Which is larger?
`1/(31)or22/(39)`

Answer

To determine which fraction is larger between \( \frac{1}{31} \) and \( \frac{22}{39} \), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM) of the denominators
The denominators are 31 and 39. Since 31 is a prime number, the LCM of 31 and 39 is simply \( 31 \times 39 \).

### Step 2: Convert both fractions to have the same denominator
We will convert \( \frac{1}{31} \) and \( \frac{22}{39} \) to have the common denominator of \( 31 \times 39 \).

- For \( \frac{1}{31} \):
\[ \frac{1}{31} = \frac{1 \times 39}{31 \times 39} = \frac{39}{31 \times 39} \]

- For \( \frac{22}{39} \):
\[ \frac{22}{39} = \frac{22 \times 31}{39 \times 31} = \frac{682}{31 \times 39} \]

### Step 3: Compare the numerators
Now we have:
- \( \frac{39}{31 \times 39} \)
- \( \frac{682}{31 \times 39} \)

Since both fractions have the same denominator, we can compare the numerators directly:
- 39 (from \( \frac{1}{31} \))
- 682 (from \( \frac{22}{39} \))

### Step 4: Determine which is larger
Clearly, \( 682 > 39 \). Therefore, \( \frac{22}{39} \) is larger than \( \frac{1}{31} \).

### Conclusion
Thus, the larger fraction is:
\[ \frac{22}{39} \]

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