Between `(1)/(7)` and `(2)/( 9 )`, which fraction is bigger ?

Answer

To determine which fraction is bigger between \( \frac{1}{7} \) and \( \frac{2}{9} \), we can follow these steps:

### Step 1: Identify the fractions
We have two fractions:
- \( \frac{1}{7} \)
- \( \frac{2}{9} \)

### Step 2: Find a common denominator
To compare the two fractions, we need to have a common denominator. The denominators are 7 and 9. The least common multiple (LCM) of 7 and 9 is 63.

### Step 3: Convert \( \frac{1}{7} \) to have a denominator of 63
To convert \( \frac{1}{7} \) to a fraction with a denominator of 63, we multiply both the numerator and the denominator by 9:
\[ \frac{1 \times 9}{7 \times 9} = \frac{9}{63} \]

### Step 4: Convert \( \frac{2}{9} \) to have a denominator of 63
To convert \( \frac{2}{9} \) to a fraction with a denominator of 63, we multiply both the numerator and the denominator by 7:
\[ \frac{2 \times 7}{9 \times 7} = \frac{14}{63} \]

### Step 5: Compare the numerators
Now we have:
- \( \frac{1}{7} = \frac{9}{63} \)
- \( \frac{2}{9} = \frac{14}{63} \)

Since \( 14 > 9 \), we can conclude that:
\[ \frac{14}{63} > \frac{9}{63} \]

### Step 6: Conclusion
Thus, \( \frac{2}{9} \) is greater than \( \frac{1}{7} \).

### Final Answer
The fraction \( \frac{2}{9} \) is bigger than \( \frac{1}{7} \).

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