The sum of two fractions is `3""5/12`. If one of them is `1""3/10`, find the other fraction.

Answer

To find the other fraction when the sum of two fractions is \(3 \frac{5}{12}\) and one of them is \(1 \frac{3}{10}\), we can follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert both mixed numbers into improper fractions.

For \(3 \frac{5}{12}\):
\[ 3 \frac{5}{12} = \frac{(3 \times 12) + 5}{12} = \frac{36 + 5}{12} = \frac{41}{12} \]

For \(1 \frac{3}{10}\):
\[ 1 \frac{3}{10} = \frac{(1 \times 10) + 3}{10} = \frac{10 + 3}{10} = \frac{13}{10} \]

### Step 2: Set Up the Equation
We know that the sum of the two fractions is:
\[ \frac{41}{12} = \frac{13}{10} + \text{Other Fraction} \]

### Step 3: Isolate the Other Fraction
To find the other fraction, we can rearrange the equation:
\[ \text{Other Fraction} = \frac{41}{12} - \frac{13}{10} \]

### Step 4: Find a Common Denominator
To subtract the fractions, we need a common denominator. The least common multiple (LCM) of 12 and 10 is 60.

### Step 5: Convert Both Fractions to the Common Denominator
Convert \(\frac{41}{12}\) to have a denominator of 60:
\[ \frac{41}{12} = \frac{41 \times 5}{12 \times 5} = \frac{205}{60} \]

Convert \(\frac{13}{10}\) to have a denominator of 60:
\[ \frac{13}{10} = \frac{13 \times 6}{10 \times 6} = \frac{78}{60} \]

### Step 6: Subtract the Fractions
Now we can subtract the two fractions:
\[ \text{Other Fraction} = \frac{205}{60} - \frac{78}{60} = \frac{205 - 78}{60} = \frac{127}{60} \]

### Step 7: Convert Back to a Mixed Number
To convert \(\frac{127}{60}\) back to a mixed number:
\[ 127 \div 60 = 2 \quad \text{(with a remainder of 7)} \]
So, \(\frac{127}{60} = 2 \frac{7}{60}\).

### Final Answer
The other fraction is:
\[ 2 \frac{7}{60} \]