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Working With Compound and Improper Fractions

Compound Fractions
A compound fraction is a fraction that, in addition to having part of a whole number (maybe ¼, ½, etc.) it also contains a whole
number. An example of a compound fraction would look like this: 4½. (Four and one-half.)

Improper Fractions
An improper fraction is actually the same thing, written differenty. Rather than having the whole number separated from the fractional portion
of the number, it is written right into the fraction! The previous compound fraction above (4½) could be written as 9/2.

Why Use Them?
If you have watched ½ of a movie, but have 2 more you want to watch, then you need to show the total of 2½. Depending on the circumstances, it may be easier to write (or easier to work with) the fraction if it looks like 5/2 instead of 2½.

Making a Improper Fraction from a Compound Fraction
If you have a compound fraction, 4¾ and need it into one fraction without whole numbers listed, you need to convert it to an improper fraction. You can do this with ease! All you need to do is take the whole number (4) and multiply it by the denominator (the bottom) of the fraction (3), then add the numerator to the top of the fraction. Put that number on top of the denominator, and you're done!


Try to convert these into improper fractions; you'll find that they are very easy! (Answers are below.)
1.   2½
2.   1¼
3.   -5½ (Hint: Don't multiply with -5; just leave the - there for the end answer, but just use 5 x 2 in your calculation!)
4.   3 ¾
5.   -7¼

There are two which contain negative numbers. In this case, you can just leave the negative sign alone until the end. That is, if you have -3½,
you would multiple 3 x 2 and then add 1, giving you 7. Put the 7 over the denominator, giving you 7/2, and then bring the negative sign down
to your answer of -7/5.

1. 5/2
2. 5/4
3. -11/2
4. 15/4
5. -29/4

Now, Turning An Improper Fraction to a Compound Fraction.
Since you used multiplication to last time, and you want to "undo" what that did, can you guess what you're going to use this time? Of course,
it's going to be division. Let's use 11/2 as our example, let's work the other way.

First, we need to find out how many times 2 goes into 11. So we divide 11 by 2. 11 ÷ 2 = 5. We have the first part of our answer! But we cannot say that it is 5 11/2, because we have taken the whole number 5 from the fraction, meaning the fraction should be much less now.
Step two: Find out how much to take away from the fraction. We know we took 5 out of it, but we cannot use 11-5 to get our answer because 11/2 is a fraction, and the 5 is a whole number. What we can do, however, is find out how many "portions" of that fraction we took.

And that's really easy!

In fact, all we have to do is multiple the whole number we took (5) by the denominator (2) to find out how many "pieces of 2" we took. 5x2 gives us ten, which is the number to subtract from the numerator, giving us our answer: 1/2. Thus, our final answer is: 5 1/2. If this sounds difficult, see the graphic below - it's actually easier to see it than to explain it.


Here, give some a try. (Answers below)
1.   13/3
2.   8/2
3.   -16/7
4.   11/4
5.   13/1

1.   4 1/3
2.   4 (4 0/2 is the same as 4)
3.   -2 2/7
4.   2¾
5.   13

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