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Divide. Simplify your answer.\newline12v2w20v2w2÷12vw2\frac{12v^2w}{20v^2w^2} \div 12vw^2

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Full solution

Q. Divide. Simplify your answer.\newline12v2w20v2w2÷12vw2\frac{12v^2w}{20v^2w^2} \div 12vw^2
  1. Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, (12v2w/20v2w2)÷(12vw2)(12v^2w/20v^2w^2) \div (12vw^2) becomes (12v2w/20v2w2)×(1/12vw2)(12v^2w/20v^2w^2) \times (1/12vw^2).
  2. Simplify by canceling factors: Simplify the expression by canceling out common factors. In the first fraction, v2wv^2w can be canceled from the numerator and denominator, and in the second fraction, vw2vw^2 can be canceled from the numerator and denominator. This gives us (1220w)×(112v)(\frac{12}{20w}) \times (\frac{1}{12v}).
  3. Further reduce fractions: Further simplify the expression by reducing the fractions. The number 1212 in the numerator and denominator can be canceled out, and the fraction 1220\frac{12}{20} can be reduced to 35\frac{3}{5} by dividing both the numerator and denominator by 44. This results in (35w)×(1v)\left(\frac{3}{5}w\right) \times \left(\frac{1}{v}\right).
  4. Multiply simplified fractions: Multiply the simplified fractions. Multiplying (35w)(\frac{3}{5w}) by (1v)(\frac{1}{v}) gives us 35vw\frac{3}{5vw}.

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