What should come in place of the question mark (?) in the following questions ?
`1(2)/(5) - 2(5)/(7) + 3(7)/(10) = ?`

Options

A. `5(17)/(70)`
B. `4(13)/(70)`
C. `2(27)/(70)`
D. `3(11)/(70)`

Answer

To solve the expression \(1\frac{2}{5} - 2\frac{5}{7} + 3\frac{7}{10}\), we will first convert the mixed numbers into improper fractions.

### Step 1: Convert mixed numbers to improper fractions
1. \(1\frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{5 + 2}{5} = \frac{7}{5}\)
2. \(2\frac{5}{7} = \frac{2 \times 7 + 5}{7} = \frac{14 + 5}{7} = \frac{19}{7}\)
3. \(3\frac{7}{10} = \frac{3 \times 10 + 7}{10} = \frac{30 + 7}{10} = \frac{37}{10}\)

So, we can rewrite the expression as:
\[ \frac{7}{5} - \frac{19}{7} + \frac{37}{10} \]

### Step 2: Find a common denominator
The denominators are 5, 7, and 10. The least common multiple (LCM) of these numbers is 70.

### Step 3: Convert each fraction to have the common denominator
1. Convert \(\frac{7}{5}\):
\[ \frac{7}{5} = \frac{7 \times 14}{5 \times 14} = \frac{98}{70} \]
2. Convert \(\frac{19}{7}\):
\[ \frac{19}{7} = \frac{19 \times 10}{7 \times 10} = \frac{190}{70} \]
3. Convert \(\frac{37}{10}\):
\[ \frac{37}{10} = \frac{37 \times 7}{10 \times 7} = \frac{259}{70} \]

Now, we can rewrite the expression:
\[ \frac{98}{70} - \frac{190}{70} + \frac{259}{70} \]

### Step 4: Combine the fractions
Combine the numerators over the common denominator:
\[ \frac{98 - 190 + 259}{70} \]

Calculating the numerator:
\[ 98 - 190 = -92 \]
\[ -92 + 259 = 167 \]

So, we have:
\[ \frac{167}{70} \]

### Final Answer
The value that should come in place of the question mark (?) is:
\[ \frac{167}{70} \]