After completing the fraction division 8 divided by StartFraction 1 Over 6 EndFraction, Patel found a quotient of mc025-2.jpg. He then used the multiplication below to check his work.

Question

StartFraction 1 Over 48 EndFraction times 6 = StartFraction 1 Over 48 EndFraction times StartFraction 6 Over 1 EndFraction = StartFraction 6 Over 48 EndFraction = StartFraction 1 Over 8 EndFraction

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

Answer 1

To analyze Patel's work, let's break down the division and his multiplication check.

1. Division:

   • Patel computed \( 8 \div \frac{1}{6} \).
   • Dividing by a fraction is the same as multiplying by its reciprocal, so: \[ 8 \div \frac{1}{6} = 8 \times 6 = 48 \] So, the correct quotient is 48.

2. Checking Work via Multiplication:

   • Patel multiplied \( \frac{1}{48} \) by 6: \[ \frac{1}{48} \times 6 = \frac{6}{48} = \frac{1}{8} \] He seemed to be trying to show that \( \frac{1}{48} \) multiplied by 6 should yield \( \frac{1}{8} \) if the division was correct.

However, to check the division accurately, he should calculate:

• \( \frac{1}{48} \times 6 \) would yield \( \frac{1}{8} \) if \( 8 \div \frac{1}{6} = 48 \) is true. Therefore, his final result should indeed verify the multiplication check.

Conclusion

• Patel found the correct quotient (48) but did multiplication incorrectly in the context of checking (he provided intermediate steps that led to confusion about \( \frac{1}{8} \)).

Thus, the most accurate description of Patel’s work is: Patel found the correct quotient but checked his work using multiplication incorrectly.