What is wrong with an IMPROPER FRACTON

Consider the following problem:

                                          ¾(30 ÷ 6) = ? 

Knowing ORDER RULES, we do what is in the PARENTHESIS first.

                                          ¾(5) = ? 

Now ¾ x 5 = 15/4


                                                       15/4 


This is the point at which I begin having disagreements with many of my
educational partners, (I endeavor to be politically correct at times).

Some of my entering freshman would tell me that you have to change it
to a smaller number, or mixed number, because the "elephant is on the mouse".  

Some would say it need s to be a decimal,  improper fractions are not allowed.

I would tell them improper fractions are my friends.


So, why the controversy.  To me there are 2 things to consider

• What is the problem about?
• Where are we going in Math?

The above problem is not a Story Problem, and since 4 does not divide evenly into

15, why spend the time.  If it did, then I would change it to the integer it is equal to.

If it was a story problem:  Mary is making waffles that requires ⅔ cup of milk.

                                         Because Mary is having her family over she is making

                                         a double recipe.  How much milk should Mary use?

                                         HOW MUCH MILK SHOULD MARY USE?

                                         DOUBLE MEANS TO MULTIPLY BY 2

                                         2(⅔) = 4/3 cups of milk

                                this is 1⅓ cups of milk

                                          Mary needs 1⅓ cups of milk for her recipe.

In this case I changed the improper fraction to a mixed number because I
need an exact number of cups.  Measuring cups do not have 4/3 on them.

As I would say to my students:

"MIXED NUMBERS ARE FOR

             MEASURING"  

Another example might be: Mr. Romero has 15 grams of salt in a container.
                                            He wishes to use only ¾ of the salt.  How many
                                            grams does Mr. Romero need?

                 HOW MANY GRAM OF SALT WILL MR. ROMERO NEED?

                       ¾(15) = ?


                      45/4 = 11.25 


                Mr. Romero will need 11.25 grams of salt.

In science we need decimal accuracy,  and our measuring equipment
is of marked that way.

As I say:

"DECIMALS ARE FOR SCIENCE" 

                  
However, being able to use improper fractions is of primary importance in Math.
Trigonometry is done completely in improper fractions.  When the numerator is
greater than the denominator, our answer is greater than 1,  and for Math,
because of where it takes us,  that is what we need to know.

As I say:

"IMPROPER FRACTIONS ARE 
OUR FRIENDS AND THEY ARE
FOR MATH"