Evaluate the difference:
`9/(20)-4/(11)`

Answer

To evaluate the difference \( \frac{9}{20} - \frac{4}{11} \), we will follow these steps:

### Step 1: Find the LCM of the denominators
The denominators are 20 and 11. We need to find the least common multiple (LCM) of these two numbers.

- The prime factorization of 20 is \( 2^2 \times 5 \).
- The prime factorization of 11 is \( 11^1 \) (since 11 is a prime number).

To find the LCM, we take the highest power of each prime number:
- From 20: \( 2^2 \) and \( 5^1 \)
- From 11: \( 11^1 \)

Thus, the LCM is:
\[ LCM = 2^2 \times 5^1 \times 11^1 = 4 \times 5 \times 11 = 220 \]

### Step 2: Rewrite each fraction with the LCM as the denominator
Now we will convert both fractions to have the common denominator of 220.

For \( \frac{9}{20} \):
\[ \frac{9}{20} = \frac{9 \times 11}{20 \times 11} = \frac{99}{220} \]

For \( \frac{4}{11} \):
\[ \frac{4}{11} = \frac{4 \times 20}{11 \times 20} = \frac{80}{220} \]

### Step 3: Subtract the fractions
Now that both fractions have the same denominator, we can subtract them:
\[ \frac{99}{220} - \frac{80}{220} = \frac{99 - 80}{220} = \frac{19}{220} \]

### Final Answer
The difference \( \frac{9}{20} - \frac{4}{11} \) is:
\[ \frac{19}{220} \]

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