To add the mixed numbers \(3 \frac{2}{3}\) and \(5 \frac{3}{4}\), we'll follow these steps:
- Convert the mixed numbers to improper fractions.
- Find a common denominator.
- Add the fractions.
- 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)
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