1Cademy - Finding the Quotient $$\frac{24a^5b^3}{48ab^4}$$

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Dividing Monomials

Example

Finding the Quotient $\frac{24a^5b^3}{48ab^4}$

Divide two monomials whose numerical coefficients simplify to a fraction rather than an integer: $\frac{24a^5b^3}{48ab^4}$ . Step 1 — Separate using fraction multiplication. Split into three fractions: $\frac{24}{48} \cdot \frac{a^5}{a} \cdot \frac{b^3}{b^4}$ . Step 2 — Simplify each part. For the coefficients: $\frac{24}{48} = \frac{1}{2}$ (the numerator coefficient is smaller than the denominator coefficient, so the result is a proper fraction). For $a$ : since $5 > 1$ , $\frac{a^5}{a} = a^{5-1} = a^4$ . For $b$ : since $4 > 3$ , $\frac{b^3}{b^4} = \frac{1}{b^{4-3}} = \frac{1}{b}$ . Step 3 — Combine. Multiply: $\frac{1}{2} \cdot a^4 \cdot \frac{1}{b} = \frac{a^4}{2b}$ . The quotient is $\frac{a^4}{2b}$ . This example demonstrates that when the numerator's coefficient is smaller than the denominator's, their quotient simplifies to a proper fraction, and its denominator becomes a numerical factor in the final expression's denominator.

Updated 2026-06-29

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OpenStax Elementary Algebra

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