Compare the following fractions using the symbols >, <, or =. Show all the calculations to support your answer.

5/8 7/12

To compare the fractions \( \frac{5}{8} \) and \( \frac{7}{12} \), we need to convert them to have a common denominator, so we can compare their numerators directly.

### Step 1: Find the least common denominator (LCD)

The denominators are 8 and 12. We need to find the least common denominator of these two numbers.

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

The LCD is the smallest number that is divisible by both 8 and 12. To find it, we take the highest powers of all prime factors involved:
- The highest power of 2 is \( 2^3 \) (from 8).
- The highest power of 3 is \( 3^1 \) (from 12).

Thus, the least common denominator is \( 2^3 \times 3 = 24 \).

### Step 2: Convert the fractions to have the common denominator

Now, convert both fractions 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: Compare the numerators

Now that both fractions have the same denominator (24), we can compare their numerators:
\[
15 \, (\text{from } \frac{15}{24}) > 14 \, (\text{from } \frac{14}{24})
\]

### Conclusion:
\[
\frac{5}{8} > \frac{7}{12}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How can you find the least common multiple (LCM) of any two numbers?
2. Can you compare fractions without finding a common denominator?
3. What is the general method to compare improper fractions?
4. How does multiplying the numerator and denominator by the same number affect a fraction?
5. How do you simplify fractions after comparing them?

**Tip**: When comparing fractions, always ensure you are working with a common denominator to avoid mistakes!

Compare the following fractions using the symbols >, <, or =. Show all the calculations to support your answer. 5/8 7/12

Learn how to compare the fractions 5/8 and 7/12 by finding the least common denominator (LCD). This detailed solution shows how to convert fractions to have a common denominator and compare their numerators. Suitable for Grades 5-7 students.

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