Question

3 wholes and five eigths plus 2 wholes and 3 fourths

Answer 1

To add \(3\) wholes and \(5\) eighths to \(2\) wholes and \(3\) fourths, we will follow these steps:

1. Convert both mixed numbers into improper fractions.
2. Find a common denominator.
3. Add the fractions.
4. 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:
\[
\boxed{6 \frac{3}{8}}
\]