6. Multiplication and division
6.07 Properties of multiplication
Lesson
Are you ready?
Remembering your work with groups and arrays will help you solve problems in this lesson. Let's give this problem a try.
Which number sentence describes the array?
There may be more than one correct answer.
$6\times2=3$6×2=3
A$3\times2=6$3×2=6
B$2\times3=6$2×3=6
C
Learn
We can use different properties of multiplication to solve problems. The properties we're interested in are:
| Name | Description | Example |
|---|---|---|
| Commutative property | Switching the order of multiplication has the same result | $2\times6=6\times2$2×6=6×2 |
| Associative property | If there is more than one multiplication in a row, we can do them in any order | $2\times\left(3\times4\right)=\left(2\times3\right)\times4$2×(3×4)=(2×3)×4 |
| Distributive property | Multiplying a sum is the same as multiplying each part and then adding | $5\times13=5\times\left(3+10\right)=\left(5\times3\right)+\left(5\times10\right)$5×13=5×(3+10)=(5×3)+(5×10) |
Apply
Question 1
Use the commutative and associative properties of multiplication to find the value of $2\times7\times5$2×7×5, filling in the blanks below.
$2\times7\times5$2×7×5 $=$= $7$7$\times$×$\editable{}$$\times$×$5$5 $=$= $7$7$\times$×$\editable{}$ $=$= $\editable{}$
Remember!
We can use these properties to help us rearrange numbers in a number sentence to make them easier to solve.