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

Step2: Convert mixed number to improper fraction

To convert $3\frac{2}{3}$ to an improper fraction, use the formula: $a\frac{b}{c}=\frac{a\times c + b}{c}$. Here, $a = 3$, $b = 2$, $c = 3$. So, $3\times3+2 = 9 + 2=11$. Thus, the improper fraction is $\frac{11}{3}$.

Answer:

(a) Mixed number: $3\frac{2}{3}$
(b) Improper fraction: $\frac{11}{3}$