Find the following:
`7/(20)-1/(5)`

Options

A. `3/(20)`
B. `4/(20)`
C. `5/(20)`
D. `6/(20)`

Answer

To solve the problem \( \frac{7}{20} - \frac{1}{5} \), we will follow these steps:

### Step 1: Identify the fractions
We have two fractions: \( \frac{7}{20} \) and \( \frac{1}{5} \).

### Step 2: Find the Least Common Multiple (LCM) of the denominators
The denominators are 20 and 5. We need to find the LCM of these two numbers.

- The factors of 20 are \( 2 \times 2 \times 5 \).
- The factors of 5 are \( 5 \).

To find the LCM, we take the highest power of each prime factor:
- For 2, the highest power is \( 2^2 \) (from 20).
- For 5, the highest power is \( 5^1 \) (from both).

Thus, the LCM is:
\[ LCM = 2^2 \times 5^1 = 4 \times 5 = 20 \]

### Step 3: Rewrite the fractions with the common denominator
Now that we have the LCM, we can rewrite both fractions with the denominator of 20.

The first fraction \( \frac{7}{20} \) remains the same since its denominator is already 20.

For the second fraction \( \frac{1}{5} \):
- We convert it to have a denominator of 20.
- To do this, we multiply both the numerator and the denominator by 4 (since \( 5 \times 4 = 20 \)):
\[ \frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20} \]

### Step 4: Subtract the fractions
Now we can subtract the two fractions:
\[ \frac{7}{20} - \frac{4}{20} = \frac{7 - 4}{20} = \frac{3}{20} \]

### Step 5: Final answer
The result of \( \frac{7}{20} - \frac{1}{5} \) is:
\[ \frac{3}{20} \]

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