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 division of fractions, the correct approach is to multiply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor). In this case, the correct operation for $\frac{3}{4}÷9$ should involve multiplying $\frac{3}{4}$ by $\frac{1}{9}$ (the reciprocal of 9). However, it seems that he may have treated the divisor incorrectly in the reciprocal step and ended up with calculations that don't align with the proper method.

So although he used the rule of multiplying by the reciprocal correctly, he didn't apply the correct reciprocal in relation to the question.