Find the sum
`3(1)/(8)+1(5)/(12)`

Answer

To find the sum of the fractions \(3\frac{1}{8} + 1\frac{5}{12}\), we will follow these steps:

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

- For \(3\frac{1}{8}\):
\[ 3\frac{1}{8} = \frac{3 \times 8 + 1}{8} = \frac{24 + 1}{8} = \frac{25}{8} \]

- For \(1\frac{5}{12}\):
\[ 1\frac{5}{12} = \frac{1 \times 12 + 5}{12} = \frac{12 + 5}{12} = \frac{17}{12} \]

### Step 2: Find a Common Denominator
Next, we need to find a common denominator to add the two fractions. The denominators are 8 and 12.

- The least common multiple (LCM) of 8 and 12 is 24.

### Step 3: Convert Fractions to Have the Common Denominator
Now we convert both fractions to have the denominator of 24.

- For \(\frac{25}{8}\):
\[ \frac{25}{8} = \frac{25 \times 3}{8 \times 3} = \frac{75}{24} \]

- For \(\frac{17}{12}\):
\[ \frac{17}{12} = \frac{17 \times 2}{12 \times 2} = \frac{34}{24} \]

### Step 4: Add the Fractions
Now that both fractions have the same denominator, we can add them:
\[ \frac{75}{24} + \frac{34}{24} = \frac{75 + 34}{24} = \frac{109}{24} \]

### Step 5: Convert the Improper Fraction to a Mixed Number
Finally, we convert \(\frac{109}{24}\) into a mixed number.

- Divide 109 by 24:
\[ 24 \times 4 = 96 \quad \text{(since \(24 \times 5 = 120\) is too high)} \]
The remainder is:
\[ 109 - 96 = 13 \]
Therefore, we can write:
\[ \frac{109}{24} = 4\frac{13}{24} \]

### Final Answer
Thus, the sum \(3\frac{1}{8} + 1\frac{5}{12} = 4\frac{13}{24}\).

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