Question

Clare said that (4/3) ÷ (5/2) is (10/3). She reasoned: (4/3) ⋅ 5 = (20/3) and (20/3) ÷ 2 = (10/3). Explain why Clare's answer and reasoning are incorrect. Find the correct quotient.

Answer 1

The answer is 8/15

Explanation:

4/3 divided by 5/2 is the same as 4/3 times 2/5

4/3 times 2/5= 8/15

8/15 is the answer

She is wrong because if you want to do it you have to multiply the fraction with 5 and then MULTIPLY it by 2 not divide it by 2.

Answer 2

Correct quotient =

`(8)/(15)`

Explanation:

We are given he following in the question:

`\text{Clare's calculation:}\\\\(4)/(3)/ (5)/(2) = (10)/(3)\\\\\text{Clare's reason:}\\\\(4)/(3)* 5 = (20)/(3), (20)/(3) / 2 = (10)/(3)`

Clare's, reason is incorrect.

The correct quotient can be calculated in the following manner:

`(4)/(3)/ (5)/(2)\\\\= (4)/(3)* (2)/(5) = (8)/(15)`

Clare simply multiplied the fraction with 5 and divided the product with 2 which is incorrect. We have to multiply the fraction with the reciprocal of divisor.