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

Question

Two-thirds divided by StartFraction 4 Over 5 EndFraction. Two-thirds times StartFraction 4 Over 5 EndFraction = StartFraction 8 Over 15 EndFraction

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

Answer 1

The most accurate description of Arianna's work is:

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

In her work, she correctly set up the fraction division but mistakenly multiplied the dividend (two-thirds) by the divisor (four-fifths) rather than multiplying the dividend by the reciprocal of the divisor. The correct operation should have been:

\[ \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} \]

This would lead to a different result.