Express the following properties with variables x, y and z.
(i) Commutative property of addition
(ii) Commutative property of multiplication
(iii) Associative property of addition
(iv) Associative property of multiplication
(v) Distributive property of multiplication over addition

(i) Commutative property of addition says that the change in order of numbers in addition will not change the result.
Therefore, $x+y=y+x$

(ii) Commutative property of multiplication says that the change in order of numbers in multiplication will not change the result.
Therefore, $x\times y=y\times x$

(iii) Associative property of addition states that the result stays the same however the numbers are grouped while adding
Therefore, $x+(y+z)=(x+y)+z$

(iv) Associative property of multiplication states that the result stays the same however the numbers are grouped while multiplying.
Therefore $x\times (y\times z)=(x\times y)\times z$.

(v) Distributive property of multiplication over addition is:
$a\times (b+c)=a\times b+a\times c$
Therefore, $x\times (y+z)=x\times y+x\times z$