Question

Verify the commutative property of multiplication $x\times y=y\times x$, for the following pairs of rational numbers:
[4 MARKS]

$i)x=\frac{-1}{5},y=\frac{2}{7}$ $ii)x=0,y=\frac{3}{4}$

Answer 1

Concept : 1 Mark
Reason : 1 Mark
Calculation : 2 Marks

$\left(i\right)x=\frac{-1}{5}y=\frac{2}{7}$
$LHS=x\times y=\frac{-1}{5}\times \frac{2}{7}=\frac{-2}{35}$
$RHS=y\times x=\frac{2}{7}\times \frac{-1}{5}=\frac{-2}{35}$
$\therefore LHS=RHS\Rightarrow x\times y=y\times x$
Hence verified.

$\left(ii\right)LHS=x\times y=0\times \frac{3}{4}=0$
$RHS=y\times x=\frac{3}{4}\times 0=0$
$\therefore LHS=RHS\Rightarrow x\times y=y\times x$
​​​​​​​Hence verified.