Which is larger?
`3(13)/(26)or3(14)/(19)`

Answer

To determine which of the two mixed fractions is larger, we will follow these steps:

### Step 1: Convert the mixed fractions to improper fractions
1. For the first fraction, \(3 \frac{13}{26}\):
- Multiply the whole number (3) by the denominator (26): \(3 \times 26 = 78\)
- Add the numerator (13): \(78 + 13 = 91\)
- Therefore, \(3 \frac{13}{26} = \frac{91}{26}\)

2. For the second fraction, \(3 \frac{14}{19}\):
- Multiply the whole number (3) by the denominator (19): \(3 \times 19 = 57\)
- Add the numerator (14): \(57 + 14 = 71\)
- Therefore, \(3 \frac{14}{19} = \frac{71}{19}\)

### Step 2: Compare the two improper fractions
Now we have:
- \( \frac{91}{26} \)
- \( \frac{71}{19} \)

To compare these fractions, we need a common denominator. The least common multiple (LCM) of 26 and 19 is 494.

### Step 3: Convert both fractions to have the same denominator
1. For \( \frac{91}{26} \):
- Multiply the numerator and denominator by \(19\):
\[ \frac{91 \times 19}{26 \times 19} = \frac{1729}{494} \]

2. For \( \frac{71}{19} \):
- Multiply the numerator and denominator by \(26\):
\[ \frac{71 \times 26}{19 \times 26} = \frac{1846}{494} \]

### Step 4: Compare the numerators
Now we compare \(1729\) and \(1846\):
- Since \(1846 > 1729\), we conclude that:
\[ \frac{71}{19} > \frac{91}{26} \]

### Step 5: State the larger mixed fraction
Thus, the larger mixed fraction is:
\[ 3 \frac{14}{19} \]

### Final Answer
The larger fraction is \(3 \frac{14}{19}\).

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