The basic Number Properties (or laws) that apply to arithmetic operations are Commutative Property, Associative Property, Identity Property and Distributive Property.

Distributive property allows you to remove the parenthesis (or brackets) in an expression. Multiply the value outside the brackets with each of the terms in the brackets.

For example:

4(a + b) = 4a + 4b

7(2c – 3d + 5) = 14c – 21d + 35

What happens if you need to multiply (a – 3)(b + 4)?

You do the same thing but with one value at a time.

For example:

Multiply a with each term to get a × b + 4 × a = ab + 4a

Then, multiply 3 with each term to get “ –3b – 12” (take note of the sign operations).

Put the two results together to get “ab + 4a – 3b – 12”

Therefore, (a – 3)(b + 4) = ab + 4a – 3b – 12

Summary of Number Properties

The following table summarizes
which number properties are applicable to the different operations:

Number Properties

×

÷

+

–

Commutative

Yes

No

Yes

No

Associative

Yes

No

Yes

No

Distributive

Yes

No

No

No

The following video shows more examples of the distributive property.

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