Mixed Fraction Subtraction - Let's Go Shopping

Mixed Fraction Subtraction - kinda rolls off the tongue, doesn't it?

OK - how about...?


     4
5  ---
     7

subtract

     5
4  ---
     7


We know the 4 and 5/7 is smaller than the 5 and 4/7.

But how to subtract 5/7 from 4/7?

Some might suggest converting both fractions to improper fractions...

...and coming up with 39/7 - 33/7 

...and arriving at 6/7.

However, if you are not particularly strong at multiplication, you might try this method...

Let's go shopping...

     4
5  ---
     7

First off - let's just make the 5 one LESS.

Why?

1) Because we can.
2) You always come away with LESS money when you go shopping. (Yes, yes, yadda, yadda, you might end up shopping for lottery tickets and win. Heard that one. Heard 'em all.)

So now our fraction is modified a bit from

     4
5  ---
     7


To...

     4
4  ---
     7


But not for long. Now let's buy a top.

Hmm, stylish. Who said I had no taste?






OK. Now remember...our top (denominator) was 4.

Better now add some pants to this stylish ensemble.

Let's add the
bottom (pants) to the
top. Can this ensemble get any more stylish? I doubt it. 


4  add  7 = 11










Remember...
     4
5  ---
     7


changed to...

     4
4  ---
     7

and we are now going to add the pants (bottom) onto the top

4  add  7 = 11


    11
4  ---
     7

Now we can finish the question.

    11
4  ---
     7

subtract

     5
4  ---
     7


Let's get rid of those whole numbers...
4 - 4 = 0

Now...

11/7 - 5/7 = 6/7


6/7 is our answer. Work SMART, not HARD!

Look "Ma", no hands!

     3
2  ----
     7


Changing a mixed number to an improper fraction?


Step One - Like every job, start at the bottom. (I think Rodney Dangerfield said that proctology is the only profession where you start at the bottom and stay there.) Start with the 7.


Step Two - Work Clockwise 


Step 3 - Remember to listen to Ma! M = Multiply, A = Add


Step 4 - Multiply 7 by 2 to get 14.


Step 5 - Add 14 to the 3. You now have 17.


Step 6 - Your denominator stays 7.


Your new improper fraction is...


  17
------
   7

Beer saves the day - again. Improper Fractions

21   What do I do with this improper fraction?

 8

You need to change it into a mixed fraction. How do you do this? Well, think of beer. You have 21 bottles but can only carry 8 bottles at a time...

You will make 1 full trip, carrying 8 bottles.

You will make a 2nd full trip carrying another 8 bottles.

You have 5 bottles left.  They do not represent a "full" trip. Your 2 "full trips" become the whole number component of the mixed fraction. 

Your 5 bottles that are "left over" go on the top shelf of the fridge. (That is where all left overs go." Your denominator was 8, so let's keep it at 8. You now have...

2  5

     8    

For a video explanation, start 2 minutes into the video here