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Divide. Simplify your answer.\newline12r216q2r÷16q2r21\frac{12r^2}{16q^2r} \div \frac{16q^2r^2}{1}

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Full solution

Q. Divide. Simplify your answer.\newline12r216q2r÷16q2r21\frac{12r^2}{16q^2r} \div \frac{16q^2r^2}{1}
  1. Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, (12r216q2r)÷(16q2r2)(\frac{12r^2}{16q^2r}) \div (16q^2r^2) becomes (12r216q2r)×(116q2r2)(\frac{12r^2}{16q^2r}) \times (\frac{1}{16q^2r^2}).
  2. Simplify first fraction: Simplify the first fraction by canceling out common factors. The rr in the numerator and denominator can be reduced, and 1216\frac{12}{16} can be simplified to 34\frac{3}{4}. So, (12r216q2r)(\frac{12r^2}{16q^2r}) becomes (3r4q2)(\frac{3r}{4q^2}).
  3. Multiply by reciprocal: Now multiply the simplified first fraction by the reciprocal of the second fraction. So, 3r4q2×116q2r2\frac{3r}{4q^2} \times \frac{1}{16q^2r^2} becomes 3r×14q2×16q2r2\frac{3r \times 1}{4q^2 \times 16q^2r^2}.
  4. Multiply numerators and denominators: Multiply the numerators and then the denominators. So, (3r×1)/(4q2×16q2r2)(3r \times 1)/(4q^2 \times 16q^2r^2) becomes 3r/(64q4r2)3r/(64q^4r^2).
  5. Simplify resulting fraction: Simplify the resulting fraction by canceling out common factors. The rr in the numerator and one rr in the denominator can be reduced, and we are left with 364q4r\frac{3}{64q^4r}.

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