Rashid solved a fraction division problem using the rule “multiply by the reciprocal.” His work is shown below.

Question

Three-fourths divided by 9. Three-fourths times StartFraction 1 Over 9 EndFraction = StartFraction 3 Over 36 EndFraction or StartFraction 1 Over 12 EndFraction

Which is the most accurate description of Rashid’s work?
Rashid solved the problem correctly.
Rashid multiplied the dividend by the divisor instead of finding the reciprocal.
Rashid multiplied the denominators instead of finding a common denominator.
Rashid multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Answer 1

The most accurate description of Rashid’s work is:

Rashid multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

In his work, Rashid correctly started with "three-fourths divided by 9," which he should have expressed as \( \frac{3}{4} \div 9 \). According to the rule of "multiply by the reciprocal," he should have multiplied \( \frac{3}{4} \) by the reciprocal of 9 (which is \( \frac{1}{9} \)), not the reciprocal of the dividend. Instead, he mistakenly represented 9 as \( \frac{1}{9} \), and his work does not show he properly handled the division by multiplying by the reciprocal of the divisor.

Correctly, it should have been:

\[ \frac{3}{4} \div 9 = \frac{3}{4} \times \frac{1}{9} = \frac{3}{36} = \frac{1}{12} \]

Rashid's answer is correct, but the description of his method is inaccurate as he misidentified what he multiplied.