Solve Mixed Number Addition: 6⅜ + 2¾ Step-by-Step

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

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Find a common denominator for the fractions.
• Step 3: Add the fractions and simplify the result.
• Step 4: Convert the result back to a mixed number if necessary.

Now, let's work through each step:

Step 1: Convert mixed numbers to improper fractions.

The first mixed number is $6\frac{3}{8}$. To convert this:

• The whole number part is 6, and the fractional part is $\frac{3}{8}$.
• Multiply the whole number by the denominator: $6 \times 8 = 48$.
• Add the numerator: $48 + 3 = 51$.
• The improper fraction is $\frac{51}{8}$.

The second mixed number is $2\frac{3}{4}$. To convert this:

• The whole number part is 2, and the fractional part is $\frac{3}{4}$.
• Multiply the whole number by the denominator: $2 \times 4 = 8$.
• Add the numerator: $8 + 3 = 11$.
• The improper fraction is $\frac{11}{4}$.

Step 2: Find a common denominator for $\frac{51}{8}$ and $\frac{11}{4}$.

The denominators are 8 and 4. The least common denominator is 8.

Step 3: Add the fractions.

Convert $\frac{11}{4}$ to the equivalent fraction with a denominator of 8:

• Multiply both the numerator and the denominator by 2: $\frac{11 \times 2}{4 \times 2} = \frac{22}{8}$.

Now add: $\frac{51}{8} + \frac{22}{8} = \frac{51 + 22}{8} = \frac{73}{8}$.

Step 4: Convert $\frac{73}{8}$ back to a mixed number.

• Divide 73 by 8: $73 \div 8 = 9$ remainder 1.
• The quotient is 9, and the remainder is 1.
• The mixed number is $9\frac{1}{8}$.

Therefore, the solution to the problem is $9\frac{1}{8}$.