1. **State the problem:** Calculate the total earnings for a person paid 2.40 per hour who worked 2 1/2, 4 3/4, and 1 2/3 hours. 2. **Convert mixed numbers to improper fractions:** - $2 \frac{1}{2} = \frac{5}{2}$ hours - $4 \frac{3}{4} = \frac{19}{4}$ hours - $1 \frac{2}{3} = \frac{5}{3}$ hours 3. **Find the total hours worked:** $$\text{Total hours} = \frac{5}{2} + \frac{19}{4} + \frac{5}{3}$$ 4. **Find a common denominator for addition:** The denominators are 2, 4, and 3. The least common denominator is 12. 5. **Convert each fraction to denominator 12:** - $\frac{5}{2} = \frac{5 \times 6}{2 \times 6} = \frac{30}{12}$ - $\frac{19}{4} = \frac{19 \times 3}{4 \times 3} = \frac{57}{12}$ - $\frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12}$ 6. **Add the fractions:** $$\frac{30}{12} + \frac{57}{12} + \frac{20}{12} = \frac{30 + 57 + 20}{12} = \frac{107}{12}$$ 7. **Convert total hours to a mixed number:** $$\frac{107}{12} = 8 \frac{11}{12} \text{ hours}$$ 8. **Calculate total earnings:** $$\text{Earnings} = \text{Hourly rate} \times \text{Total hours} = 2.40 \times \frac{107}{12}$$ 9. **Multiply:** $$2.40 \times \frac{107}{12} = \frac{2.40 \times 107}{12} = \frac{256.8}{12} = 21.4$$ **Final answer:** She earned **21.4** in total.