Question

How would I start the problem?

Answer 1

You have to assume that the area of the circle is 1.

You know the area of the two given sectors, and asked for the area of the third sectors. Since the area of the three sectors together is the area of the whole circle, we know that the three sector areas together sum up to one.

Think, for example, that you have to paint the circle, and you need 1 liter of paint for the whole circle. You used
`(5)/(7)` liters of paint for the first sector, and
`(1)/(14)` liters of paint for the second sector.

So, the amount of paint you need for the third sector is how much paint your left with, after painting the other two.

So, you had one liter, and used
`(5)/(7)` liters of paint for the first sector. You're left with

`1 - (5)/(7) = (7)/(7) - (5)/(7) = (2)/(7)`

liters of paint.

Then, you use
`(1)/(14)` liters of paint for the second sector. You're left with

`(2)/(7) - (1)/(14) = (4)/(14) - (1)/(14) = (3)/(14)`