1. **State the problem:** We need to subtract mixed numbers in the following expressions: - $5 \frac{1}{3} - 2 \frac{2}{3}$ - $6 \frac{7}{10} - 3 \frac{3}{10}$ - $3 \frac{4}{5} - 1 \frac{7}{10}$ - $7 \frac{5}{8} - 3$ 2. **Formula and rules:** To subtract mixed numbers, convert them to improper fractions or break the whole number if needed. If the fractional part of the minuend (first number) is smaller than the subtrahend's fractional part, borrow 1 from the whole number. 3. **Calculate $5 \frac{1}{3} - 2 \frac{2}{3}$:** - Convert to improper fractions: $$5 \frac{1}{3} = \frac{16}{3}, \quad 2 \frac{2}{3} = \frac{8}{3}$$ - Subtract: $$\frac{16}{3} - \frac{8}{3} = \frac{8}{3} = 2 \frac{2}{3}$$ 4. **Calculate $6 \frac{7}{10} - 3 \frac{3}{10}$:** - Convert to improper fractions: $$6 \frac{7}{10} = \frac{67}{10}, \quad 3 \frac{3}{10} = \frac{33}{10}$$ - Subtract: $$\frac{67}{10} - \frac{33}{10} = \frac{34}{10} = 3 \frac{4}{10} = 3 \frac{2}{5}$$ 5. **Calculate $3 \frac{4}{5} - 1 \frac{7}{10}$:** - Convert to improper fractions: $$3 \frac{4}{5} = \frac{19}{5}, \quad 1 \frac{7}{10} = \frac{17}{10}$$ - Find common denominator 10: $$\frac{19}{5} = \frac{38}{10}$$ - Subtract: $$\frac{38}{10} - \frac{17}{10} = \frac{21}{10} = 2 \frac{1}{10}$$ 6. **Calculate $7 \frac{5}{8} - 3$:** - Convert to improper fraction: $$7 \frac{5}{8} = \frac{61}{8}$$ - Convert 3 to fraction with denominator 8: $$3 = \frac{24}{8}$$ - Subtract: $$\frac{61}{8} - \frac{24}{8} = \frac{37}{8} = 4 \frac{5}{8}$$ 7. **Observations:** - When the fractional part of the first number is smaller than the second, borrowing from the whole number is necessary. - Subtraction is easier when fractions have the same denominator. - Breaking the whole number helps to subtract fractions when needed. **Final answers:** - $5 \frac{1}{3} - 2 \frac{2}{3} = 2 \frac{2}{3}$ - $6 \frac{7}{10} - 3 \frac{3}{10} = 3 \frac{2}{5}$ - $3 \frac{4}{5} - 1 \frac{7}{10} = 2 \frac{1}{10}$ - $7 \frac{5}{8} - 3 = 4 \frac{5}{8}$