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Divide. Simplify your answer.\newline5q13q2r÷13qr\frac{5q}{13q^2r} \div 13qr

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Q. Divide. Simplify your answer.\newline5q13q2r÷13qr\frac{5q}{13q^2r} \div 13qr
  1. Write as multiplication problem: Write the division problem as a multiplication problem by taking the reciprocal of the second fraction.\newlineWe have the division problem: 5q13q2r÷13qr\frac{5q}{13q^2r} \div 13qr. To divide by a fraction, we multiply by its reciprocal. So, we rewrite the problem as 5q13q2r×113qr\frac{5q}{13q^2r} \times \frac{1}{13qr}.
  2. Simplify by multiplying: Simplify the expression by multiplying the numerators and denominators.\newlineNow we multiply the numerators together and the denominators together: (5q×1)/(13q2r×13qr)(5q \times 1) / (13q^2r \times 13qr).
  3. Simplify denominators: Simplify the multiplication of the denominators.\newlineWe have 13q2r×13qr=13×13×q2×q×r×r=169q3r213q^2r \times 13qr = 13 \times 13 \times q^2 \times q \times r \times r = 169q^3r^2.
  4. Simplify numerators: Simplify the multiplication of the numerators.\newlineWe have 5q×1=5q5q \times 1 = 5q.
  5. Combine numerator and denominator: Combine the simplified numerator and denominator. Now we have 5q169q3r2\frac{5q}{169q^3r^2}.
  6. Cancel common factors: Cancel out the common factors in the numerator and denominator. The qq in the numerator and one qq in the denominator cancel out, leaving us with 5169q2r2.\frac{5}{169q^2r^2}.
  7. Check for further simplification: Check for any further simplification.\newlineThe fraction 5169q2r2\frac{5}{169q^2r^2} cannot be simplified further since 55 and 169169 have no common factors other than 11, and there are no more common variables to cancel out.

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