Explore the commutative, associative, and identity properties of multiplication.
In this article, we'll learn the three main properties of multiplication. Here's a quick summary of these properties:
Commutative property of multiplication: Changing the order of factors does not change the product. For example, 4×3=3×44 \times 3 = 3 \times 4.
Associative property of multiplication: Changing the grouping of factors does not change the product. For example, (2×3)×4=2×(3×4)(2 \times 3) \times 4 = 2 \times (3 \times 4).
Identity property of multiplication: The product of 11 and any number is that number. For example, 7×1=77 \times 1 = 7.

Commutative property of multiplication

The commutative property of multiplication says that changing the order of factors does not change the product. Here's an example:
4×3=3×44 \times 3 = 3 \times 4
Notice how both products are 1212 even though the ordering is reversed.
Here's another example with more factors:
1×2×3×4=4×3×2×11 \times 2 \times 3 \times 4 = 4 \times 3 \times 2 \times 1
Notice that both products are 2424.
Which of these is an example of the commutative property of multiplication?
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Associative property of multiplication

The associative property of multiplication says that changing the grouping of the factors does not change the product. Here's an example:
(2×3)×4=2×(3×4)\blueD{(2 \times 3) \times 4} = \goldD{2 \times (3 \times 4)}
Remember that parentheses tell us to do something first. So here's how we evaluate the left-hand side:
=(2×3)×4\phantom{=}\blueD{(2 \times 3) \times 4}
=6×4= 6 \times 4
=24=24
And here's how we evaluate the right-hand side:
=2×(3×4)\phantom{=}\goldD{2 \times (3 \times 4)}
=2×12= 2 \times12
=24=24
Notice that both sides equal 2424 even though we multiplied the 22 and the 33 first on the left-hand side, and we multiplied the 33 and the 44 first on the right-hand side.
Which of these is an example of the associative property of multiplication?
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Identity property of multiplication

The identity property of multiplication says that the product of 11 and any number is that number. Here's an example:
7×1=77 \times 1 = 7
The commutative property of multiplication tells us that it doesn't matter if the 11 comes before or after the number. Here's an example of the identity property of multiplication with the 11 before the number:
1×6=61 \times 6 =6
Which of these is an example of the identity property of multiplication?
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