Distributive Property of Real Numbers

The distributive property connects the operations of multiplication and addition or subtraction. It tells us how to simplify expressions where a number is multiplied by a group of terms.

Expressions

Distributivity of multiplication over addtion.

a(b+c)=ab+aca(b + c) = ab + ac

Distributivity of multiplication over subtraction.

a(b−c)=ab−aca(b - c) = ab - ac

In formal terms:

∀a,b,c∈R, a⋅(b+c)=a⋅b+a⋅c\forall a, b, c \in \mathbb{R},\ a \cdot (b + c) = a \cdot b + a \cdot c

∀a,b,c∈R, a⋅(b−c)=a⋅b−a⋅c\forall a, b, c \in \mathbb{R},\ a \cdot (b - c) = a \cdot b - a \cdot c

Examples

  • 2(3+4)=2⋅3+2⋅4=6+8=142(3 + 4) = 2 \cdot 3 + 2 \cdot 4 = 6 + 8 = 14
  • 5(10−2)=5⋅10−5⋅2=50−10=405(10 - 2) = 5 \cdot 10 - 5 \cdot 2 = 50 - 10 = 40

True or False Activity!!!

Read each statement carefully and decide if it is true or false.

1

The distributive property allows us to multiply a number by a sum or difference.

or
2

The distributive property only works with addition.

or
3

Distributivity only applies to multiplication over addition or subtraction.

or
4

a(b + c) = ab + c is an example of the distributive property.

or

Build the Distributive Equations

Build the Correct Equations Activity

Distributive Property over Addition

Distributive Property over Subtraction


End of Lesson

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Inverse of Real Numbers
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Task 03 - Identify Property of Real Numbers