Question

each circle counts as one whole. write a mixed number giving the amount shaded. then, write this amount as an improper fraction. (a) mixed number: (b) improper fraction:

Explanation:

Step1: Analyze the shaded circles

There are 2 full shaded circles (each is 1 whole) and a third circle with 2 out of 3 parts shaded. So the mixed number has a whole number part of 2 and a fractional part of $\frac{2}{3}$. Thus, the mixed number is $2\frac{2}{3}$.

Step2: Convert mixed number to improper fraction

To convert $2\frac{2}{3}$ to an improper fraction, use the formula: $a\frac{b}{c}=\frac{a\times c + b}{c}$. Here, $a = 2$, $b = 2$, $c = 3$. So $2\times3 + 2 = 6 + 2 = 8$. Thus, the improper fraction is $\frac{8}{3}$.

Answer:

(a) Mixed number: $2\frac{2}{3}$
(b) Improper fraction: $\frac{8}{3}$