Sakura solved a fraction division problem using the rule “multiply by the reciprocal.” Look at her work.

Question

7 ÷
2
5

1
7
×
2
5
=
2
35

Did she solve the problem correctly?
Yes. She solved the problem correctly.
No. She multiplied the dividend by the divisor instead of finding the reciprocal.
No. She multiplied the denominators instead of finding a common denominator.
No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Answer 1

To check if Sakura solved the problem correctly, let's analyze her work step by step.

The division problem she has is:

\[ 7 \div \frac{2}{5} \]

According to the rule for dividing fractions, we multiply by the reciprocal of the divisor. The reciprocal of \( \frac{2}{5} \) is \( \frac{5}{2} \).

So the correct operation would be:

\[ 7 \times \frac{5}{2} \]

When converting 7 into a fraction for multiplication, we write it as \( \frac{7}{1} \):

\[ \frac{7}{1} \times \frac{5}{2} = \frac{7 \times 5}{1 \times 2} = \frac{35}{2} \]

Therefore, the correct answer should be \( \frac{35}{2} \), or \( 17.5 \) in decimal form.

Now, looking at Sakura's work:

She had:

\[ 7 \div \frac{2}{5} \]

and wrote:

\[ 7 \times \frac{2}{5} = \frac{14}{5} \]

This indicates she multiplied by \( \frac{2}{5} \) (the divisor) instead of its reciprocal \( \frac{5}{2} \).

So the correct option is:

No. She multiplied the dividend by the divisor instead of finding the reciprocal.