18 x^{3} y}{- 3 x y} - \frac{36 x y^{2}}{- 3 x y}$

Step 3 - Simplify.

Find the qoutient: $(48 a^{2} b^{2} + 30 a b) \div (6 a b)$ .

Compare your answer:

$8 a b + 5$

Find the quotient: $(- 72 g^{4} h^{6} - 45 g^{7} h^{3}) \div (9 g^{3} h^{3})$ .

Compare your answer:

$- 8 g h^{3} - 5 g^{4}$

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
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- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
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- Section URL: https://openstax.org/books/algebra-1/pages/6-3-1-dividing-by-monomials

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