Solve: 7⅔ + 6⅙ + 4⅑ Mixed Number Addition Problem

$7\frac{2}{3}+6\frac{1}{6}+4\frac{1}{9}=\text{?}$

To solve this problem, we'll follow these steps:

• Step 1: Convert mixed numbers to improper fractions.
• Step 2: Find a common denominator.
• Step 3: Add the fractions.
• Step 4: Convert the resulting improper fraction back to a mixed number.

Now, let's work through each step:

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

• $7\frac{2}{3} = \frac{7 \times 3 + 2}{3} = \frac{23}{3}$
• $6\frac{1}{6} = \frac{6 \times 6 + 1}{6} = \frac{37}{6}$
• $4\frac{1}{9} = \frac{4 \times 9 + 1}{9} = \frac{37}{9}$

Step 2: Find a common denominator for the fractions.

The denominators are 3, 6, and 9. The least common multiple (LCM) is 18.

Step 3: Convert all fractions to have this common denominator.

• $\frac{23}{3} = \frac{23 \times 6}{3 \times 6} = \frac{138}{18}$
• $\frac{37}{6} = \frac{37 \times 3}{6 \times 3} = \frac{111}{18}$
• $\frac{37}{9} = \frac{37 \times 2}{9 \times 2} = \frac{74}{18}$

Step 4: Add the fractions.

$\frac{138}{18} + \frac{111}{18} + \frac{74}{18} = \frac{323}{18}$

Step 5: Convert this improper fraction back to a mixed number.

Divide 323 by 18.

$323 \div 18 = 17$ with a remainder of 17, so

$\frac{323}{18} = 17\frac{17}{18}$

Therefore, the solution to the problem is $17\frac{17}{18}$.