In 1-4, find each sum. 1. \( \frac{1}{2}+\frac{1}{6} \) Least multiple that is the same: Add using renamed fractions: 2. \( \frac{1}{9}+\frac{5}{6} \) \[ +1=2 \text { or }- \]

Sure, let's solve each of the given fraction addition problems step by step. --- ## **Problem 1:** **Add** \( \frac{1}{2} + \frac{1}{6} \) ### **Step 1: Find the Least Common Denominator (LCD)** The denominators are 2 and 6. - The least common multiple (LCM) of 2 and 6 is **6**. Thus, the LCD is **6**. ### **Step 2: Rewrite Each Fraction with the LCD** - \( \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \) - \( \frac{1}{6} \) is already with the denominator 6, so it remains **\( \frac{1}{6} \)**. ### **Step 3: Add the Fractions** - \( \frac{3}{6} + \frac{1}{6} = \frac{3 + 1}{6} = \frac{4}{6} \) ### **Step 4: Simplify the Result** - \( \frac{4}{6} \) can be simplified by dividing both numerator and denominator by **2**: - \( \frac{4 ÷ 2}{6 ÷ 2} = \frac{2}{3} \) **Final Answer:** \( \frac{1}{2} + \frac{1}{6} = \frac{2}{3} \) --- ## **Problem 2:** **Add** \( \frac{1}{9} + \frac{5}{6} \) ### **Step 1: Find the Least Common Denominator (LCD)** The denominators are 9 and 6. - The least common multiple (LCM) of 9 and 6 is **18**. Thus, the LCD is **18**. ### **Step 2: Rewrite Each Fraction with the LCD** - \( \frac{1}{9} = \frac{1 \times 2}{9 \times 2} = \frac{2}{18} \) - \( \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \) ### **Step 3: Add the Fractions** - \( \frac{2}{18} + \frac{15}{18} = \frac{2 + 15}{18} = \frac{17}{18} \) ### **Step 4: Simplify the Result** - \( \frac{17}{18} \) is already in its simplest form. **Final Answer:** \( \frac{1}{9} + \frac{5}{6} = \frac{17}{18} \) --- If you have **Problems 3 and 4** or any other questions, feel free to provide them, and I'll be happy to help!