Let's find the sum [tex]\(4 \frac{3}{4} + 2 \frac{1}{3}\)[/tex] step-by-step.
### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers to improper fractions.
For [tex]\(4 \frac{3}{4}\)[/tex]:
[tex]\[4 \frac{3}{4} = 4 + \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4}\][/tex]
For [tex]\(2 \frac{1}{3}\)[/tex]:
[tex]\[2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}\][/tex]
### Step 2: Find a Common Denominator
We need a common denominator to add these fractions. The least common denominator of 4 and 3 is 12.
### Step 3: Convert Fractions to Have the Common Denominator
Convert the fractions to have the common denominator of 12.
For [tex]\(\frac{19}{4}\)[/tex]:
[tex]\[\frac{19}{4} = \frac{19 \times 3}{4 \times 3} = \frac{57}{12}\][/tex]
For [tex]\(\frac{7}{3}\)[/tex]:
[tex]\[\frac{7}{3} = \frac{7 \times 4}{3 \times 4} = \frac{28}{12}\][/tex]
### Step 4: Add the Fractions
Now, we add the two fractions:
[tex]\[\frac{57}{12} + \frac{28}{12} = \frac{57 + 28}{12} = \frac{85}{12}\][/tex]
### Step 5: Convert the Improper Fraction to a Mixed Number
To convert [tex]\(\frac{85}{12}\)[/tex] into a mixed number, we divide 85 by 12.
The integer part of the quotient:
[tex]\[85 \div 12 = 7\text{ R1}\][/tex]
This means [tex]\(85 = 12 \times 7 + 1\)[/tex], so the whole number part is 7 and the remainder is 1.
Thus, [tex]\(\frac{85}{12}\)[/tex] can be written as:
[tex]\[7 \frac{1}{12}\][/tex]
### Result
Therefore, the sum [tex]\(4 \frac{3}{4} + 2 \frac{1}{3}\)[/tex] is:
[tex]\[\boxed{7 \frac{1}{12}}\][/tex]
So, to recap the important intermediate values:
- The fractions with common denominators: [tex]\(14.25\)[/tex] and [tex]\(9.333\)[/tex]
- The sum as an improper fraction: [tex]\(23.583\)[/tex]
- Simplified to a mixed number: [tex]\(23 \frac{7}{12}\)[/tex]
