Discussion
The value of \(\frac{4}{7} + \frac{5}{14} - \frac{7}{8}\) is :
Answer: A
The value is \(\frac{3}{56}\).
The denominators are 7, 14 and 8. Their LCM is 56, so
\[ \begin{aligned} \frac{4}{7} + \frac{5}{14} - \frac{7}{8} &= \frac{32}{56} + \frac{20}{56} - \frac{49}{56} \\ &= \frac{32 + 20 - 49}{56} = \frac{3}{56} \end{aligned} \]
Each fraction is converted by multiplying top and bottom by the same number: \(\frac{4}{7}\) by 8, \(\frac{5}{14}\) by 4 and \(\frac{7}{8}\) by 7.
\(\frac{5}{56}\), \(\frac{3}{14}\) and \(\frac{5}{28}\) come from conversion slips; \(\frac{3}{14} = \frac{12}{56}\), for instance, is four times the correct value.
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