Question

Please help meHow much of a circle is shaded write in simplest form as a fraction in simplest form

Answer 1

$\frac{4}{15}$

Explanation

Step 1

the shaded area is equal to

shaded area = total circle -not shaded area

a) the full circle equals 1 ( one unit)

b) let x represents the shaded area

c) the not shaded area is the sum of 2/5 and 1/3

Now , rewrite the expression

$\begin{gathered} shadedarea=totalcircle-notshadedarea \\ \text{ shaded area=1-}(\frac{2}{5}+\frac{1}{3}) \\ so \\ x=1-(\frac{2}{5}+\frac{1}{3}) \end{gathered}$

Step 2

Now, let's calculate

$\begin{gathered} x=1-(\frac{2}{5}+\frac{1}{3}) \\ x=1-(\frac{2\cdot3+5\cdot1}{5\cdot3}) \\ x=1-(\frac{6+5}{15}) \\ x=1-(\frac{11}{15}) \end{gathered}$

now, the subtraction

$\begin{gathered} x=1-(\frac{11}{15}) \\ \text{tip: } \\ 1=\frac{15}{15},\text{ so} \\ x=\frac{15}{15}-(\frac{11}{15}) \\ x=\frac{15-11}{15} \\ x=\frac{4}{15} \end{gathered}$

therefore, the answer is

$\frac{4}{15}$

I hope this helps you