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Select ALL statements that show correct reasoning for finding \(\frac{14}{15} \div \frac{7}{5}\).

A. Multiplying \(\frac{14}{15}\) by 5 and then by \(\frac{1}{7}\).

B. Dividing \(\frac{14}{15}\) by 5, and then multiplying by \(\frac{1}{7}\).

C. Multiplying \(\frac{14}{15}\) by 7, and then multiplying by \(\frac{1}{5}\).

D. Multiplying \(\frac{14}{15}\) by 5 and then dividing by 7.

Answer :

The correct reasoning for finding 14/15 ÷ 7/5

  • Multiplying 14/15 by 5 and then by 1/7.
  • Multiplying 14/15 by 5 and then dividing by 7

What is Fraction?

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

  • The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.
  • How many sections of the fraction are represented or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.

Given:

14/15 ÷ 7/5

Now, For dividing both of fraction

First, Multiplying 14/15 by 5

and, then Multiplying the resultant value of (14/ 15 x 5) by 1/7.

Also, it can be written as Multiplying 14/15 by 5 and then dividing by 7

Learn more about fraction here:

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Final answer:

The correct reasoning for the operation 14/15 ÷ 7/5 is to multiply 14/15 by the reciprocal of 7/5, which is 5/7. Two ways to do this are: a) multiplying 14/15 by 5, then by 1/7, and d) multiplying 14/15 by 5, then dividing by 7.

Explanation:

The correct reasoning for finding 14/15 ÷ 7/5 is achieved by multiplying 14/15 by the reciprocal of 7/5. The reciprocal of 7/5 is 5/7. Hence, you need to multiply 14/15 by 5/7. This can be interpreted in two ways:

  • Multiplying 14/15 by 5 and then by 1/7, which corresponds to option a.
  • Multiplying 14/15 by 5 and then dividing by 7, which corresponds to option d.

Therefore, options a and d are correct. Options b and c are incorrect because they do not properly utilize the reciprocal property in division.

Learn more about Division with Fractions here:

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