Solve Mixed Number Subtraction: 3⅓ - 2⅕ Step by Step

To solve this problem, follow these steps:

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Find a common denominator for the fractions.
• Step 3: Subtract the fractions.
• Step 4: Simplify the result if needed.

Let's begin with Step 1:
Convert $3\frac{1}{3}$ to an improper fraction:
$3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}$
Convert $2\frac{14}{15}$ to an improper fraction:
$2\frac{14}{15} = \frac{2 \times 15 + 14}{15} = \frac{44}{15}$

Step 2: Find a common denominator for $\frac{10}{3}$ and $\frac{44}{15}$.
The least common multiple of 3 and 15 is 15, so we'll use 15 as the common denominator.

Step 3: Convert $\frac{10}{3}$ to have the denominator of 15:
$\frac{10}{3} = \frac{10 \times 5}{3 \times 5} = \frac{50}{15}$

Now, perform the subtraction:
$\frac{50}{15} - \frac{44}{15} = \frac{50 - 44}{15} = \frac{6}{15}$

Step 4: Simplify $\frac{6}{15}$.
The greatest common divisor of 6 and 15 is 3, so divide the numerator and denominator by 3:
$\frac{6}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}$

Thus, the final answer is $\frac{2}{5}$.