To solve the given problem of adding the fractions [tex]\(\frac{1}{8}\)[/tex], [tex]\(\frac{3}{10}\)[/tex], and [tex]\(\frac{4}{5}\)[/tex], let's break it down step-by-step.
### Step 1: Understanding the fractions
We have:
[tex]\[
\frac{1}{8}, \quad \frac{3}{10}, \quad \text{and} \quad \frac{4}{5}
\][/tex]
### Step 2: Find a common denominator
To add these fractions, we need a common denominator. In this case, the denominators are 8, 10, and 5.
The least common multiple (LCM) of these numbers is 40.
### Step 3: Convert each fraction to have the common denominator
Convert each fraction to have the denominator 40.
1. [tex]\(\frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40}\)[/tex]
2. [tex]\(\frac{3}{10} = \frac{3 \times 4}{10 \times 4} = \frac{12}{40}\)[/tex]
3. [tex]\(\frac{4}{5} = \frac{4 \times 8}{5 \times 8} = \frac{32}{40}\)[/tex]
### Step 4: Add the fractions
Now, we can add the fractions:
[tex]\[
\frac{5}{40} + \frac{12}{40} + \frac{32}{40} = \frac{5 + 12 + 32}{40} = \frac{49}{40}
\][/tex]
### Step 5: Simplify the fraction
The fraction [tex]\(\frac{49}{40}\)[/tex] is already in its simplest form.
### Step 6: Convert to decimal form (if needed)
To convert [tex]\(\frac{49}{40}\)[/tex] to a decimal:
[tex]\[
\frac{49}{40} = 1.225
\][/tex]
### Step 7: Final Answer
The final answer in fractional form is [tex]\(\frac{49}{40}\)[/tex].
Among the given choices:
[tex]\[
\frac{49}{40}, \quad \frac{8}{5}, \quad \frac{8}{23}, \quad \frac{4}{17}, \quad \frac{1}{5}
\][/tex]
The correct answer is [tex]\(\frac{49}{40}\)[/tex].
