Question

1. in the circle, one \piece of pie\ is not labeled. what is the size of this region? show your work and support your answer.

Explanation:

Step1: Find a common denominator

The fractions given are $\frac{1}{3}$ and $\frac{2}{5}$. The common - denominator of 3 and 5 is $3\times5 = 15$.

Step2: Rewrite the fractions with the common denominator

$\frac{1}{3}=\frac{1\times5}{3\times5}=\frac{5}{15}$ and $\frac{2}{5}=\frac{2\times3}{5\times3}=\frac{6}{15}$.

Step3: Add the fractions

$\frac{5}{15}+\frac{6}{15}=\frac{5 + 6}{15}=\frac{11}{15}$.

Step4: Subtract the sum from 1

Since the whole circle is represented by 1, the un - labeled part is $1-\frac{11}{15}$. Rewrite 1 as $\frac{15}{15}$, then $\frac{15}{15}-\frac{11}{15}=\frac{15 - 11}{15}=\frac{4}{15}$.

Answer:

$\frac{4}{15}$