`(15)/(20)+(4)/(5)xx(2)/(3)xx(8)/(5)=?`

Options

A. 0
B. 1.6
C. 3
D. 5

Explanation

To solve the expression \(\frac{15}{20} + \frac{4}{5} \times \frac{2}{3} \times \frac{8}{5}\), we will follow the order of operations (BODMAS/BIDMAS rules), which dictate that we perform multiplication before addition.

### Step-by-step solution:

1. **Calculate the multiplication part first:**
\[ \frac{4}{5} \times \frac{2}{3} \times \frac{8}{5} \]
- Multiply the numerators: \(4 \times 2 \times 8 = 64\)
- Multiply the denominators: \(5 \times 3 \times 5 = 75\)
- So, we have:
\[ \frac{4}{5} \times \frac{2}{3} \times \frac{8}{5} = \frac{64}{75} \]

2. **Now, add \(\frac{15}{20}\) to the result from step 1:**
- First, simplify \(\frac{15}{20}\):
\[ \frac{15}{20} = \frac{3}{4} \quad \text{(dividing both numerator and denominator by 5)} \]

3. **Find a common denominator for \(\frac{3}{4}\) and \(\frac{64}{75}\):**
- The least common multiple (LCM) of 4 and 75 is 300.
- Convert \(\frac{3}{4}\) to have a denominator of 300:
\[ \frac{3}{4} = \frac{3 \times 75}{4 \times 75} = \frac{225}{300} \]
- Convert \(\frac{64}{75}\) to have a denominator of 300:
\[ \frac{64}{75} = \frac{64 \times 4}{75 \times 4} = \frac{256}{300} \]

4. **Now, add the two fractions:**
\[ \frac{225}{300} + \frac{256}{300} = \frac{225 + 256}{300} = \frac{481}{300} \]

5. **Convert the improper fraction to a mixed number (if needed):**
- Divide 481 by 300:
\[ 481 \div 300 = 1 \quad \text{(whole number part)} \]
- Remainder: \(481 - 300 = 181\)
- So, we can express it as:
\[ 1 \frac{181}{300} \]

Thus, the final answer is:
\[ \frac{481}{300} \quad \text{or} \quad 1 \frac{181}{300} \]