Three of the four parts lettered (A) (B) ( C) and (D) are exactly equal. You have to find that part which is not equal to the other three. If all the four parts are equal, that the answer is (E).

Options

A. (A) `2/5+7/5+2 2/5+ 3 1/5+ 1 3/5`
B. (B)`4/6 + 1 1/3+ 2 2/3+ 5/6`
C. (C)`6/7+3/7-1/7+2/7+6/7+ 6 5/7`
D. (D)`1 1/3+ 6 2/3- 4 1/3+ 5+ 1/3`.

Answer

To solve the problem, we need to determine which of the four parts (A, B, C, D) is not equal to the other three. If all four parts are equal, the answer will be (E).

Let's analyze each part step by step:

### Step 1: Analyze Part A
Part A is given as \( \frac{2}{5} \).

### Step 2: Analyze Part B
Part B is given as \( \frac{2}{5} + \frac{7}{5} + \frac{5}{10} \).
- First, convert \( \frac{5}{10} \) to a fraction with a common denominator:
\[ \frac{5}{10} = \frac{1}{2} = \frac{5}{10} = \frac{5}{10} \]
- Now, convert \( \frac{2}{5} \) and \( \frac{7}{5} \) to a common denominator of 10:
\[ \frac{2}{5} = \frac{4}{10}, \quad \frac{7}{5} = \frac{14}{10} \]
- Now add them together:
\[ \frac{4}{10} + \frac{14}{10} + \frac{5}{10} = \frac{4 + 14 + 5}{10} = \frac{23}{10} \]

### Step 3: Analyze Part C
Part C is given as \( \frac{4}{6} + \frac{3}{1} + \frac{3}{3} + \frac{2}{3} + \frac{5}{6} \).
- Convert \( \frac{4}{6} \) to \( \frac{2}{3} \) and \( \frac{3}{3} = 1 \):
\[ \frac{2}{3} + 3 + 1 + \frac{2}{3} + \frac{5}{6} \]
- Convert everything to a common denominator of 6:
\[ \frac{4}{6} + \frac{18}{6} + \frac{6}{6} + \frac{4}{6} + \frac{5}{6} = \frac{4 + 18 + 6 + 4 + 5}{6} = \frac{37}{6} \]

### Step 4: Analyze Part D
Part D is given as \( \frac{6}{7} + \frac{3}{7} - \frac{1}{7} + \frac{2}{7} + \frac{6}{7} \).
- Combine the fractions:
\[ \frac{6 + 3 - 1 + 2 + 6}{7} = \frac{16}{7} \]

### Step 5: Compare All Parts
Now we compare the values of each part:
- Part A: \( \frac{2}{5} = 0.4 \)
- Part B: \( \frac{23}{10} = 2.3 \)
- Part C: \( \frac{37}{6} \approx 6.17 \)
- Part D: \( \frac{16}{7} \approx 2.29 \)

### Conclusion
From the calculations:
- Part A is different from Parts B, C, and D.
- The only part that is not equal to the others is **Part A**.

Thus, the answer is **(A)**.

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