Divide. Simplify your answer. 12r^2/16q^2r ÷ 16q^2r^2 ______

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, (12r^2/16q^2r) ÷ (16q^2r^2) becomes (12r^2/16q^2r) × (1/16q^2r^2).Simplify first fraction: Simplify the first fraction by canceling out common factors. The r in the numerator and denominator can be reduced, and 12/16 can be simplified to 3/4. So, (12r^2/16q^2r) becomes (3r/4q^2).Multiply by reciprocal: Now multiply the simplified first fraction by the reciprocal of the second fraction. So, (3r/4q^2) × (1/16q^2r^2) becomes (3r × 1)/(4q^2 × 16q^2r^2).Multiply numerators and denominators: Multiply the numerators and then the denominators. So, (3r × 1)/(4q^2 × 16q^2r^2) becomes 3r/(64q^4r^2).Simplify resulting fraction: Simplify the resulting fraction by canceling out common factors. The r in the numerator and one r in the denominator can be reduced, and we are left with 3/(64q^4r).

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Math Problems

Algebra 1

Multiply and divide rational expressions

Full solution

Q. Divide. Simplify your answer.

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\frac{12r^2}{16q^2r} \div \frac{16q^2r^2}{1}

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, $(\frac{12r^2}{16q^2r}) \div (16q^2r^2)$ becomes $(\frac{12r^2}{16q^2r}) \times (\frac{1}{16q^2r^2})$ .
Simplify first fraction: Simplify the first fraction by canceling out common factors. The $r$ in the numerator and denominator can be reduced, and $\frac{12}{16}$ can be simplified to $\frac{3}{4}$ . So, $(\frac{12r^2}{16q^2r})$ becomes $(\frac{3r}{4q^2})$ .
Multiply by reciprocal: Now multiply the simplified first fraction by the reciprocal of the second fraction. So, $\frac{3r}{4q^2} \times \frac{1}{16q^2r^2}$ becomes $\frac{3r \times 1}{4q^2 \times 16q^2r^2}$ .
Multiply numerators and denominators: Multiply the numerators and then the denominators. So, $(3r \times 1)/(4q^2 \times 16q^2r^2)$ becomes $3r/(64q^4r^2)$ .
Simplify resulting fraction: Simplify the resulting fraction by canceling out common factors. The $r$ in the numerator and one $r$ in the denominator can be reduced, and we are left with $\frac{3}{64q^4r}$ .