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  • Categories of Numbers

                                                  

    Every number you have rolling around in your head is probably a Real Number. (Yes...there are imaginary ones too...). Money you earn for doing chores around the house, your age, your shoe size, your goldfish Larry's favorite number...all of those are REAL numbers.

    Most every number that you already know is a RATIONAL number.

    Any number that can be expressed as a fraction is a rational number.

    How else are numbers categorized other than just being a REAL number?? Check out this organizational chart below:

    Real Number Hierarchy

     So...this means if you have a number like -12...since it's in the integer category, it's also a rational number, and it's also in the Real Number category. Cool, huh!?

       Activity 1

       Activity 2

    • Be RATIONAL -- All About Rational Numbers

                                          

       

      A rational number is any number you can express as a fraction.

      It can be positive or negative.

      It may be expressed as a mixed number.

      It may even be in decimal form.

       

      Let's check out those decimals for a bit -- there are two kinds of decimals. They either terminate or repeat.

      Check out these links to:

      see an example worked out  

      or practice some on your own!  

      • What an IRRATIONAL thing to say!!

                                               

         

        Hey --- Irrational Numbers are numbers too! They aren't weird...they are just a little ~different~ from their rational cousins.

        Irrational numbers are those that CANNOT be written as a fraction. Like the square root of 7. There is not a whole number that you can multiply BY ITSELF to get 7...therefore, the square root of seven is an irrational number.

        More info? Sure...check this out. 

        Irrational numbers can be easier to think of if we can turn them into a rational number...or something close to it!

        For example, it's hard to think of the square root of 20. If a square table measured 20 feet2, how long is one side? Can you picture in your head how large that table is? Not an easy thing to do, is it?

        What if I said, I have a table that is about a 4 1/2 foot square. That's easier to visualize, right? It's because we know what 4 1/2 looks like. I don't know how long the square root of 20 is!!

        Let's start with what we know: Perfect Squares. Sixteen is a perfect square, because 4 times 4 is 16. Twenty-five is also a perfect square, 5 times 5. Well, 20 is about halfway between 16 and 25...so that means that the square root of 20 is about halfway between 4 and 5.

         

         

        • ABSOLUTE VALUE made absolutely simple

                                                        

           

          Think of your home as being our starting point. Whether you ride to the MALL two miles down the road or to a RESTAURANT two miles in the opposite direction. You have travelled two miles.

          Same thing works on a number line.

           

          The "starting point" is zero. 5 is five spaces from zero, our starting point. -5 is also five spaces away from zero. So the absolute value (away from our starting point) of BOTH of these numbers is five. Here's an easy trick...an absolute value can never be a negative amount.

           Show what you know! 

          • Real Number PROPERTIES at work

                                           

            • Associative Property: think of the friends you "associate" with. Whether the group of friends hanging out is you, Chad, and Michelle, or Chad, you and Michelle. It's still the same group of people, right?? Same thing with the associative property: (2 + 3) + 4 is the same thing as 2 + (3 + 4).

             

             

            • Commutative Property: your "commute" to Wal-Mart is the same whether you are going from your house to there, or from there to your house. Same thing with the commutative property: 7 + 9 = 9 + 7. It also works for multiplication: 6 x 3 = 3 x 6.

             

             

            • Distributive Property: when someone comes to the classroom door with papers to pass out, they will "distribute" one to every student. Everyone inside the room gets a handout. Same thing with the distributive property: a number outside the parentheses will multiply every number inside the parentheses. So 3(y+8) really means "3 times y plus 3 times 8."
            • Distributive Property example 

             

            Try all the properties together    in this activity.

            • Operations with Real Numbers

                                                                                         


               

              Need more help with some operations? These videos will give you example problems worked out and explained along the way. Very helpful! Check them out!

               

                Adding and Subtracting Fractions and Mixed Numbers

                MultiplyingDecimals                                 Dividing Decimals 

               Multiplying Fractions                                 Multiplying Mixed Numbers

               Dividing Fractions                                      Dividing Mixed Numbers