Commutative and Associative Laws

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