Question

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

Answer 1

(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, $x\times (y+z)=x\times y+x\times z$