Basic Math Fraction Concepts and Simplest Form

Welcome back to Educator.com.0000

This lesson is going to go over some concepts of fractions and how to simplify them.0002

When we have a fraction, we are representing it as a part.0013

If we have something that is whole, we are going to take parts of it, break it up into parts.0020

That is how we write fractions.0026

Let's pretend it is your birthday; this is your cake.0030

We are obviously going to have to cut the cake.0037

Since it is your birthday, you would probably want the biggest piece.0040

If we take this cake, let's say we are going to cut it up into 4 equal pieces.0045

If you get 1 piece of this cake, you are getting 1 piece out of how many total pieces?0055

1, 2, 3, 4; you will be getting 1/4 of your cake.0067

Let's say I cut the cake up into smaller pieces.0076

Here if you take 1 piece of your cake,0091

then you are going to take 1 out of 2, 3, 4, 5, 6, 7, 8.0099

Out of 8 total slices, you are getting 1.0107

Let's say you want more cake; you ate 3.0114

I can write this as 3 out of 8.0122

Look at this one right here; pretend that this is a chocolate bar.0131

Your chocolate bar, you are going to break it up into pieces.0137

We can break up the chocolate bar into 8 pieces.0139

If you eat 1 little piece, you are eating 1 out of 1, 2, 3, 4, 5, 6, 7, 8 pieces.0145

Let's say you eat another one; that is 2 out of 8 pieces.0159

I can also write this in a different way.0169

If the chocolate bar is broken up into 4 pieces, you break it up into 4 pieces,0182

then this right here that you ate is going to be the same thing as 1 out of 4 pieces.0188

If you look at this, 1, 2 out of 8 that you ate here0200

is going to be the same as 1 out of 4.0207

That is when we are going to learn how to simply these fractions.0220

Here we have 8 pieces.0226

4 out of 8 would be 1, 2, 3, and 4.0230

This is 4 out of 8.0244

Instead of having 8 pieces, I am only going to have 4.0251

In this case, having 4 out of 8 would be the same thing as 2 out of 40265

because I have 4 pieces and I ate 2 out of those 4.0274

If I wanted to show 4 out of 10, I need to have something... I can have a circle.0284

Or I can have something rectangular like the chocolate bar.0291

I need to 10 equal pieces; I can do this.0300

Let's say these were 10 equal pieces.0318

To show 4 out of 10... that would be 4 out of 10.0321

How can you represent this in a different way?0337

Instead of breaking this up into 10 pieces, let's say you broke it up into 5 pieces.0341

In that case, if it was 5 pieces, this would be 1.0346

This would be 2, 3, 4, and 5.0351

4 out of 10 could be the same as 2 out of 5.0357

This one, we have 6 pieces; 6 pieces.0374

If I do this, this would be 1 out of 6.0381

If I take this piece, then that would be 2 out of 6.0389

Maybe if I ate this piece, then that would be 3 out of 6.0397

If you think about it, if I have 6 pieces and I ate 3 of them, I ate 1/2.0408

I ate half of this chocolate bar.0418

Let's say I don't have a picture; I don't have a chocolate bar.0425

I just have a fraction, 5 over 25.0427

How can I write this in simplest form?0430

In this case, I can take a common factor, a number that multiplies into 5 and 25.0437

I can divide both numbers by that number.0447

5 and 25; I know that 5 goes into 5 and 5 goes into 25.0452

That means I can divide this number by 5 and divide this number by 5.0458

They have to be divided by the same number.0469

Or else you are not going to get the right answer.0471

5 divided by 5 is 1; 25 divided by 5 is 5.0475

Let's look at this fraction again, 1 and 5.0484

We have to make sure that they have no common factors besides 1.0488

For 1 and 5, that is the only common factor they have.0494

That means we are done; this is the answer.0497

The simplest form of 5 over 25 would be 1 over 5.0501

To find the simplest form of 14 over 49, we are going to look for a common factor.0514

Meaning we are going to look for a number amongst 14 and 490525

that can be multiplied to get 14 and it can be multiplied to get 49.0532

A common factor between these two numbers would be 7.0539

In order to get the simplest form, I can take this fraction,0544

divide the top number and the bottom number by that common factor.0548

Again they have to be the same number.0557

You have to divide both numbers by that same number.0560

14 divided by 7 is 2; 49 divided by 7 is 7.0566

I look at these two numbers now.0576

I want to see if there is a common factor between 2 and 7.0579

The only common factor is 1; that means I am done.0584

The simplest form of 14 over 49 would be 2 over 7.0590

That is it for this lesson; thank you for watching Educator.com.0599