What should be added to `(3)/(8)` to get `(5)/(12)`?

Answer

To solve the problem of what should be added to \( \frac{3}{8} \) to get \( \frac{5}{12} \), we can follow these steps:

### Step 1: Set Up the Equation
Let \( x \) be the number that we need to add to \( \frac{3}{8} \). According to the problem, we can write the equation as:
\[ \frac{3}{8} + x = \frac{5}{12} \]

### Step 2: Isolate \( x \)
To find \( x \), we need to isolate it on one side of the equation. We can do this by subtracting \( \frac{3}{8} \) from both sides:
\[ x = \frac{5}{12} - \frac{3}{8} \]

### Step 3: Find a Common Denominator
To subtract the fractions, we need a common denominator. The denominators are 12 and 8. The least common multiple (LCM) of 12 and 8 is 24.

### Step 4: Convert the Fractions
Now we convert both fractions to have the common denominator of 24:
\[ \frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24} \]
\[ \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \]

### Step 5: Subtract the Fractions
Now we can subtract the two fractions:
\[ x = \frac{10}{24} - \frac{9}{24} = \frac{1}{24} \]

### Step 6: Conclusion
Thus, the value of \( x \) that should be added to \( \frac{3}{8} \) to get \( \frac{5}{12} \) is:
\[ \frac{1}{24} \]

### Summary
The answer is \( \frac{1}{24} \).

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