Add. Write your answer as a mixed number in simplest form.

Ask by Vaughn Barber. in the United States

Jan 24,2025

Question

Add. Write your answer as a mixed number in simplest form. $$ 5 \frac{5}{6}+4 \frac{1}{9} $$

UpStudy AI · Accepted Answer

To add the mixed numbers $$ 5 \frac{5}{6} $$ and $$ 4 \frac{1}{9} $$, follow these steps:

1. **Convert each mixed number to an improper fraction:**

$$
   5 \frac{5}{6} = \frac{5 \times 6 + 5}{6} = \frac{35}{6}
   $$

$$
   4 \frac{1}{9} = \frac{4 \times 9 + 1}{9} = \frac{37}{9}
   $$

2. **Find a common denominator:**  
   The least common multiple of 6 and 9 is 18.

$$
   \frac{35}{6} = \frac{35 \times 3}{6 \times 3} = \frac{105}{18}
   $$

$$
   \frac{37}{9} = \frac{37 \times 2}{9 \times 2} = \frac{74}{18}
   $$

3. **Add the fractions:**

$$
   \frac{105}{18} + \frac{74}{18} = \frac{179}{18}
   $$

4. **Convert back to a mixed number:**

$$
   \frac{179}{18} = 9 \frac{17}{18}
   $$

**Answer:** $$ 9 \frac{17}{18} $$
$$ 9 \frac{17}{18} $$

Add. Write your answer as a mixed number in simplest form.