1. **State the problem:** We need to put the fractions $\frac{1}{2}$, $\frac{4}{5}$, and $\frac{3}{4}$ in order from least to greatest. 2. **Formula and rules:** To compare fractions, we can find a common denominator or convert them to decimals. The common denominator method involves finding the least common multiple (LCM) of the denominators. 3. **Find the LCM of denominators 2, 5, and 4:** $$\text{LCM}(2,5,4) = 20$$ 4. **Convert each fraction to an equivalent fraction with denominator 20:** $$\frac{1}{2} = \frac{1 \times 10}{2 \times 10} = \frac{10}{20}$$ $$\frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}$$ $$\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$$ 5. **Compare the numerators:** $$10 < 15 < 16$$ 6. **Order the fractions from least to greatest:** $$\frac{1}{2} < \frac{3}{4} < \frac{4}{5}$$ **Final answer:** $\frac{1}{2}$, $\frac{3}{4}$, $\frac{4}{5}$