The document discusses the commutative and associative laws for addition and multiplication. The commutative laws state that the order of numbers can be swapped without changing the result, such as A + B = B + A. The associative laws state that the grouping of numbers does not affect the result, for example (A + B) + C = A + (B + C). Examples are provided to illustrate both the commutative and associative laws for addition and multiplication.

2. COMMUTATIVE AND ASSOCIATIVE
LAWS

3. ADDITION MULTIPLICATION
COMMUTATIVE LAWS
The "Commutative Laws" say we can swap numbers over and still get the same answer
A + B = C = B + A =
C
A x B = C = B x A = C

4. COMMUTATIVE LAW EXAMPLES
6+3=9 = 3+6=9
4+2=6 = 2+4=6
2+3=5 = 3+2=5
1+5=6 = 5+1=6
2 x 4 = 8 = 4 x 2 = 8
3 x 4 = 12 = 4 x 3 = 12
1 x 2 = 2 = 2 x 1 = 2
5 x 3 = 15 = 3 x 5 = 15
Addition Multiplication

5. ADDITION
(a + b) + c = a + ( b + c
)
(a x b) x c = a x ( b x c )
MULTIPLICATION
ASSOCIATIVE LAWS
The "Associative Laws" say that it doesn't matter how we group the numbers (i.e. which we calculate first)

6. ADDITION MULTIPLY
ASSOCIATIVE LAW EXAMPLES
(6 + 3) + 4 = 6 + ( 3 + 4
)
(7 + 2) + 9 = 7 + ( 2 + 9
)
(1 + 2) + 3) = 1 + ( 2 + 3 )
(3 x 4) x 5 = 3 x ( 4 x 5 )
(1 x 6) x 4 = 1 x ( 6 x 4 )
(8 x 2) x 7 = 8 x ( 2 x 7 )
(0 x 1) x 7 = 0 x ( 1 x 7 )

7. NOW YOU TRY
Associative:
https://www.khanacademy.org/math/pr
e-algebra/pre-algebra-arith-prop/pre-
algebra-arithmetic-
properties/e/associative-property-of-
multiplication-
Communitive:
https://www.khanacademy.org/math/pr
e-algebra/pre-algebra-arith-prop/pre-
algebra-arithmetic-
properties/e/commutative-property-of-
multiplication