Question

How much of the circle is shaded? Write your answer as a fraction in simplest form.

3
7
1
2

Answer 1

Subtracting Fractions

To subtract two fractions, we must find a common denominator and subtract the numerators.

Solving the Question

The entire circle represents one whole.

To find the fraction for the shaded region, we must subtract
`(1)/(2)` and
`(3)/(7)` from one whole:

`1-(1)/(2)-(3)/(7)`

One whole minus half the whole would leave us with just half:

`(1)/(2)-(3)/(7)`

Now, to find a common denominator, multiply the numerator and denominator of each fraction by the denominator of the other fraction:

`(1*7)/(2*7)-(3*2)/(7*2)\\\\= (7)/(14)-(6)/(14)`

Now, subtract normally:

`(7)/(14)-(6)/(14)\\\\= (1)/(14)`

Answer

`(1)/(14)`