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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.

  1. $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.

  1. $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.

Outcomes

MA.3.AR.1.1

Apply the distributive property to multiply a one-digit number and two-digit number. Apply properties of multiplication to find a product of one-digit whole numbers.

MA.3.AR.2.2

Determine and explain whether an equation involving multiplication or division is true or false.

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