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Properties of multiplication

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=3×4.
Associative property of multiplication: Changing the grouping of factors does not change the product. For example, (2×3)×4=2×(3×4).
Identity property of multiplication: The product of 1 and any number is that number. For example, 7×1=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=3×4
Notice how both products are 12 even though the ordering is reversed.
Here's another example with more factors:
1×2×3×4=4×3×2×1
Notice that both products are 24.
Which of these is an example of the commutative property of multiplication?
Choose 1 answer:

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)
Remember that parentheses tell us to do something first. So here's how we evaluate the left-hand side:
=(2×3)×4
=6×4
=24
And here's how we evaluate the right-hand side:
=2×(3×4)
=2×12
=24
Notice that both sides equal 24 even though we multiplied the 2 and the 3 first on the left-hand side, and we multiplied the 3 and the 4 first on the right-hand side.
Which of these is an example of the associative property of multiplication?
Choose 1 answer:

Identity property of multiplication

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

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