4 Add. \( 4 \frac{5}{6}+3 \frac{5}{9} \)

Certainly! Let's add the mixed numbers \( 4 \frac{5}{6} \) and \( 3 \frac{5}{9} \) step by step. ### Step 1: Add the Whole Numbers First, add the whole number parts of each mixed number: \[ 4 + 3 = 7 \] ### Step 2: Add the Fractional Parts Next, add the fractional parts: \[ \frac{5}{6} + \frac{5}{9} \] To add these fractions, they must have the **same denominator**. #### Find the Least Common Denominator (LCD) The denominators are 6 and 9. The least common multiple (LCM) of 6 and 9 is 18. So, the LCD is 18. #### Convert Fractions to Equivalent Fractions with LCD \[ \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \] \[ \frac{5}{9} = \frac{5 \times 2}{9 \times 2} = \frac{10}{18} \] #### Add the Equivalent Fractions \[ \frac{15}{18} + \frac{10}{18} = \frac{25}{18} \] ### Step 3: Simplify the Fraction (if necessary) \(\frac{25}{18}\) is an improper fraction, which can be converted to a mixed number: \[ \frac{25}{18} = 1 \frac{7}{18} \] ### Step 4: Combine the Whole Numbers and the Fraction Add the whole number from Step 1 and the simplified fraction: \[ 7 + 1 \frac{7}{18} = 8 \frac{7}{18} \] ### Final Answer \[ 4 \frac{5}{6} + 3 \frac{5}{9} = 8 \frac{7}{18} \]