Add, answer as a mixed number in simplest form.

3 2/3 + 5 3/4
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1 answer

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)