The value of $\frac{4}{7}$+$\frac{5}{14}$-$\frac{7}{8}$ is:

Q: The value of $\frac{4}{7}$+$\frac{5}{14}$-$\frac{7}{8}$ is:

To solve the expression $\frac{4}{7} + \frac{5}{14} - \frac{7}{8}$, we need to find a common denominator for the fractions involved. The denominators are 7, 14, and 8. The least common multiple (LCM) of these numbers is 56. 1. **Convert each fraction to have a denominator of 56:** - $\frac{4}{7}$: Multiply both the numerator and the denominator by 8 to get $\frac{32}{56}$. - $\frac{5}{14}$: Multiply both the numerator and the denominator by 4 to get $\frac{20}{56}$. - $\frac{7}{8}$: Multiply both the numerator and the denominator by 7 to get $\frac{49}{56}$. 2. **Perform the operations:** - Add $\frac{32}{56}$ and $\frac{20}{56}$: \[ \frac{32}{56} + \frac{20}{56} = \frac{52}{56} \] - Subtract $\frac{49}{56}$ from $\frac{52}{56}$: \[ \frac{52}{56} - \frac{49}{56} = \frac{3}{56} \] 3. **Conclusion:** The result of the expression $\frac{4}{7} + \frac{5}{14} - \frac{7}{8}$ is $\frac{3}{56}$, which corresponds to Option 1. 4. **Explanation of why other options are incorrect:** - **Option 2: $\frac{5}{56}$** is incorrect because the calculation shows the result is $\frac{3}{56}$, not $\frac{5}{56}$. - **Option 3: $\frac{3}{14}$** is incorrect because $\frac{3}{14}$ is equivalent to $\frac{12}{56}$, which is not the result of the calculation. - **Option 4: $\frac{5}{28}$** is incorrect because $\frac{5}{28}$ is equivalent to $\frac{10}{56}$, which does not match the calculated result of $\frac{3}{56}$. Therefore, based on the calculations and logical reasoning, Option 1 is indeed the correct answer.

Question

Accepted Answer

To solve the expression $\frac{4}{7} + \frac{5}{14} - \frac{7}{8}$, we need to find a common denominator for the fractions involved. The denominators are 7, 14, and 8. The least common multiple (LCM) of these numbers is 56.

1. **Convert each fraction to have a denominator of 56:**

- $\frac{4}{7}$: Multiply both the numerator and the denominator by 8 to get $\frac{32}{56}$.
   - $\frac{5}{14}$: Multiply both the numerator and the denominator by 4 to get $\frac{20}{56}$.
   - $\frac{7}{8}$: Multiply both the numerator and the denominator by 7 to get $\frac{49}{56}$.

2. **Perform the operations:**

- Add $\frac{32}{56}$ and $\frac{20}{56}$: 
     $$
     \frac{32}{56} + \frac{20}{56} = \frac{52}{56}
     $$

- Subtract $\frac{49}{56}$ from $\frac{52}{56}$:
     $$
     \frac{52}{56} - \frac{49}{56} = \frac{3}{56}
     $$

3. **Conclusion:**

The result of the expression $\frac{4}{7} + \frac{5}{14} - \frac{7}{8}$ is $\frac{3}{56}$, which corresponds to Option 1.

4. **Explanation of why other options are incorrect:**

- **Option 2: $\frac{5}{56}$** is incorrect because the calculation shows the result is $\frac{3}{56}$, not $\frac{5}{56}$.
   - **Option 3: $\frac{3}{14}$** is incorrect because $\frac{3}{14}$ is equivalent to $\frac{12}{56}$, which is not the result of the calculation.
   - **Option 4: $\frac{5}{28}$** is incorrect because $\frac{5}{28}$ is equivalent to $\frac{10}{56}$, which does not match the calculated result of $\frac{3}{56}$.

Therefore, based on the calculations and logical reasoning, Option 1 is indeed the correct answer.