Question

Which is the best reason why 2/5 is the exact quotient for 1/4÷ 5/8 ?

Answer 1

As
`(a)/(b)/ (c)/(d)=(a)/(b)* (d)/(c)`

Explanation:

Given that 2/5 is the exact quotient for 1/4 ÷ 5/8 . We need to give the reason behind the answer .

We know that for fractions of form
`(a)/(b)\,,\,(c)/(d)`,

`(a)/(b)/ (c)/(d)=(a)/(b)* (d)/(c)`

i.e sign ÷ changes to × and we take reciprocal of fraction after the sign ÷

Here, let a = 1, b = 4 , c = 5 and d = 8

So, as per the explanation given above,

`(1)/(4)/ (5)/(8)=(1)/(4)* (8)/(5)\\=(2)/(5)`

Therefore, 2/5 is the exact quotient for 1/4÷ 5/8 as
`(a)/(b)/ (c)/(d)=(a)/(b)* (d)/(c)`