Question

Add, answer as a mixed number in simplest form.
3 2/3 + 5 3/4
[__] [__]/[__]

Answer 1

To add the mixed numbers \(3 \frac{2}{3}\) and \(5 \frac{3}{4}\), we'll follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Find a common denominator.
3. Add the fractions.
4. Convert the result back to a mixed number if necessary.

**Step 1: Convert to improper fractions.**

For \(3 \frac{2}{3}\):
\[
3 \times 3 + 2 = 9 + 2 = 11 \quad \Rightarrow \quad \frac{11}{3}
\]

For \(5 \frac{3}{4}\):
\[
5 \times 4 + 3 = 20 + 3 = 23 \quad \Rightarrow \quad \frac{23}{4}
\]

Now we have:
\[
\frac{11}{3} + \frac{23}{4}
\]

**Step 2: Find a common denominator.**

The least common multiple of 3 and 4 is 12. Now, we will convert each fraction to have a denominator of 12.

For \(\frac{11}{3}\):
\[
\frac{11}{3} \times \frac{4}{4} = \frac{44}{12}
\]

For \(\frac{23}{4}\):
\[
\frac{23}{4} \times \frac{3}{3} = \frac{69}{12}
\]

Now we can add the two fractions:
\[
\frac{44}{12} + \frac{69}{12} = \frac{44 + 69}{12} = \frac{113}{12}
\]

**Step 3: Convert back to a mixed number.**

To convert \(\frac{113}{12}\) to a mixed number, divide 113 by 12:
- \(113 \div 12 = 9\) remainder \(5\).

So \( \frac{113}{12} = 9 \frac{5}{12}\).

Putting it all together, the answer as a mixed number in simplest form is:
\[
9 \frac{5}{12}
\]

Thus, the final answer is:
\[
9 \quad 5 \quad 12
\]
(you can fill the blanks accordingly)