To find the sum of [tex]\(2 \frac{5}{6}\)[/tex] and [tex]\(9 \frac{1}{3}\)[/tex], let's break it down into clear steps.
### Step 1: Convert mixed numbers to improper fractions
First, convert each mixed number to an improper fraction.
- For [tex]\(2 \frac{5}{6}\)[/tex]:
[tex]\[
2 \frac{5}{6} = 2 + \frac{5}{6} = \frac{2 \cdot 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6}
\][/tex]
- For [tex]\(9 \frac{1}{3}\)[/tex]:
[tex]\[
9 \frac{1}{3} = 9 + \frac{1}{3} = \frac{9 \cdot 3 + 1}{3} = \frac{27 + 1}{3} = \frac{28}{3}
\][/tex]
### Step 2: Find a common denominator
To add the fractions, we need a common denominator. The least common multiple (LCM) of 6 and 3 is 6.
### Step 3: Adjust fractions to have the common denominator
Convert each fraction to have the common denominator of 6.
- For [tex]\(\frac{17}{6}\)[/tex]:
[tex]\[
\frac{17}{6} \text{ is already with denominator } 6.
\][/tex]
- For [tex]\(\frac{28}{3}\)[/tex]:
[tex]\[
\frac{28}{3} \times \frac{2}{2} = \frac{28 \cdot 2}{3 \cdot 2} = \frac{56}{6}
\][/tex]
### Step 4: Add the fractions
Now that both fractions have a common denominator, we can add them:
[tex]\[
\frac{17}{6} + \frac{56}{6} = \frac{17 + 56}{6} = \frac{73}{6}
\][/tex]
### Step 5: Convert the improper fraction to a mixed number
Convert [tex]\(\frac{73}{6}\)[/tex] into a mixed number.
- Divide 73 by 6 to get the whole number part and the remainder:
[tex]\[
73 \div 6 = 12 \quad \text{ remainder } 1
\][/tex]
So, [tex]\(\frac{73}{6} = 12 \frac{1}{6}\)[/tex].
### Final Answer:
Therefore, the sum of [tex]\(2 \frac{5}{6}\)[/tex] and [tex]\(9 \frac{1}{3}\)[/tex] is [tex]\(12 \frac{1}{6}\)[/tex].
