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

The word commute, meaning to move from place to place, is in the prefix of the word commutative.The Commutative Property shows that number order in a multiplication problem is irrelevant when factoring the product of two numbers, 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.Whenever a multiplication or addition problem calls for the use of the Commutative Property, it is simply stating that numbers can be moved around.

The Associative Property is named for associating or grouping and is also used in addition and multiplication.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.

An example of the Associative Property is demonstrated as: a(cb)=c(ba) and a+(c+b)=b+(a+c).

If a problem were to ask for rearrangement through the Associative Property, all one need do is to regroup the order of numbers.

The Multiplicative Identity Property states that the product of one with a number is the same number being multiplied to one.This property is displayed as, 1*5=5 as well as 1*10is 10.

The most complex of the four properties, the Distributive Property, is used to factor out a set of numbers.The term distributive comes from the properties use of 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.Although the definition of the Distributive Property is that multiplication is distributed through addition, the addition of a negative integer can be used as well; essentially this is subtraction.

How and why we certain math rules are used is defined through these four properties of multiplication.Math skills are sharpened and ready for more complex quantitative problems once these essentials of multiplication are understood.

For more information on times tables, go to www.timestablesmaths.com.