Distributive Property

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.

number properties - distributive

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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