Wow! What a mouthful of words! But the ideas are simple.
a × b = b × a
(a × b) × c = a × (b × c)
This: | (2 + 4) + 5 = 6 + 5 = 11 |
Has the same answer as this: | 2 + (4 + 5) = 2 + 9 = 11 |
This: | (3 × 4) × 5 = 12 × 5 = 60 |
Has the same answer as this: | 3 × (4 × 5) = 3 × 20 = 60 |
3 lots of (2+4) is the same as 3 lots of 2 plus 3 lots of 4
a × (b + c) = a × b + a × c
6 × 204 = 6×200 + 6×4
= 1,200 + 24
= 1,224
16 × 6 + 16 × 4 = 16 × (6+4)
= 16 × 10
= 160
Commutative Laws: | a + b = b + a a × b = b × a |
Associative Laws: | (a + b) + c = a + (b + c) (a × b) × c = a × (b × c) |
Distributive Law: | a × (b + c) = a × b + a × c |