Question

After completing the fraction division StartFraction 7 Over 3 EndFraction divided by StartFraction 2 Over 9 EndFraction, Bai used the multiplication below to check his work.

StartFraction 21 Over 2 EndFraction times StartFraction 2 Over 9 EndFraction = StartFraction 42 Over 18 EndFraction = StartFraction 7 Over 3 EndFraction

Which is the most accurate description of Bai’s work?
Bai found the correct quotient and checked his work using multiplication correctly.
Bai found the correct quotient but checked his work using multiplication incorrectly.
Bai found an incorrect quotient but checked his work using multiplication correctly.
Bai found an incorrect quotient and checked his work using multiplication incorrectl

Answer 1

To assess Bai's work, we first need to compute the division of the fractions:

\[
\frac{7}{3} \div \frac{2}{9}
\]

To divide by a fraction, we multiply by its reciprocal:

\[
\frac{7}{3} \times \frac{9}{2} = \frac{7 \times 9}{3 \times 2} = \frac{63}{6} = \frac{21}{2}
\]

Now, according to Bai's multiplication check, he multiplied \(\frac{21}{2}\) by \(\frac{2}{9}\):

\[
\frac{21}{2} \times \frac{2}{9} = \frac{21 \times 2}{2 \times 9} = \frac{42}{18}
\]

Now we simplify \(\frac{42}{18}\):

\[
\frac{42 \div 6}{18 \div 6} = \frac{7}{3}
\]

This is indeed equal to the original dividend.

Overall, Bai's calculations yield that he found the correct quotient \(\frac{21}{2}\) for the division, and his multiplication check is also correct, as it verifies that multiplying his quotient by the divisor gives back the dividend.

Therefore, the most accurate description of Bai's work is:

**Bai found the correct quotient and checked his work using multiplication correctly.**