Compare the fractions `5/(12) and 7/(13)`.

Answer

To compare the fractions \( \frac{5}{12} \) and \( \frac{7}{13} \), we can follow these steps:

### Step 1: Identify the fractions
We have two fractions to compare:
- \( \frac{5}{12} \)
- \( \frac{7}{13} \)

### Step 2: Find a common denominator
Since these fractions have different denominators (12 and 13), we need to convert them into like fractions by finding a common denominator. The least common multiple (LCM) of 12 and 13 is 156.

### Step 3: Convert \( \frac{5}{12} \) to a fraction with a denominator of 156
To convert \( \frac{5}{12} \):
- Multiply both the numerator and the denominator by 13 (the denominator of the second fraction).

\[ \frac{5 \times 13}{12 \times 13} = \frac{65}{156} \]

### Step 4: Convert \( \frac{7}{13} \) to a fraction with a denominator of 156
To convert \( \frac{7}{13} \):
- Multiply both the numerator and the denominator by 12 (the denominator of the first fraction).

\[ \frac{7 \times 12}{13 \times 12} = \frac{84}{156} \]

### Step 5: Compare the numerators
Now we can compare the two fractions:
- \( \frac{65}{156} \)
- \( \frac{84}{156} \)

Since the denominators are the same, we only need to compare the numerators:
- 65 (from \( \frac{5}{12} \))
- 84 (from \( \frac{7}{13} \))

### Step 6: Determine which fraction is larger
Since \( 84 > 65 \), we can conclude that:
\[ \frac{5}{12} < \frac{7}{13} \]

### Final Answer
Thus, \( \frac{5}{12} \) is less than \( \frac{7}{13} \).

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