What should be subtracted from `((5)/(14) + (3)/(7))` to get `(1)/(5)`?

Answer

To solve the problem step by step, we need to determine what should be subtracted from \(\frac{5}{14} + \frac{3}{7}\) to yield \(\frac{1}{5}\).

### Step 1: Add the fractions \(\frac{5}{14}\) and \(\frac{3}{7}\).

To add these fractions, we need a common denominator. The denominator of \(\frac{5}{14}\) is 14, and the denominator of \(\frac{3}{7}\) is 7. The least common multiple (LCM) of 14 and 7 is 14.

Convert \(\frac{3}{7}\) to have a denominator of 14:
\[ \frac{3}{7} = \frac{3 \times 2}{7 \times 2} = \frac{6}{14} \]

Now we can add:
\[ \frac{5}{14} + \frac{6}{14} = \frac{5 + 6}{14} = \frac{11}{14} \]

### Step 2: Set up the equation.

Let \(X\) be the number that needs to be subtracted. According to the problem:
\[ \frac{11}{14} - X = \frac{1}{5} \]

### Step 3: Rearrange the equation to solve for \(X\).

We can rearrange the equation:
\[ X = \frac{11}{14} - \frac{1}{5} \]

### Step 4: Find a common denominator to subtract the fractions.

The denominators are 14 and 5. The LCM of 14 and 5 is 70.

Convert both fractions:
\[ \frac{11}{14} = \frac{11 \times 5}{14 \times 5} = \frac{55}{70} \]
\[ \frac{1}{5} = \frac{1 \times 14}{5 \times 14} = \frac{14}{70} \]

### Step 5: Subtract the fractions.

Now we can subtract:
\[ X = \frac{55}{70} - \frac{14}{70} = \frac{55 - 14}{70} = \frac{41}{70} \]

### Final Answer:
Thus, the value that should be subtracted is:
\[ X = \frac{41}{70} \]

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