Gujarat BoardEnglish MediumSTD 8MATHSRational Numbers1 Mark
Question
Give an example to show that subtraction is not associative for rational numbers.
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Answer
For rational numbers $\frac{5}{4}, \frac{3}{4}$ and $\frac{1}{4}$, we see that $\frac{5}{4}-\left(\frac{3}{4}-\frac{1}{4}\right)=\frac{5}{4}-\frac{2}{4}=\frac{3}{4}$ and $\left(\frac{5}{4}-\frac{3}{4}\right)-\frac{1}{4}=\frac{2}{4}-\frac{1}{4}=\frac{1}{4}$ Thus, $\quad \frac{5}{4}-\left(\frac{3}{4}-\frac{1}{4}\right) \neq\left(\frac{5}{4}-\frac{3}{4}\right)-\frac{1}{4}$ So, we can say that subtraction is not associative for rational numbers.
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