3. Why is this the same?
• You decide to buy a healthy snack at Food Tiger.
You pick up $2 worth of apples and a $1 water.
You know you have enough because 2 + 1 = 3.
4. Why is this the same?
• You decide to buy a healthy snack at Food Tiger.
You pick up $2 worth of apples and a $1 water.
You know you have enough because 2 + 1 = 3.
• The cashier rings up your purchase but scans the
water first and then the apples. In-other-words,
1 + 2 = 3.
5. Why is this the same?
• You decide to buy a healthy snack at Food Tiger.
You pick up $2 worth of apples and a $1 water.
You know you have enough because 2 + 1 = 3.
• The cashier rings up your purchase but scans the
water first and then the apples. In-other-words,
1 + 2 = 3.
• Why were they the same?
6. Why is this the same?
• You decide to buy a healthy snack at Food Tiger.
You pick up $2 worth of apples and a $1 water.
You know you have enough because 2 + 1 = 3.
• The cashier rings up your purchase but scans the
water first and then the apples. In-other-words,
1 + 2 = 3.
• Why were they the same?
• Because addition is commutative.
7. Commutative Property
Image from http://cdn5.wn.com/pd/2b/
e6/292699f3d14d42837fb79a6dea26_grande.jpg
8. Commutative Property
• A commuter train moves from
station A to station B. Does the
distance change depending on
the direction?
Image from http://cdn5.wn.com/pd/2b/
e6/292699f3d14d42837fb79a6dea26_grande.jpg
9. Commutative Property
• A commuter train moves from
station A to station B. Does the
distance change depending on
the direction?
• Nope. That’s what the Image from http://cdn5.wn.com/pd/2b/
e6/292699f3d14d42837fb79a6dea26_grande.jpg
Commutative Property is like.
10. Commutative Property
• A commuter train moves from
station A to station B. Does the
distance change depending on
the direction?
• Nope. That’s what the Image from http://cdn5.wn.com/pd/2b/
e6/292699f3d14d42837fb79a6dea26_grande.jpg
Commutative Property is like.
• Things move around, but the result is the same.
13. Addition
• What is 3.5 + 8.6?
• That’s right! It’s 12.1.
• What is 8.6 + 3.5?
14. Addition
• What is 3.5 + 8.6?
• That’s right! It’s 12.1.
• What is 8.6 + 3.5?
• Correct again! It’s 12.1.
15. Addition
• What is 3.5 + 8.6?
• That’s right! It’s 12.1.
• What is 8.6 + 3.5?
• Correct again! It’s 12.1.
• Why did you get the same answer?
16. Addition
• What is 3.5 + 8.6?
• That’s right! It’s 12.1.
• What is 8.6 + 3.5?
• Correct again! It’s 12.1.
• Why did you get the same answer?
• Addition is commutative. This
means we can move the numbers
around but when we add we get
the same result.
22. Subtraction
• What is 8 - 3?
• 5 is correct.
• What is 3 - 8
• -5 is correct.
• Did we get the same answer?
23. Subtraction
• What is 8 - 3?
• 5 is correct.
• What is 3 - 8
• -5 is correct.
• Did we get the same answer?
• Because the answers are different, this means
subtraction is not commutative.
28. Multiplication
• What is ⅓ * ²⁄₅?
• ²⁄₁₅ is correct!
• What is ²⁄₅ * ⅓?
• ²⁄₁₅ is correct again!
29. Multiplication
• What is ⅓ * ²⁄₅?
• ²⁄₁₅ is correct!
• What is ²⁄₅ * ⅓?
• ²⁄₁₅ is correct again!
• Notice we got the same answer even though the
numbers moved around.
30. Multiplication
• What is ⅓ * ²⁄₅?
• ²⁄₁₅ is correct!
• What is ²⁄₅ * ⅓?
• ²⁄₁₅ is correct again!
• Notice we got the same answer even though the
numbers moved around.
• This means multiplication is commutative.
35. Division
• What is 5.4 ÷ 0.2?
• 42 is correct!
• What is 0.2 ÷ 5.4?
• Tricky one, huh? This answer here
is 0.037037....
36. Division
• What is 5.4 ÷ 0.2?
• 42 is correct!
• What is 0.2 ÷ 5.4?
• Tricky one, huh? This answer here
is 0.037037....
• So the results are different which
tells us division is not commutative.
37. Commutative Property
• Here’s what the Commutative Properties look like
in Algebra.
• Notice only the variable changed position.
38. Commutative Property
• Here’s what the Commutative Properties look like
in Algebra.
a+b=b+a
• Notice only the variable changed position.
39. Commutative Property
• Here’s what the Commutative Properties look like
in Algebra.
a+b=b+a
xy = yx
• Notice only the variable changed position.
40. Commutative Property
• Here’s what the Commutative Properties look like
in Algebra.
a+b=b+a
xy = yx
• Notice only the variable changed position.
42. Recap about the Commutative Property
• Commutative Property allows us to
move stuff around.
43. Recap about the Commutative Property
• Commutative Property allows us to
move stuff around.
• Addition and Multiplication are
Commutative.
44. Recap about the Commutative Property
• Commutative Property allows us to
move stuff around.
• Addition and Multiplication are
Commutative.
• Subtraction and Division are not
Commutative.
