## Introduction: Multiplying Fractions

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.

## 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.*

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Burning Questions Round 6.5