Solve Mixed Number Addition: 2½ + 3⅐ Step-by-Step

$2\frac{1}{2}+3\frac{1}{7}=$

To solve the addition of $2\frac{1}{2} + 3\frac{1}{7}$, we will follow these steps:

• Convert each mixed number to an improper fraction.
• Find a common denominator for the fractions.
• Add the fractions together.
• Convert the resulting improper fraction back to a mixed number.

Now, let's perform the calculations:
Step 1: Convert to improper fractions.
$2\frac{1}{2}$ becomes $\frac{5}{2}$ because $(2 \times 2) + 1 = 5$.
$3\frac{1}{7}$ becomes $\frac{22}{7}$ because $(3 \times 7) + 1 = 22$.

Step 2: Find a common denominator.
The least common denominator of 2 and 7 is 14. We convert $\frac{5}{2}$ and $\frac{22}{7}$ to have this common denominator:
$\frac{5}{2} = \frac{35}{14}$ (because $5 \times 7 = 35$)
$\frac{22}{7} = \frac{44}{14}$ (because $22 \times 2 = 44$)

Step 3: Add the resulting fractions.
$\frac{35}{14} + \frac{44}{14} = \frac{79}{14}$

Step 4: Convert the improper fraction back to a mixed number.
$\frac{79}{14}$ can be expressed as $5\frac{9}{14}$ because 79 divided by 14 is 5 with a remainder of 9.

Therefore, the solution to the problem is $5\frac{9}{14}$.