Basic Mathematics

The Commutative Property

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The Commutative Property
This is the commutative property of adddition:
A + B = B + A
Changing the order of the addends does not change the sum.
3 + 7 = 7 + 3 = 10
5 + 9 = 9 + 5 = 14
The Commutative Property
Using the commutative property sometimes offers a short cut to finding the missing number in an equation.

What is the value of the box in the following number sentence?
14 + □ = 37 + 14
14 + 37 = 37 + 14
There is no need to find the sum of 37 + 14. The commutative property shows that the missing addend is 37.
The Commutative Property
This is the commutative property of multiplication:
A × B = B × A
Changing the order of the factors does not change the product.
5 × 7 = 7 × 5 = 35
68 × 3 = 3 × 68 = 204
The Commutative Property
The commutative property does not apply to subtraction or division.
8 − 2 ≠ 2 − 8
Since 8 − 2 = 6 but 2 − 8 = − 6,
this example shows subtraction is not commutative.

10 ÷ 5 ≠ 5 ÷ 10
Since 10 ÷ 5 = 2 but 5 ÷ 10 = \(\frac{1}{2}\),
this example shows division is not commutative.
The Commutative Property
Click on the number that belongs in the box.
42 + 18 = 18 + ⃞
42
52
32
20
None of these
Question 1 of 8
42 + 18 = 18 + 42 is an example of the commutative property.
42 + 18 is not equal to 18 + 52. Try again.
42 + 18 is not equal to 18 + 32. Try again.
42 + 18 is not equal to 18 + 20. Try again.
One of these numbers makes a true sentence. Try again.
The commutative property says that the sum does not change when the order of the addends is changed.
The Commutative Property
Click on the number that belongs in the box.
21 × 2 = 2 × ⃞
14
21
19
  7
None of these
Question 2 of 8
21 × 2 is not equal to 2 × 14. Try again.
21 × 2 = 2 × 21 is an example of the commutative property.
21 × 2 is not equal to 2 × 19. Try again.
21 × 2 is not equal to 2 × 7. Try again.
One of these numbers makes a true number sentence. Try again.
The commutative property says that the product does not change when the order of the factors is changed.
The Commutative Property
Click on the number that belongs in the box.
10,788 × 691 = 691 × ⃞
     691
10,788
     788
11,000
None of these
Question 3 of 8
10,788 × 691 is not equal to 691 × 691. Try again.
10,788 × 691 = 691 × 10,788 is an example of the commutative property.
10,788 × 691 is not equal to 691 × 788. Try again.
10,788 × 691 is not equal to 691 × 11,000. Try again.
One of these numbers makes a true number sentence. Try again.
The commutative property says that the product does not change when the order of the factors is changed.
The Commutative Property
Click on the example of the commutative property.
3 + 4 = 2 + 5
3 + 4 = 4 + 3
3 × 4 = 2 × 6
3 × 4 = 12
None of these
Question 4 of 8
3 + 4 = 2 + 5 is a true sentence, but it does not show the commutative property. Try again.
3 + 4 = 4 + 3 shows the same addends in a different order.
3 × 4 = 2 × 6 is a true sentence, but it does not show the commutative property. Try again.
3 × 4 = 12 is a true sentence, but it does not show the commutative property. Try again.
One number sentence shows the commutative property of addition. Try again.
The commutative property says that the sum does not change when the order of the addends is changed.
The Commutative Property
Click on the example of the commutative property.
14 × 9 = 9 × 14
14 + 9 = 17 + 6
14 × 9 = 18 × 7
14 + 9 = 23
None of these
Question 5 of 8
14 × 9 = 9 × 14 shows the same factors in a different order.
14 + 9 = 17 + 6 is a true sentence, but it does not show the commutative property. Try again.
14 × 9 = 18 × 7 is a true sentence, but it does not show the commutative property. Try again.
14 + 9 = 23 is a true sentence, but it does not show the commutative property. Try again.
One number sentence shows the commutative property of multiplication. Try again.
The commutative property says that the product does not change when the order of the factors is changed.
The Commutative Property
Click on the number that belongs in the box.
4.7 + 2.53 = ⃞ + 4.7
4.7
2
2.53
4
None of these
Question 6 of 8
4.7 + 2.53 is not equal to 4.7 + 4.7. Try again.
4.7 + 2.53 is not equal to 2 + 4.7. Try again.
4.7 + 2.53 = 2.53 + 4.7 is an example of the commutative property.
4.7 + 2.53 is not equal to 4 + 4.7. Try again.
One of these numbers makes a true number sentence. Try again.
The commutative property applies to decimals and mixed numbers as well as whole numbers.
The Commutative Property
Click on the symbol that belongs in both boxes.
43 ⃞ 2 = 2 ⃞ 43
+
÷
>
−
<
Question 7 of 8
43 + 2 = 2 + 43 is an example of the commutative property.
43 ÷ 2 is not equal to 2 ÷ 43. The commutative property does not apply to division. Try again.
A sign of operation is needed, not an inequality symbol. Try again.
43 − 2 is not equal to 2 − 43. The commutative property does not apply to subtraction. Try again.
A sign of operation is needed, not an inequality symbol. Try again.
The commutative property applies only to addition and multiplication.
The Commutative Property
Click on the symbol that belongs in both boxes.
831 ⃞ 104 = 104 ⃞ 831
÷
×
−
<
>
Question 8 of 8
831 ÷ 104 is not equal to 104 ÷ 831. The commutative property does not apply to division. Try again.
831 × 104 = 104 × 831 is an example of the commutative property.
831 − 104 is not equal to 104 − 831. The commutative property does not apply to subtraction. Try again.
A sign of operation is needed, not an inequality symbol. Try again.
A sign of operation is needed, not an inequality symbol. Try again.
The commutative property applies only to addition and multiplication.
The Commutative Property