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.

Respuesta :

Answer:

Correct quotient =

[tex]\dfrac{8}{15}[/tex]

Step-by-step explanation:

We are given he following in the question:

[tex]\text{Clare's calculation:}\\\\\dfrac{4}{3}\div \dfrac{5}{2} = \dfrac{10}{3}\\\\\text{Clare's reason:}\\\\\dfrac{4}{3}\times 5 = \dfrac{20}{3}, \dfrac{20}{3} \div 2 = \dfrac{10}{3}[/tex]

Clare's, reason is incorrect.

The correct quotient can be calculated in the following manner:

[tex]\dfrac{4}{3}\div \dfrac{5}{2}\\\\= \dfrac{4}{3}\times \dfrac{2}{5} = \dfrac{8}{15}[/tex]

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.

Answer:

The answer is 8/15

Step-by-step 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.