Certainly! Let's solve the problem step-by-step:
### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert each mixed number to an improper fraction.
#### Converting [tex]\(13 \frac{1}{3}\)[/tex]
1. Multiply the whole number part by the denominator: [tex]\(13 \times 3 = 39\)[/tex].
2. Add the numerator to this product: [tex]\(39 + 1 = 40\)[/tex].
3. Thus, [tex]\(13 \frac{1}{3} = \frac{40}{3}\)[/tex].
#### Converting [tex]\(16 \frac{3}{8}\)[/tex]
1. Multiply the whole number part by the denominator: [tex]\(16 \times 8 = 128\)[/tex].
2. Add the numerator to this product: [tex]\(128 + 3 = 131\)[/tex].
3. Thus, [tex]\(16 \frac{3}{8} = \frac{131}{8}\)[/tex].
### Step 2: Find the Common Denominator
To add the fractions [tex]\(\frac{40}{3}\)[/tex] and [tex]\(\frac{131}{8}\)[/tex], we must find a common denominator. The least common denominator (LCD) of 3 and 8 is 24.
Now, adjust both fractions to have this common denominator:
#### Adjusting [tex]\(\frac{40}{3}\)[/tex]
1. Find the factor to multiply 3 by to reach 24: [tex]\(24 \div 3 = 8\)[/tex].
2. Multiply both the numerator and the denominator by this factor: [tex]\(\frac{40 \times 8}{3 \times 8} = \frac{320}{24}\)[/tex].
#### Adjusting [tex]\(\frac{131}{8}\)[/tex]
1. Find the factor to multiply 8 by to reach 24: [tex]\(24 \div 8 = 3\)[/tex].
2. Multiply both the numerator and the denominator by this factor: [tex]\(\frac{131 \times 3}{8 \times 3} = \frac{393}{24}\)[/tex].
### Step 3: Add the Fractions
Now that the fractions have the same denominator, we can add them:
[tex]\[
\frac{320}{24} + \frac{393}{24} = \frac{320 + 393}{24} = \frac{713}{24}
\][/tex]
### Step 4: Simplify if Necessary
[tex]\(\frac{713}{24}\)[/tex] is already in its simplest form, as the numerator and denominator have no common factors other than 1.
### Step 5: Convert the Improper Fraction to a Mixed Number
To convert [tex]\(\frac{713}{24}\)[/tex] back to a mixed number:
1. Divide the numerator by the denominator: [tex]\(713 \div 24 = 29\)[/tex] with a remainder of [tex]\(17\)[/tex].
2. Thus, the mixed number is [tex]\(29 \frac{17}{24}\)[/tex].
### Final Answer
[tex]\[
13 \frac{1}{3} + 16 \frac{3}{8} = 29 \frac{17}{24}
\][/tex]
