Find
`(7)/(24) - (17)/(36)`

Answer

To solve the problem \( \frac{7}{24} - \frac{17}{36} \), we will follow these steps:

### Step 1: Identify the denominators
The denominators of the fractions are 24 and 36.

### Step 2: Find the Least Common Multiple (LCM)
To subtract the fractions, we need a common denominator. We will find the LCM of 24 and 36.

- The prime factorization of 24 is \( 2^3 \times 3^1 \).
- The prime factorization of 36 is \( 2^2 \times 3^2 \).

To find the LCM, we take the highest power of each prime factor:
- For 2, the highest power is \( 2^3 \).
- For 3, the highest power is \( 3^2 \).

Thus, the LCM is:
\[ LCM = 2^3 \times 3^2 = 8 \times 9 = 72 \]

### Step 3: Convert the fractions to have the common denominator
Now we will convert each fraction to have the denominator of 72.

- For \( \frac{7}{24} \):
\[ \frac{7}{24} = \frac{7 \times 3}{24 \times 3} = \frac{21}{72} \]

- For \( \frac{17}{36} \):
\[ \frac{17}{36} = \frac{17 \times 2}{36 \times 2} = \frac{34}{72} \]

### Step 4: Subtract the fractions
Now we can subtract the two fractions:
\[ \frac{21}{72} - \frac{34}{72} = \frac{21 - 34}{72} = \frac{-13}{72} \]

### Final Answer
The result of \( \frac{7}{24} - \frac{17}{36} \) is:
\[ \frac{-13}{72} \]

---