1. The problem asks: How many thirds are there in the mixed number $6 \frac{1}{3}$? 2. First, convert the mixed number to an improper fraction. The formula is: $$\text{Improper fraction} = \frac{\text{whole number} \times \text{denominator} + \text{numerator}}{\text{denominator}}$$ 3. For $6 \frac{1}{3}$, the whole number is 6, numerator is 1, and denominator is 3. So: $$6 \frac{1}{3} = \frac{6 \times 3 + 1}{3} = \frac{18 + 1}{3} = \frac{19}{3}$$ 4. Each "third" is $\frac{1}{3}$. To find how many thirds are in $\frac{19}{3}$, divide $\frac{19}{3}$ by $\frac{1}{3}$: $$\frac{19}{3} \div \frac{1}{3} = \frac{19}{3} \times \frac{3}{1} = 19$$ 5. Therefore, there are 19 thirds in $6 \frac{1}{3}$. --- 1. Now, solve $\frac{1}{2} + \frac{1}{5}$ and give the answer in simplest form. 2. Find the least common denominator (LCD) of 2 and 5, which is 10. 3. Convert each fraction to have denominator 10: $$\frac{1}{2} = \frac{5}{10}, \quad \frac{1}{5} = \frac{2}{10}$$ 4. Add the fractions: $$\frac{5}{10} + \frac{2}{10} = \frac{7}{10}$$ 5. The fraction $\frac{7}{10}$ is already in simplest form. --- 1. For the shaded circles problem: - Left circle: 6 parts, all 6 shaded. - Right circle: 6 parts, 2 shaded. 2. Total shaded parts = $6 + 2 = 8$ parts out of 6 parts per whole. 3. a) As a mixed number: $$8 \div 6 = 1 \text{ remainder } 2 \Rightarrow 1 \frac{2}{6}$$ 4. Simplify $\frac{2}{6}$: $$\frac{2}{6} = \frac{1}{3}$$ 5. Final mixed number: $$1 \frac{1}{3}$$ 6. b) As an improper fraction: $$1 \frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3}$$ 7. Both answers are in simplest form.