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

Answer:

Fraction of cloth that turns green =  $\frac{3}{40}$

Step-by-step explanation:

Let total cloth be of length = 1 unit

Given $\frac{5}{8}$ of it is dipped in blue dye.

Fraction which is not dipped in blue is given as:

⇒ $1-\frac{5}{8}$

Taking LCD to subtract fractions.

⇒ $\frac{8}{8}-\frac{5}{8}$

⇒ $\frac{3}{8}$

She dips $\frac{9}{20}$ in yellow.

Comparing the fraction dipped in yellow which is $\frac{9}{20}$ and fraction which is not dipped in blue i.e. $\frac{3}{8}$

$\frac{9}{20},\frac{3}{8}$

Taking LCD between 8 and 20 = 40

We have:

$\frac{9\times 2}{20\times 2},\frac{3\times 5}{8\times 5}$

$\frac{18}{40},\frac{15}{40}$

Thus, we can say  $\frac{9}{20}>\frac{3}{8}$

Since $\frac{9}{20}>\frac{3}{8}$, 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:

⇒ $\frac{9}{20}-\frac{3}{8}$

Subtracting by taking LCD =40.

⇒ $\frac{9\times 2}{20\times 2}-\frac{3\times 5}{8\times 5}$

⇒ $\frac{18}{40}-\frac{15}{40}$

⇒ $\frac{3}{40}$  (Answer)