To add \(3\) wholes and \(5\) eighths to \(2\) wholes and \(3\) fourths, we will follow these steps:
- Convert both mixed numbers into improper fractions.
- Find a common denominator.
- Add the fractions.
- Convert back to a mixed number, if necessary.
Step 1: Convert to Improper Fractions
For \(3\) wholes and \(5\) eighths: \[ 3 = \frac{3 \times 8}{8} = \frac{24}{8} \] Now add \(5\) eighths: \[ 3 , \text{wholes} , 5 , \text{eighths} = \frac{24}{8} + \frac{5}{8} = \frac{29}{8} \]
For \(2\) wholes and \(3\) fourths: \[ 2 = \frac{2 \times 4}{4} = \frac{8}{4} \] Now add \(3\) fourths: \[ 2 , \text{wholes} , 3 , \text{fourths} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4} \]
Step 2: Find a Common Denominator
The denominators are \(8\) and \(4\). The least common multiple of \(8\) and \(4\) is \(8\).
Now, convert \(\frac{11}{4}\) to have a denominator of \(8\): \[ \frac{11}{4} = \frac{11 \times 2}{4 \times 2} = \frac{22}{8} \]
Step 3: Add the Fractions
Now add \(\frac{29}{8}\) and \(\frac{22}{8}\): \[ \frac{29}{8} + \frac{22}{8} = \frac{29 + 22}{8} = \frac{51}{8} \]
Step 4: Convert Back to a Mixed Number
To convert \(\frac{51}{8}\) back to a mixed number, divide \(51\) by \(8\):
- \(8\) goes into \(51\) a total of \(6\) times (because \(6 \times 8 = 48\)).
- The remainder is \(51 - 48 = 3\).
Thus, \(\frac{51}{8}\) can be expressed as: \[ 6 , \text{whole} , \frac{3}{8} \]
So, the final answer is: \[ \boxed{6 \frac{3}{8}} \]