Question

If $(\frac{a}{b}-\frac{c}{d})-\frac{e}{f}=\frac{a}{b}-(\frac{c}{d}-\frac{e}{f})$, then it follows the ___ property which does not hold true for subtraction.

Answer 1

If $(\frac{a}{b}-\frac{c}{d})-\frac{e}{f}=\frac{a}{b}-(\frac{c}{d}-\frac{e}{f})$

Then this is called the associative property which does not hold true for subtraction

Example : Let's take $\frac{2}{3}$ , $\frac{8}{6}$ and $\frac{4}{9}$

$(\frac{2}{3}-\frac{8}{6})-\frac{4}{9}$

= $\frac{4-8}{6}-\frac{4}{9}$

= $\frac{-4}{6}-\frac{4}{9}$

= $\frac{-4\times 3}{18}-\frac{4\times 2}{18}$

= $\frac{-12-8}{18}$ = $\frac{-20}{18}$

Now, Taking $\frac{2}{3}-(\frac{8}{6}-\frac{4}{9})$

we get : $\frac{2}{3}-(\frac{8}{6}-\frac{4}{9})$

= $\frac{2}{3}-(\frac{8\times 3}{18}-\frac{4\times 2}{18})$

= $\frac{2}{3}-(\frac{24}{18}-\frac{8}{18})$

= $\frac{2}{3}-\frac{16}{18}$

= $\frac{12-16}{18}$

= $\frac{-4}{18}$ which is $\ne$ $\frac{-20}{18}$