1. **State the problem:** We need to find the sum of the numbers $-\frac{3}{5}$, $-0.75$, and $4 \frac{7}{10}$. 2. **Convert all numbers to a common form:** - $-\frac{3}{5}$ is already a fraction. - $-0.75$ is a decimal, which can be written as $-\frac{3}{4}$. - $4 \frac{7}{10}$ is a mixed number, which can be converted to an improper fraction: $$4 \frac{7}{10} = \frac{4 \times 10 + 7}{10} = \frac{47}{10}$$ 3. **Find a common denominator:** The denominators are 5, 4, and 10. The least common denominator (LCD) is 20. 4. **Convert each fraction to have denominator 20:** - $-\frac{3}{5} = -\frac{3 \times 4}{5 \times 4} = -\frac{12}{20}$ - $-\frac{3}{4} = -\frac{3 \times 5}{4 \times 5} = -\frac{15}{20}$ - $\frac{47}{10} = \frac{47 \times 2}{10 \times 2} = \frac{94}{20}$ 5. **Add the fractions:** $$-\frac{12}{20} + -\frac{15}{20} + \frac{94}{20} = \frac{-12 - 15 + 94}{20} = \frac{67}{20}$$ 6. **Convert the improper fraction to a mixed number:** $$\frac{67}{20} = 3 \frac{7}{20}$$ **Final answer:** $3 \frac{7}{20}$