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Mathematic Properties of Multiplication

Date Added: February 26, 2011 02:39:12 PM
Author: Olivia Chandler
Category: Education

An easier insight into how problems are factored can be shown through the four properties of multiplication.

The Commutative Property receives its name from the definition of commute, meaning to move from place to place.Number order when factoring two numbers together in a multiplication problem does not matter, according to the Commutative Property 2*3=6 and 3*2=6.

The Commutative Property is used in addition and multiplication as demonstrated in the following example: a+b=b+a and a*b*c=c*b*a.An addition or multiplication problem may cite the Commutative Property, which will simply mean that it is okay to move numbers around.

Grouping and associating are references of the Associative Property, which is also used in both multiplication and addition.The number order within a group of numbers that are multiplied or summed is irrelevant, according to the Associative Property.

In the example, a(cb)=c(ba) and a+(c+b)=b+(a+c), the Associative Property is demonstrated.

Only the order of numbers would be need to be regrouped if a problem asked for rearrangement through the Associative Property.

Any number multiplied by one remains the same number, as stated by the Multiplicative Identity Property.1*5=5 as well as 1*10=10as defined by this property.

The Distributive Property is the more complex of the four properties in that it can be used to factor a set of numbers out. Distributive is used as a description to this property as it calls for distribution of multiplication over addition.

Through the example, a(b+c)=ab+ac, and also as ax+b=a(x+b), the Distributive Property is shown.

This property can also be used for multiplication over subtraction as displayed in the example: 5x-15=5(x-3), in that the 5 is distributed to factor into parentheses just as it is factored out of the parentheses.Flexibility within the Distributive Property's definition is shown through the above example as subtraction is used; subtraction can also be the addition of a negative number.

The examples and definitions of these four properties show how and why math rules are used.The building blocks of math skills create a path towards more complex quantitative problems once these multiplication properties are realized.

For more information on times tables, go to

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