Compare the fractions given below:
`(5)/(8), (7)/(12)`

Answer

To compare the fractions \( \frac{5}{8} \) and \( \frac{7}{12} \), we can follow these steps:

### Step 1: Find the Least Common Multiple (LCM) of the denominators.
The denominators are 8 and 12. To find the LCM, we can list the multiples of each number or use the prime factorization method.

- 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 (LCM).
Now we will convert both fractions to have the 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: Compare the numerators.
Now we can compare the two fractions:
- \( \frac{15}{24} \) and \( \frac{14}{24} \).

Since \( 15 > 14 \), we conclude that:
\[ \frac{5}{8} > \frac{7}{12}. \]

### Final Conclusion:
Thus, \( \frac{5}{8} \) is greater than \( \frac{7}{12} \).

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