Find the difrencence
`(5)/(8)-(7)/(12)`

Answer

To find the difference between \( \frac{5}{8} \) and \( \frac{7}{12} \), we will follow these steps:

### Step 1: Find the LCM of the denominators
The denominators are 8 and 12. We need to find the least common multiple (LCM) of these two numbers.

- The prime factorization of 8 is \( 2^3 \).
- The prime factorization of 12 is \( 2^2 \times 3^1 \).

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 \( 3^1 \).

Thus, the LCM is:
\[ LCM = 2^3 \times 3^1 = 8 \times 3 = 24 \]

### Step 2: Convert each fraction to have the same denominator
Now that we have the LCM, we will convert each fraction to have a denominator of 24.

For \( \frac{5}{8} \):
\[ \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24} \]

For \( \frac{7}{12} \):
\[ \frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24} \]

### Step 3: Subtract the two fractions
Now we can subtract the two fractions:
\[ \frac{15}{24} - \frac{14}{24} = \frac{15 - 14}{24} = \frac{1}{24} \]

### Final Answer
The difference \( \frac{5}{8} - \frac{7}{12} \) is:
\[ \frac{1}{24} \]

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