What is wrong in the following?
`7/4 + 5/2 = 7/4 + 5/2 = 12/6 = 2`

Answer

To solve the problem step by step, we need to identify what is wrong with the expression given:

**Expression:**
\[ \frac{7}{4} + \frac{5}{2} = \frac{7}{4} + \frac{5}{2} = \frac{12}{6} = 2 \]

### Step 1: Identify the fractions to be added
We have two fractions:
\[ \frac{7}{4} \text{ and } \frac{5}{2} \]

**Hint:** When adding fractions, it's important to ensure they have a common denominator.

### Step 2: Find the least common multiple (LCM) of the denominators
The denominators are 4 and 2. The LCM of 4 and 2 is 4.

**Hint:** To find the LCM, list the multiples of each denominator and find the smallest common multiple.

### Step 3: Rewrite the fractions with the common denominator
Since the LCM is 4, we can rewrite the fractions:
- The first fraction \(\frac{7}{4}\) remains the same.
- The second fraction \(\frac{5}{2}\) needs to be converted. To convert \(\frac{5}{2}\) to a denominator of 4, we multiply both the numerator and denominator by 2:
\[ \frac{5}{2} = \frac{5 \times 2}{2 \times 2} = \frac{10}{4} \]

**Hint:** When changing the denominator, remember to multiply both the numerator and the denominator by the same number.

### Step 4: Add the fractions
Now we can add the two fractions:
\[ \frac{7}{4} + \frac{10}{4} = \frac{7 + 10}{4} = \frac{17}{4} \]

**Hint:** When adding fractions with the same denominator, simply add the numerators and keep the denominator the same.

### Step 5: Conclusion
The correct answer is:
\[ \frac{17}{4} \]

The mistake in the original expression was in the calculation of the LCM and the addition of the numerators. The original expression incorrectly stated that \(\frac{7}{4} + \frac{5}{2} = \frac{12}{6}\), which is not correct.

**Final Answer:**
The correct sum of \(\frac{7}{4} + \frac{5}{2}\) is \(\frac{17}{4}\), not 2.