Integers: Part Two, Multiplication & Division

Multiplication and Division of Integers, especially when mixing  positive and negative numbers can be tricky!  Luckily mathematics provides us with some rules that always prove true and can help to guide us through this, sometimes confusing process.

Just as subtraction is the opposite of addition, division is the opposite of multiplication.  When we multiply we combine groups together, when we divide we split them apart.

The first step:  Learn your Multiplication facts!  I cannot stress the importance of memorizing these enough.  You will use them from early elementary school right through advanced math in high school, and on into adulthood for practical, real-life situations.  Knowing these simple facts will save you valuable time that can be spent on the more complex aspects of solving multiple step problems.

 

It seems that students often have the most difficulty with the sevens and eights.  Rhymes or other tricks to remember these facts can be helpful ("You can’t have 7 and 8 before you have 5 and 6… 7 x 8 = 56", "I know now and you do too! 6 x 7 is 42", or "Say this when you're in a fix. 7 x 8 is 56"), it may seem silly, but it can help!

Basic Rules for Multiplying & Dividing:  

When working with positive and negative numbers and trying to determine whether the product or quotient will be negative or positive remember this; same signs result in positive, different signs result in negative answer.  The chart below illustrates this rule:

Rule for the relationship between Multiplication Division:

a / b = c
if and only if
c x b = a
(when be does not = 0) 

4 Properties that Guide Multiplication Process: 

(Click heading for Helpful Link:)

Closure Property of Mulitiplication  when dividing a and b, the product ab is a unique integer (neither a or b), unless a or b is the integer 1 or zero, see below.

Multiplicative Identity Property  any integer that is multiplied by the integer 1 does not change, it keeps it's "identity"!

Commutative Property  the order in which the multiplication is preformed does not effect the product at all, for example 3x2=2x3.

Associative Property  similarly to how you order integers in the commutative property, the associative property tells us that how you GROUP integers also has no effect on the product, for example (2x3)4=2(3x4)

More information on the rules governing muliplication and division, as well as many links to fun games and toutorials can be found on the MindMap I created on the subject, visit mindomo.com

 

***Especially for Parents***

Sometimes as our children get into the higher grades and begin exploring more advanced mathematical concepts we can feel inadequate providing effective homework help.  Multiplication and division are concepts that we, as adults are generally comfortable with, in the beginning.  Once addition of unknown variables, multiple steps and opperations, exponents, parentheses and brackets that call for knowledge of Order of Opperations , formulas and rules.  Fortunate for us the internet has supplied us with unlimited resources for learning and knowledge.  This too can be a bit intimidating so I have put together a short list of the most helpful sites I have found.

Khan Academy  over 3000 educational videos!  Concise and easy to follow.

Purple Math  from beginning to advanced algebra lessons & practice.

Math.com  homework help, calculators and tools.

IXL.com  pre-k to 8th grade, links to standards, practice, track & progress reports available.