What should be added to the sum of `1//8` and `1//7` so that the sum is `5//14` ?

Explanation

To solve the problem, we need to find out what should be added to the sum of \( \frac{1}{8} \) and \( \frac{1}{7} \) so that the result is \( \frac{5}{14} \). Let's break it down step by step.

### Step 1: Find the sum of \( \frac{1}{8} \) and \( \frac{1}{7} \)

To add the fractions, we need a common denominator. The denominators here are 8 and 7.

- The least common multiple (LCM) of 8 and 7 is 56.

Now we can convert both fractions to have this common denominator:

\[ \frac{1}{8} = \frac{1 \times 7}{8 \times 7} = \frac{7}{56} \]

\[ \frac{1}{7} = \frac{1 \times 8}{7 \times 8} = \frac{8}{56} \]

Now we can add them:

\[ \frac{1}{8} + \frac{1}{7} = \frac{7}{56} + \frac{8}{56} = \frac{15}{56} \]

### Step 2: Set up the equation

Let \( x \) be the number we need to add to \( \frac{15}{56} \) to get \( \frac{5}{14} \).

So, we can write the equation:

\[ \frac{15}{56} + x = \frac{5}{14} \]

### Step 3: Solve for \( x \)

To isolate \( x \), we can subtract \( \frac{15}{56} \) from both sides:

\[ x = \frac{5}{14} - \frac{15}{56} \]

### Step 4: Find a common denominator for the subtraction

The LCM of 14 and 56 is 56. We need to convert \( \frac{5}{14} \) to have a denominator of 56:

\[ \frac{5}{14} = \frac{5 \times 4}{14 \times 4} = \frac{20}{56} \]

Now we can perform the subtraction:

\[ x = \frac{20}{56} - \frac{15}{56} = \frac{20 - 15}{56} = \frac{5}{56} \]

### Conclusion

Thus, the value that should be added to the sum of \( \frac{1}{8} \) and \( \frac{1}{7} \) to get \( \frac{5}{14} \) is:

\[ \boxed{\frac{5}{56}} \]

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