Mathematic Properties of Multiplication

The four properties of multiplication provide easier insight into how problems are factored.

The word commute, meaning to move from place to place, is in the prefix of the word commutative.The Commutative Property shows how two numbers in a multiplication number will result in the same answer despite the order, 3*2=6 and 2*3=6.

Multiplication and addition both use the Commutative Property, for example: a+b=b+a and a*b*c=b*c*a.Whenever a multiplication or addition problem calls for the use of the Commutative Property, it is simply stating that numbers can be moved around.

Grouping and associating are references of the Associative Property, which is also used in both multiplication and addition.This property states that the order of a group of numbers is irrelevant, and will result in the same answer whichever way the group is multiplied or summed.

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 most complex of the four properties, the Distributive Property, is used to factor out a set of numbers.The distribution of multiplication over addition is the basis of the Distributive Property.

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

Multiplication can also be distributed over subtraction as displayed in the example: 5x-15=5(x-3), where 5 is factored out through 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.Math skills are sharpened and ready for more complex quantitative problems once these essentials of multiplication are understood.

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