M11
Associative and Commutative Properties
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Sign inDEFINITION:
The "Commutative Laws" state that when we add or multiply, we can move the numbers around and still get the same answer. The "Associative Laws" state that we will get the same answer no matter how we group numbers when adding or multiplying.
HOW IT WORKS
Commutative: 5+3=8 or 3+5=8
Associative: (3 × 4) × 5 = 60 or 3 × (4 × 5) = 60
HOW IT'S USED IN EVERYDAY LIFE:
Law of Associative Properites: If we were making a cake, we could add the eggs, milk, and flour to the bowl or we could change the order and add the flour, eggs, and milk to the bowl. It wouldn't matter what order the ingredients were added to the bowl. We would still have the same cake in the end.
Links:
Associative Law of Addition: https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-algebra-arithmetic-properties/v/associative-law-of-addition
Associative Law of Multiplication: https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-algebra-arithmetic-properties/v/associative-law-of-multiplication
Commutative Law of Addition: https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-algebra-arithmetic-properties/v/commutative-law-of-addition
Communtative Law of Multiplication: https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-algebra-arithmetic-properties/a/commutative-multiplication
Lyrics
Associative and Commutative Properties
Ha ha, yes sir
Yo let’s talk about the associative properties
It’s a common word, but many don’t even know what it means
Associate is another word for group
So when you solve math problems you can use it as a tool
You got 2 + 4 + 3= 2 + 4 + 3
Then you add parenthesis around the 4+3 when you on the left side
And the 2+4 when you on the right side
So, when you add it all up no matter how you do it
You get the same value no matter how you choose it
See, 4+3 = 7 (hah) Plus 2 = 9 see it’s easy when you get it
And 2+4 = 6 Plus 3 = 9 see now you know the trick
Na, now the other way you to do it is called the commutative
The property is focused on the way the numbers are moving
So, 4+ 2 = 2+4
No matter how you arrange it they have the same score
Like 2+3= 3+2 both sides equals 5
No you know just what do (hah)
Standards
- CCSS.MATH.CONTENT.3.OA.B.6 — Apply properties of operations as strategies to multiply and divide 2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
- CCSS.MATH.CONTENT.1.OA.B.3 — Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition)