Question

how much of the circle is shaded? write your answer as a fraction in simplest form.
1/3
2/5

Explanation:

Step1: Find the common denominator

The denominators of the two un - shaded fractions are \(3\) and \(5\). The least common multiple of \(3\) and \(5\) is \(15\).

Step2: Rewrite the fractions with the common denominator

\(\frac{1}{3}=\frac{1\times5}{3\times5}=\frac{5}{15}\), \(\frac{2}{5}=\frac{2\times3}{5\times3}=\frac{6}{15}\)

Step3: Calculate the sum of the un - shaded parts

\(\frac{5}{15}+\frac{6}{15}=\frac{5 + 6}{15}=\frac{11}{15}\)

Step4: Calculate the shaded part

Since the whole circle is \(1=\frac{15}{15}\), the shaded part is \(1-\frac{11}{15}=\frac{15-11}{15}=\frac{4}{15}\)

Answer:

\(\frac{4}{15}\)