The value of `((3)/(5) + (1)/(5)-(3)/(10)) xx ((36)/(45) div (16)/(5))` is

Options

A. `1/8`
B. `1/(20)`
C. `(32)/(25)`
D. `(64)/(125)`

Answer

To solve the expression \(\left(\frac{3}{5} + \frac{1}{5} - \frac{3}{10}\right) \times \left(\frac{36}{45} \div \frac{16}{5}\right)\), we will break it down step by step.

### Step 1: Solve the first part of the expression inside the brackets
We start with:
\[ \frac{3}{5} + \frac{1}{5} - \frac{3}{10} \]
Since \(\frac{3}{5}\) and \(\frac{1}{5}\) have the same denominator, we can add them directly:
\[ \frac{3 + 1}{5} = \frac{4}{5} \]
Now we subtract \(\frac{3}{10}\). To do this, we need a common denominator. The least common multiple of 5 and 10 is 10. We convert \(\frac{4}{5}\) to have a denominator of 10:
\[ \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} \]
Now we can perform the subtraction:
\[ \frac{8}{10} - \frac{3}{10} = \frac{8 - 3}{10} = \frac{5}{10} = \frac{1}{2} \]

### Step 2: Solve the second part of the expression
Next, we need to solve:
\[ \frac{36}{45} \div \frac{16}{5} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{36}{45} \times \frac{5}{16} \]
Now we can simplify before multiplying. The greatest common divisor of 36 and 45 is 9, so:
\[ \frac{36 \div 9}{45 \div 9} = \frac{4}{5} \]
Now we multiply:
\[ \frac{4}{5} \times \frac{5}{16} = \frac{4 \times 5}{5 \times 16} \]
The 5s cancel out:
\[ = \frac{4}{16} = \frac{1}{4} \]

### Step 3: Combine the results from Step 1 and Step 2
Now we multiply the results from Step 1 and Step 2:
\[ \frac{1}{2} \times \frac{1}{4} = \frac{1 \times 1}{2 \times 4} = \frac{1}{8} \]

### Final Answer
The value of the expression \(\left(\frac{3}{5} + \frac{1}{5} - \frac{3}{10}\right) \times \left(\frac{36}{45} \div \frac{16}{5}\right)\) is:
\[ \frac{1}{8} \]