Solve: 6 1/9 - 2 2/3 Mixed Number Subtraction

To solve this problem, we will follow a structured approach to subtract the given mixed numbers:

• Step 1: Convert mixed numbers to improper fractions.

• Step 2: Find a common denominator for the fractions.

• Step 3: Subtract the improper fractions.

• Step 4: Convert the result back to a mixed number if necessary.

Let's begin with each step in detail:
Step 1: Convert each mixed number to an improper fraction.
- $6\frac{1}{9}$ becomes $\frac{55}{9}$ because $6 \times 9 + 1 = 55$.
- $2\frac{2}{3}$ becomes $\frac{8}{3}$ because $2 \times 3 + 2 = 8$.

Step 2: Convert $\frac{8}{3}$ to have a common denominator with $\frac{55}{9}$.
The least common denominator (LCD) is 9.
Multiply the numerator and the denominator of $\frac{8}{3}$ by 3 to get $\frac{24}{9}$.

Step 3: Subtract the improper fractions:
$\frac{55}{9} - \frac{24}{9} = \frac{31}{9}$.

Step 4: Convert the improper fraction back to a mixed number.
$\frac{31}{9}$ simplifies to $3\frac{4}{9}$, because $31 \div 9$ equals 3 with a remainder of 4.

Therefore, the solution to the problem is $3\frac{4}{9}$.