Answer
(refer to the step-by-step part for the explanation)
Examples in which the given property is used:
(i) Commutative Property
$2+3 = 3+2$;
$2(3) = 3(2)$
(ii) Associative Property
$2+(3+4) = (2+3)+4$;
$2(3 \cdot 4) = (2\cdot 3)(4)$
(iii) Distributive Property
$2(3+4) = 2\cdot3 + 2\cdot 4$
Work Step by Step
(i) Commutative Property
The commutative property states that for any real numbers $a$ and $b$,
(1) $a+b = b+a$ (for addition)
(2) $a\cdot b= b \cdot a$ (for multiplication)
Examples in which this property is used are:
$2+3 = 3+2$
$2(3) = 3(2)$
(ii) Associative Property
The associative property states that for any real numbers $a, b,$ and $c$,
(1) $a+(b+c) = (a+b)+c$ (for addition)
(2) $a\cdot (b \cdot c)= (a \cdot b) \cdot c$ (for multiplication)
Examples in which this property is used are:
$2+(3+4) = (2+3)+4$
$2(3 \cdot 4) = (2\cdot 3)(4)$
(iii) Distributive Property
The distributive property states that for any real numbers $a, b, $ and $c$:
$a(b+c) = ab+ac$
An example in which this property is used is:
$2(3+4) = 2\cdot3 + 2\cdot 4$
