Discussion
If \(a = -\frac{3}{4}\) and \(b = \frac{5}{6}\), then which of the following does not lie between a and b ?
Answer: D
The number that does not lie between a and b is \(-\frac{7}{9}\).
Here \(a = -\frac{3}{4} = -0.75\) and \(b = \frac{5}{6} \approx 0.83\), so a number lies between them only if it is greater than \(-0.75\) and less than 0.83.
\[ \begin{aligned} -\tfrac{7}{9} &\approx -0.778 \lt -0.75 \\ -\tfrac{1}{2} &= -0.5 \gt -0.75 \\ -\tfrac{2}{5} &= -0.4 \gt -0.75 \end{aligned} \]
So \(-\frac{7}{9}\) is to the left of a on the number line. 0, \(-\frac{1}{2}\) and \(-\frac{2}{5}\) all lie between \(-0.75\) and 0.83. Comparing \(\frac{7}{9}\) with \(\frac{3}{4}\) by cross-multiplication (\(28 \gt 27\)) gives the same result without decimals.
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