Write the fraction (4/5)+(8/3) in decimal form-

Options

A. 2.73
B. 3.74
C. 3.46
D. 4.3

Answer

To convert the fraction \( \frac{4}{5} + \frac{8}{3} \) into decimal form, we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM)
To add the fractions, we first need to find the LCM of the denominators (5 and 3).

The LCM of 5 and 3 is 15.

### Step 2: Convert each fraction to have the same denominator
Now we convert each fraction to have the common denominator of 15.

- For \( \frac{4}{5} \):
\[ \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15} \]

- For \( \frac{8}{3} \):
\[ \frac{8}{3} = \frac{8 \times 5}{3 \times 5} = \frac{40}{15} \]

### Step 3: Add the fractions
Now that both fractions have the same denominator, we can add them:
\[ \frac{12}{15} + \frac{40}{15} = \frac{12 + 40}{15} = \frac{52}{15} \]

### Step 4: Convert the fraction to decimal form
To convert \( \frac{52}{15} \) into decimal form, we perform the division:
\[ 52 \div 15 \]

- 15 goes into 52 three times (since \( 15 \times 3 = 45 \)).
- Subtract 45 from 52, which gives us 7.
- Now, we add a decimal point and a zero, making it 70.
- 15 goes into 70 four times (since \( 15 \times 4 = 60 \)).
- Subtract 60 from 70, which gives us 10.
- Add another zero, making it 100.
- 15 goes into 100 six times (since \( 15 \times 6 = 90 \)).
- Subtract 90 from 100, which gives us 10 again.
- This process will repeat, giving us a repeating decimal.

Thus, we can conclude that:
\[ 52 \div 15 = 3.4666... \text{ (which can be written as } 3.46\overline{6} \text{)} \]

### Final Answer
The decimal form of \( \frac{4}{5} + \frac{8}{3} \) is approximately \( 3.4667 \).

---