1Cademy - Finding the Quotient $$\frac{45a^2b^3}{-5ab^5}$$

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Dividing Monomials

Example

Finding the Quotient $\frac{45a^2b^3}{-5ab^5}$

Divide two monomials that each contain two variables and a negative denominator: $\frac{45a^2b^3}{-5ab^5}$ .

Step 1 — Separate using fraction multiplication. Break the fraction into three parts — one for the coefficients and one for each variable: $\frac{45}{-5} \cdot \frac{a^2}{a} \cdot \frac{b^3}{b^5}$ .

Step 2 — Simplify each part. For the coefficients: $\frac{45}{-5} = -9$ (positive divided by negative gives a negative quotient). For $a$ : since $2 > 1$ , $\frac{a^2}{a} = a^{2-1} = a$ . For $b$ : since $5 > 3$ , $\frac{b^3}{b^5} = \frac{1}{b^{5-3}} = \frac{1}{b^2}$ .

Step 3 — Combine. Multiply: $-9 \cdot a \cdot \frac{1}{b^2} = -\frac{9a}{b^2}$ .

The quotient is $-\frac{9a}{b^2}$ . This example introduces two additional complications beyond single-variable division: dividing by a negative coefficient (which makes the result negative) and having a variable whose larger exponent is in the denominator (which places that variable below the fraction bar in the final answer).

Updated 2026-04-21

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OpenStax Elementary Algebra

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