Question

For x =1/10,y =-3/5,z =7/20,find the values of the expressions (x-y)-z and x-(y-z).Are they equal.

Answer 1

1/10 - 3/5 - 7/20= (2-12-7)/20
= - 18/20
= - 9/10

Answer 2

(x-y)-z = 7/20 and x-(y-z) =21/20 and they are not equal.

Step-by-step explanation:

Given values of x, y and z are

$x=\frac{1}{10},\\ \\y=\frac{-3}{5}\\ \\\& \ z= \frac{7}{20}$

We have to find the value of the expressions $(x-y)-z\ \& \ x-(y-z)$ and check whether they are equal or not.

In short, we have to check whether subtraction of rational numbers is associative or not, using the given values.

So, lets find the values of expressions first,

$\because (x-y)-z = (\frac{1}{10}-[\frac{-3}{5}])- \frac{7}{20}$

$\Rightarrow (x-y)-z = (\frac{1}{10}+\frac{3}{5})- \frac{7}{20}\\ \\\Rightarrow (x-y)-z = (\frac{1+6}{10})- \frac{7}{20}\\\\\Rightarrow (x-y)-z = \frac{7}{10}- \frac{7}{20}\\ \\\Rightarrow (x-y)-z = \frac{14-7}{20} \\\\\Rightarrow (x-y)-z = \frac{7}{20}$

Now, $x-(y-z) = \frac{1}{10}-(\frac{-3}{5}- \frac{7}{20})$

$\Rightarrow x-(y-z) = \frac{1}{10}+(\frac{-12-7}{20})\\ \\\Rightarrow x-(y-z) = \frac{1}{10}-(- \frac{19}{20})\\\\\Rightarrow x-(y-z) = \frac{1}{10}+ \frac{19}{20}\\ \\\Rightarrow x-(y-z) = \frac{2+19}{20} \\\\\Rightarrow x-(y-z) = \frac{21}{20}$

It is clear that,

$(x-y)-z \neq x-(y-z)\\ \\As \ \frac{7}{20} \neq \frac{21}{20}$

i.e. the given expressions are not equal.

This example also proves that subtraction of rational numbers is not associative.