Question

alyssa claims that dividing by 4/5 is the same thing as multiplying by 5 then dividing by 4, is she correct? Explain why or why not.

Answer 1

Solution :-

Yes, Alyssa is totally correct about dividing by 4/5 is the same thing as multiplying by 5 and then dividing by 4.

Here is the explanation -

Suppose we have to divide 4/7 by 4/5. Then, 3/4 will be multiplied by the reciprocal of 4/5, which is 5/4.

⇒ 4/7 × 5/4

⇒ 4 as numerator of the first fraction and 4 as the denominator of the second fraction are cancelled.

The answer is 5/7.

So, dividing by 4/5 is same thing as multiplying by 5 and then dividing by 4.

Answer.

Answer 2

The given statement is
Alyssa claims that dividing by 4/5 is the same thing as multiplying by 5 then dividing by 4.
We have to tell whether it is true or not.
Well the above statement is absolutely true. Let me explain the reason also.
Since, multiplying by a number say 'x ' and dividing the number with it's reciprocal (1 / x) has the same meaning. Thus, in the light of this statement, Alyssa gets the same answer whether she divides the number by 4/5 or multiply the number by 5 and then divide by 4.
Hopefully you understand. Thanks.