Question

Mia has a rectangle cloth

She dips 5/8 of it in blue dye
She dips 9/20 in yellow
The part of the cloth that is dipped in both colours turns green.
Work out the fraction of cloth that turns green.
plz show working

Answer 1

Fraction of cloth that turns green =
`(3)/(40)`

Explanation:

Let total cloth be of length = 1 unit

Given
`(5)/(8)` of it is dipped in blue dye.

Fraction which is not dipped in blue is given as:

⇒
`1-(5)/(8)`

Taking LCD to subtract fractions.

⇒
`(8)/(8)-(5)/(8)`

⇒
`(3)/(8)`

She dips
`(9)/(20)` in yellow.

Comparing the fraction dipped in yellow which is
`(9)/(20)` and fraction which is not dipped in blue i.e.
`(3)/(8)`

`(9)/(20),(3)/(8)`

Taking LCD between 8 and 20 = 40

We have:

`(9* 2)/(20* 2),(3* 5)/(8* 5)`

`(18)/(40),(15)/(40)`

Thus, we can say
`(9)/(20)>(3)/(8)`

Since
`(9)/(20)>(3)/(8)`, so the part dipped in yellow will also cover some part which is blue.

Thus, fraction dipped in yellow and blue which turns green will be given as:

⇒
`(9)/(20)-(3)/(8)`

Subtracting by taking LCD =40.

⇒
`(9* 2)/(20* 2)-(3* 5)/(8* 5)`

⇒
`(18)/(40)-(15)/(40)`

⇒
`(3)/(40)` (Answer)