Multiplying Fractions

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You may be asking yourself: What are fractions?
Well, in this Instructable I will teach you what fractions are, how to multiply basic fractions,how to multiply improper fractions, and also, how to multiply algebraic fractions.

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Step 1: What Are Fractions?

If you already know what fractions are then skip to step 2.
What are fractions?
First I will teach you what fractions are.

Fractions are parts of a whole.

Lets say you are having a party with 8 people(including you), so you cut your pizza into 8 slices.
The way you would write that is:
8 - how many slices remaining
-- - over
8 - how many slices will make up a whole pizza
or 8/8

After everyone ate their slice(subtract 8 parts), you have:
0 - how many slices remaining
-- - over
8 - how many slices will make up a whole pizza
Everyone is happy because they got a slice. :)
0/8 or just plain 0.

You say that like: "8 over 8" or "eight eighths".
8
-- is equal to 1.
8
So now you have 1 whole pizza or 8 slices of 8 slices. Get it?
8/8 or 1

Now, you are having another party with the same people,so you cut the pizza into 8 slices, but two people don't want their slices.
After everyone ate their slice, you have:
2 (how many slices remaining)
-- (over)
8 (how many slices will make up a whole pizza)
or 2/8

Now you have 2 parts of a whole 8 parts(2/8), yay left overs! But it would be easier to know that you have 1/4(one fourth) of a pizza instead of 2/8(two eighths) right? This is called simplifying or reducing. To make the same fraction look smaller but equal the same amount.

50/100 can be simplified(or reduced) into 1/2(one half).
25/100 can be simplified(or reduced) into 1/4(one fourth).
2/8 can be simplified(or reduced) into 1/4(one fourth).

A fraction can also be a whole(1) and a fraction.
1 1/2 (one and one half)

The top number of a fraction(how many parts of the whole) is called the numerator.
The bottom number of a fraction(how many parts make up a whole) is called the denominator.

Do you get it?
A fraction is simply how many parts are in a whole, in this case,who many slices in a pizza are left.
It can be slices of pie, parts of the day(1/24 is equal to 1 hour), or just about anything.

Step 2: Multiplying Fractions

Now that you know what fractions are we can finally get to what this Instructable is meant for, multiplying fractions.

Multiplying Fractions
Before we continue I would recommend you know how to multiply, otherwise you will be 100%(or 100/100 of you) lost.

So lets get started.
Multiplying fractions is just like multiplying but you are multiplying parts.

What you do is multiply across:
1 -> 2 = 2
--.....--....--
2 -> 5 = 10

So you would multiply 1 x 2 and get 2 then you would multiply 2 x 5 and get 10.
So you would end up with:
2
--
10

But wait that can be reduced(simplified) to:
1
--
5
and the way you do that is by finding out if any number can go in both of these, in this case 2 could go in both.
So you divide both the numerator and the denominator by 2.
2 / 2 = 1
--...........--
10 / 2 = 5

So you end up with 1/5.
Not every problem will need to be reduced.
and here is all that in 1:
1 -> 2 = 2 / 2 = 1
--.....--....--............--
10 -> 5 = 10 / 2 = 5

Do you get it?
Solve the following problem and leave a comment with the answer, if you want to.

Step 3: Multiplying Whole Numbers With Fractions and Improper Fractions

Multiplying Whole Numers With Fractions
To multiply whole numbers with fractions we need to turn it into an improper fraction because you cant multiply:
3 3/4 X 5 1/2

So you have to turn the number into an improper fraction.

Improper Fractions
Before we continue I recommend you know how to use fractions and know what they are.

An improper fraction is a whole number and a fraction turned into a fraction or a fraction with more parts than is in 1 whole.

An improper fraction:
15
---
12
That is equal to 1 1/4.

2
--
1
That is equal to 2 because there are 2 pieces when 1 piece makes up 1 whole.

To get that you take 3 3/4 then you multiply the whole number(3) by the denominator(4) and add the numerator(3), and you get:
15
---
14
See Image.

Now that you have an Improper fraction you can mutliply that with other fractions or improper fractions all day long.

Solve:
15 4
--X--
14 3

Step 4: Multiplying Fractions in Algebra

Reciprocals
Before we continue I recommend you know how to Improper fractions.

When multiplying fractions in algrebra somtimes you will need to get X alone, and to do that when fractions are with X you need to Reciprocate the fraction to get rid of it.
Lost?

Reciprocating is flipping the fraction.

If you reciprocate 1/2 then it becomes 2/1.
Remember 2/1 is equal to 2.
That will become very important in the next section.

50/100 becomes 100/50
3/5 becomes 5/3
5/6 becomes 6/5
9/7 becomes 7/9

Finally the algebra
Before we continue I recommend you know how to Multiply basic fractions, use improper fractions, and reciprocate.

When working algebra problems remember these VERY important rules:
A negative number multiplied or divided by a negative number is a positive number.
A positive number multiplied or divided by a positive number is a positive number.
A negative number multiplied or divided by a positive number is a negative number.
A positive number multiplied or divided by a negative number is a negative number.

Look at this problem:
3/4X = 4

Most of us can figure out what X is just by dividing 4 by 3/4, that will work but when you get into much harder problems that contain both that, dividing, adding, and subtracting just to find out what X is, it will no longer be the easy way.

See image1.

So to figure out what X is we have to get X alone. To do that we have to get rid of 3/4. In order to get rid of 3/4 we have to reciprocate it and multiply by itself. But because we did it to one side we have to do it to the other side. So now we have 1X = 16/3. We have to turn 16/3 into a proper fraction. So we divide 16 by 3 and add the remainder 1 as a third. Now X will equal 5 1/3.

To check ourself, we replace X with 5 1/3.

Solve:
3/4 {times} 5 1/3 = 4

If i tought you right and you checked right then 3/4 {times} 5 1/3 should equal 4.

Thus ends my Instructable. Feel free to ask questions and post comments. Please vote for my instructable in the Burning Questions Round 6.5 contest.

*No pizzas were hurt in the making of this Instructable.* Participated in the
Burning Questions Round 6.5