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The Distributive Property

The Distributive Property: If a, b and c are any numbers, then a ( b+ c ) = ab + ac

When expressions such as those above contain â€œlike quantitiesâ€ inside the parenthesis, you can first perform the addition or subtraction inside the parentheses, and then perform the multiplication, and you will get the same answer as if you had used the distributive property. However, if the quantity inside the parenthesis contains â€œunlike quantitiesâ€, you canâ€™t do the addition or subtraction first, so you must use the distributive property in order to simplify.

Distributive property and the multiplication algorithm:

The multiplication algorithm is based on the distributive property. To see this, consider the following example:

Example:

25 (12)	= 25 ( 10 + 2 )
	= 25â€¢10 + 25â€¢2
	= 250 + 50
	= 300

Use this fact to multiply the following numbers in your head.

a. 25(14)

b. 15(12)

c. 22(13)