1. **State the problem:** We need to put the fractions $\frac{1}{2}$, $\frac{7}{10}$, and $\frac{2}{3}$ in order from least to greatest. 2. **Formula and rules:** To compare fractions, we can convert them to have a common denominator or convert them to decimals. 3. **Find a common denominator:** The denominators are 2, 10, and 3. The least common denominator (LCD) is the least common multiple of 2, 10, and 3. - Multiples of 10: 10, 20, 30, 40... - 30 is divisible by 2 and 3, so LCD = 30. 4. **Convert each fraction to have denominator 30:** $$\frac{1}{2} = \frac{1 \times 15}{2 \times 15} = \frac{15}{30}$$ $$\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}$$ $$\frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30}$$ 5. **Compare the numerators:** $15$, $21$, and $20$. - $15 < 20 < 21$ 6. **Order the fractions from least to greatest:** $$\frac{1}{2} < \frac{2}{3} < \frac{7}{10}$$ **Final answer:** $\frac{1}{2}$, $\frac{2}{3}$, $\frac{7}{10}$