Divide. Simplify your answer. 12v^2w/20v^2w^2 ÷ 12vw^2 ______

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, (12v^2w/20v^2w^2) ÷ (12vw^2) becomes (12v^2w/20v^2w^2) × (1/12vw^2).Simplify by canceling factors: Simplify the expression by canceling out common factors. In the first fraction, v^2w can be canceled from the numerator and denominator, and in the second fraction, vw^2 can be canceled from the numerator and denominator. This gives us (12/20w) × (1/12v).Further reduce fractions: Further simplify the expression by reducing the fractions. The number 12 in the numerator and denominator can be canceled out, and the fraction 12/20 can be reduced to 3/5 by dividing both the numerator and denominator by 4. This results in (3/5w) × (1/v).Multiply simplified fractions: Multiply the simplified fractions. Multiplying (3/5w) by (1/v) gives us 3/(5vw).

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Algebra 1

Multiply and divide rational expressions

Full solution

Q. Divide. Simplify your answer.

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\frac{12v^2w}{20v^2w^2} \div 12vw^2

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, $(12v^2w/20v^2w^2) \div (12vw^2)$ becomes $(12v^2w/20v^2w^2) \times (1/12vw^2)$ .
Simplify by canceling factors: Simplify the expression by canceling out common factors. In the first fraction, $v^2w$ can be canceled from the numerator and denominator, and in the second fraction, $vw^2$ can be canceled from the numerator and denominator. This gives us $(\frac{12}{20w}) \times (\frac{1}{12v})$ .
Further reduce fractions: Further simplify the expression by reducing the fractions. The number $12$ in the numerator and denominator can be canceled out, and the fraction $\frac{12}{20}$ can be reduced to $\frac{3}{5}$ by dividing both the numerator and denominator by $4$ . This results in $\left(\frac{3}{5}w\right) \times \left(\frac{1}{v}\right)$ .
Multiply simplified fractions: Multiply the simplified fractions. Multiplying $(\frac{3}{5w})$ by $(\frac{1}{v})$ gives us $\frac{3}{5vw}$ .