Questions: Add. Write your answer as a mixed number in simplest form. 5 7/9 + 4 5/9

Transcript text: Add. Write your answer as a mixed number in simplest form. \[ 5 \frac{7}{9}+4 \frac{5}{9} \]

Solution

Solution Steps

Step 1: Convert Mixed Numbers to Improper Fractions

Convert \( 5 \frac{7}{9} \) and \( 4 \frac{5}{9} \) to improper fractions: \[ 5 \frac{7}{9} = \frac{5 \times 9 + 7}{9} = \frac{45 + 7}{9} = \frac{52}{9} \] \[ 4 \frac{5}{9} = \frac{4 \times 9 + 5}{9} = \frac{36 + 5}{9} = \frac{41}{9} \]

Step 2: Add the Improper Fractions

Add the two improper fractions: \[ \frac{52}{9} + \frac{41}{9} = \frac{52 + 41}{9} = \frac{93}{9} \]

Step 3: Simplify the Fraction

Simplify \( \frac{93}{9} \) by dividing the numerator and denominator by their greatest common divisor (GCD), which is 3: \[ \frac{93 \div 3}{9 \div 3} = \frac{31}{3} \]

Step 4: Convert the Improper Fraction Back to a Mixed Number

Convert \( \frac{31}{3} \) back to a mixed number: \[ \frac{31}{3} = 10 \frac{1}{3} \]