Basic Number Properties Unit One

Basic Operations + - * /

One could argue that everything you need to learn in math you learned before you entered school.

How can that be you might say? What if I told you that the only thing you can do in math is count!

Counting

If this were true then the Addition, Subtraction, Multiplication, and Division would all just be a name for the way your are counting. Umm? Lets think about this..


Click here to complete the exercise

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Equal Sign

You have used the equal sign before but what does it mean?? Would you be surprised to find out the = means "the same as".

Lets investigate: For instance could you say...

Dogcount.jpgDogcount.jpgDogcount.jpg and Dogcount.jpgDogcount.jpg is the same as Dogcount.jpgDogcount.jpgDogcount.jpgDogcount.jpgDogcount.jpg ?

How would you write this as a mathematic sentence?

Reveal Answer


More on Counting and using Negatives

Math is also used to express distance and time. For example if it is two o'clock now what time was it 3 hours ago? Obviously eleven o'clock. What happened when you got to one o'clock and had to count backwards, you automatically knew that you had to start at twelve again right?

Well its the same thing with negative numbers. Look at the number line:

NumberLine.jpg

Start at 5 and count 7 steps backwards (to the left). Where did you wind up?

At -2 right? So could say 5 and (-7) is (-2) or 5 - 7 = -2

Negative numbers are often used in accounting as well. If you borrow $5 from your friend on Monday and he borrows $7 from you on Tuesday who owes who how much? He owes you $2 right? Therefore you are -2 dollars, until he pays you back.



What the heck is a variable anyway?

A lot of people say they were fine in math until somebody added letters! What do letters have to do with math? Shouldn't they just stay in sentences where they belong!

By now you should know that all numbers have certain consistent behaviors. These consistent behaviors allow us to create rules that we can use to solve for unknown values.

As your math skills gain proficiency you will notice that the problems get longer (not necessarily harder). It becomes important to hold our place. Because numbers behave consistently we can use letters to represent an unknown number.

This gives us two advantages. First if we need to use the same number twice in an equation but we don’t know what that number is we can just use the same letter. As in a(a - 7) = 3

Second if we are presented with a problem with two unknown values we can just use two different letters to represent the different values. x + y = 10


So all you have to remember about letters in math is that they mean a number with a specific value which at the moment is unknown.



Putting it all together

Now that we have reviewed all we ever need to know to become proficient Mathematicians. Let's apply what we remember.

Consider the following algebraic expression:

AlgExp1.jpg

How many terms in this expression? Reveal Terms

Can you identify the Coefficients? Reveal Coefficients

Can you identify the constant? Reveal Constants



Quick Check

Right click on the quick check below and open the link in a new window

Quick check before you proceed.



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