Multiplication Properties In Mathematics

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

The name commutative holds definition in the prefix of the word, 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 following example a+b=b+a, and a*b*c=c*b*a, shows how the Commutative Property is used in multiplication and addition.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.The number order within a group of numbers that are multiplied or summed is irrelevant, according to the Associative Property.

The Associative Property is demonstrated in the example: a(cb)=c(ba) and a+(c+b)=b+(a+c).

Rearrangement of the numbers in a group is all that is necessary if the Associative Property is referred to in a problem.

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 term distributive comes from the properties use of distribution of multiplication over addition.

This property can be show through an example, such as: a(b+c)=ab+ac, and also as ax+b=a(x+b).

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.The Distributive Property creates flexibility in its definition as it can be used in multiplication over addition and subtraction, in that subtraction can also be viewed as the addition of a negative number.

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.