Solve Mixed Number Addition: 2⅓ + 1¼ Step by Step

To solve the addition of the mixed numbers $2\frac{1}{3} + 1\frac{1}{4}$, we'll go through the following steps:

• Step 1: Convert the mixed numbers to improper fractions.
• Step 2: Find a common denominator for the fractions.
• Step 3: Add the fractions together.
• Step 4: Convert, if necessary, back to a mixed number for the final answer.

Let's go through each step in detail:

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

For $2\frac{1}{3}$:
Convert by using the formula $a\frac{b}{c} = \frac{ac + b}{c}$.
This gives us $2\frac{1}{3} = \frac{2 \cdot 3 + 1}{3} = \frac{7}{3}$.

For $1\frac{1}{4}$:
Similarly, $1\frac{1}{4} = \frac{1 \cdot 4 + 1}{4} = \frac{5}{4}$.

Step 2: Find a common denominator.

The denominators are 3 and 4, so the least common denominator (LCD) is 12.
Convert $\frac{7}{3}$ to an equivalent fraction with denominator 12:
$\frac{7}{3} = \frac{7 \cdot 4}{3 \cdot 4} = \frac{28}{12}$.

Convert $\frac{5}{4}$ to an equivalent fraction with denominator 12:
$\frac{5}{4} = \frac{5 \cdot 3}{4 \cdot 3} = \frac{15}{12}$.

Step 3: Add the fractions together.
$\frac{28}{12} + \frac{15}{12} = \frac{28 + 15}{12} = \frac{43}{12}$.

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

The improper fraction $\frac{43}{12}$ can be converted back to a mixed number.
Perform the division $43 \div 12$ to get the quotient as 3 and a remainder of 7.
Thus, $\frac{43}{12} = 3\frac{7}{12}$.

Therefore, the solution to the problem is $3\frac{7}{12}$.