Sure, let's simplify [tex]\(\frac{3}{4}\)[/tex] of the sum of the mixed numbers [tex]\(1 \frac{11}{3} + 1 \frac{1}{3}\)[/tex].
### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers [tex]\(1 \frac{11}{3}\)[/tex] and [tex]\(1 \frac{1}{3}\)[/tex]:
1. For [tex]\(1 \frac{11}{3}\)[/tex]:
- The whole number part is [tex]\(1\)[/tex].
- The fraction part is [tex]\(\frac{11}{3}\)[/tex].
- To convert this mixed number to an improper fraction: [tex]\(1 \frac{11}{3} = 1 + \frac{11}{3} = \frac{3}{3} + \frac{11}{3} = \frac{14}{3}\)[/tex].
2. For [tex]\(1 \frac{1}{3}\)[/tex]:
- The whole number part is [tex]\(1\)[/tex].
- The fraction part is [tex]\(\frac{1}{3}\)[/tex].
- To convert this mixed number to an improper fraction: [tex]\(1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3}\)[/tex].
### Step 2: Sum the Improper Fractions
Next, we sum the improper fractions [tex]\(\frac{14}{3} + \frac{4}{3}\)[/tex]:
- Add the numerators: [tex]\(14 + 4 = 18\)[/tex].
- The common denominator remains the same: [tex]\(3\)[/tex].
- Therefore, [tex]\(\frac{14}{3} + \frac{4}{3} = \frac{18}{3}\)[/tex].
### Step 3: Simplify the Sum
Simplify [tex]\(\frac{18}{3}\)[/tex]:
- Divide the numerator by the denominator: [tex]\(18 \div 3 = 6\)[/tex].
- Therefore, [tex]\(\frac{18}{3} = 6\)[/tex].
### Step 4: Calculate [tex]\(\frac{3}{4}\)[/tex] of the Sum
Now, we need to find [tex]\(\frac{3}{4}\)[/tex] of the simplified sum [tex]\(6\)[/tex]:
- Multiply [tex]\(6\)[/tex] by [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[
6 \times \frac{3}{4} = \frac{6 \times 3}{4} = \frac{18}{4} = 4.5
\][/tex]
Therefore, [tex]\(\frac{3}{4}\)[/tex] of the sum [tex]\(1 \frac{11}{3} + 1 \frac{1}{3}\)[/tex] is [tex]\(4.5\)[/tex].
