1. **State the problem:** We need to order the fractions $\frac{1}{2}$, $\frac{7}{10}$, and $\frac{5}{8}$ from least to greatest. 2. **Formula and rules:** To compare fractions, convert them to a common denominator or convert to decimals. 3. **Find a common denominator:** The denominators are 2, 10, and 8. The least common denominator (LCD) is the least common multiple of 2, 10, and 8. - Prime factors: 2 = 2, 10 = 2 \times 5, 8 = 2^3 - LCD = $2^3 \times 5 = 8 \times 5 = 40$ 4. **Convert each fraction to have denominator 40:** $$\frac{1}{2} = \frac{1 \times 20}{2 \times 20} = \frac{20}{40}$$ $$\frac{7}{10} = \frac{7 \times 4}{10 \times 4} = \frac{28}{40}$$ $$\frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40}$$ 5. **Compare numerators:** $20 < 25 < 28$ 6. **Order from least to greatest:** $$\frac{1}{2} < \frac{5}{8} < \frac{7}{10}$$ **Final answer:** $\boxed{\frac{1}{2} < \frac{5}{8} < \frac{7}{10}}$