Calculate the Sum: 6⅔ + 1⅔ + 1⅝ Mixed Number Addition

$6\frac{2}{9}+1\frac{2}{3}+1\frac{5}{9}=$

To solve this problem, we will follow these steps:

• Step 1: Convert each mixed number into an improper fraction.
• Step 2: Identify the least common denominator (LCD) for the fractions.
• Step 3: Add the fractions together.
• Step 4: Convert the resulting improper fraction back to a mixed number.

Now, let's work through each step in detail:

Step 1: Convert each mixed number into an improper fraction.

• $6\frac{2}{9} = \frac{(6 \times 9) + 2}{9} = \frac{54 + 2}{9} = \frac{56}{9}$
• $1\frac{2}{3} = \frac{(1 \times 3) + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}$
• $1\frac{5}{9} = \frac{(1 \times 9) + 5}{9} = \frac{9 + 5}{9} = \frac{14}{9}$

Step 2: Identify the least common denominator (LCD) for the fractions.

The denominators are 9 and 3. The least common multiple of these is 9.

Step 3: Add the fractions.

• First, convert all fractions to have the same denominator.
• $\frac{5}{3}$ should be converted: $\frac{5 \times 3}{3 \times 3} = \frac{15}{9}$.
• Add: $\frac{56}{9} + \frac{15}{9} + \frac{14}{9} = \frac{85}{9}$.

Step 4: Convert $\frac{85}{9}$ back to a mixed number.

• Perform the division: $85 ÷ 9 = 9$ remainder $4$.
• Therefore, $\frac{85}{9} = 9\frac{4}{9}$.

Therefore, the solution to the problem is $9\frac{4}{9}$.