Show work and simplify your answer: \( 13 \frac{10}{20} \) \( +9 \frac{3}{4} \)

Sure! Let's add the mixed numbers \( 13 \frac{10}{20} \) and \( 9 \frac{3}{4} \) step by step. ### Step 1: Simplify the Mixed Numbers First, simplify the fractional parts of each mixed number if possible. 1. **Simplify \( \frac{10}{20} \):** \[ \frac{10}{20} = \frac{10 \div 10}{20 \div 10} = \frac{1}{2} \] So, \( 13 \frac{10}{20} \) simplifies to \( 13 \frac{1}{2} \). 2. **Simplify \( \frac{3}{4} \):** This fraction is already in its simplest form. Now, the problem looks like: \[ 13 \frac{1}{2} + 9 \frac{3}{4} \] ### Step 2: Add the Whole Numbers Add the whole number parts of the mixed numbers: \[ 13 + 9 = 22 \] ### Step 3: Add the Fractional Parts Now, add the fractional parts: \[ \frac{1}{2} + \frac{3}{4} \] To add these fractions, they need a common denominator. The least common denominator (LCD) of 2 and 4 is 4. 1. **Convert \( \frac{1}{2} \) to fourths:** \[ \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \] 2. **Add the fractions:** \[ \frac{2}{4} + \frac{3}{4} = \frac{5}{4} \] 3. **Simplify \( \frac{5}{4} \) to a mixed number:** \[ \frac{5}{4} = 1 \frac{1}{4} \] ### Step 4: Combine the Whole Numbers and Fractions Add the sum of the whole numbers to the sum of the fractions: \[ 22 + 1 \frac{1}{4} = 23 \frac{1}{4} \] ### Final Answer \[ 13 \frac{10}{20} + 9 \frac{3}{4} = 23 \frac{1}{4} \]