Basic Math Connecting Decimals and Fractions

Welcome back to Educator.com; this lesson is on connecting decimals and fractions.0000

When we connect fractions to decimals and decimals to fractions, let's think about money.0007

For fractions and decimals, I can represent each with a dollar.0017

If I have half a dollar, 1/2 is half.0024

If I have half a dollar, I have fifty cents.0029

Keep in mind that 0.5 is the same thing as 0.50 or 50 cents.0035

When the numbers are after the decimal place, I can put as many 0s as I want.0045

The number does not change.0051

I know that half a dollar is the same as 50 cents or 0.5.0056

1/2 would be the same as 0.5.0065

If I have 1/4 from a dollar, how can I divide the dollar up into 4 parts?0070

4 of what makes a dollar?--the answer is quarters.0082

We know that 4 quarters make 1 dollar.0089

If I have 1 out of 4 quarters, if I have 1 quarter, then I have 25 cents or 0.25.0093

How about this one?0107

What would I have if I divide the dollar up into 10 parts?0110

I would have 1 dime.0115

1/10 would be the same thing as having 1 dime which is 0.1 or 0.10.0118

Remember this is the same as this.0131

How about this one?0136

If I divide up the dollar into 100 parts, then I would have 100 pennies.0139

Having 1 of those parts, having 1 penny, is going to be 0.01 or 1 cent.0149

1/100 is having 1 cent, 0.01.0160

Let's look at this again; this fraction right here, 3/4.0170

I am going to again relate it to the fraction 1/4; remember 1/4.0177

If I have 1 part out of the 4 that I divided the dollar into, then I have 1 quarter which is 0.25.0183

This is the value of 1 quarter.0200

If you look at this fraction, this is 3/4.0203

The dollar is still divided into 4 parts which is still the quarter.0207

If I have 3 quarters, how much do I have?0213

I have 0.75 or 75 cents.0218

If I want to do this mathematically, I can take the 3 and divide it by 4.0229

3, this right here means divide; 3 divided by 4.0237

That means I can take 3 divided by 4.0242

This is a whole number; I have to put a decimal after it.0249

Then I can add as many 0s as I want; let's make this longer.0254

4 goes into 3 zero times; I am going to raise up this decimal.0263

4 goes into 30 how many times?--let's see.0268

4 times 7 is 28; subtract this; this is 2; bring down the 0.0273

4 goes into 20 five times.0286

If I want to convert 3/4, this fraction into a decimal, I can just do 3 divided by 4.0297

I am still going to get the same answer of 0.75.0305

But if I know that I can take this and think of the dollar,0309

and I know I can divide the dollar into 4 parts which is 4 quarters,0315

and I have 3 of those parts, then I have 75 cents.0319

Right here, 0.7; 0.7 is the same thing as 0.70.0327

0.7 is the same thing as having 70 cents; what gives me 70 cents?0344

If I have 7 dimes, then I will have 70 cents.0351

Then I can say that this is having 7 over... the value of a dime is 10 cents.0359

7/10 would be the same thing as 70 cents.0370

If I want to just take this without relating it to the dollar0377

and just convert it back to a fraction, I can take this number right here, 7.0382

I am going count how many numbers I have after the decimal place.0388

It has to be after the decimal place; 7, I only have one number.0392

Take that number; place it over a 10.0398

One 0 because I have only one number after the decimal place.0405

So I am only going to have one 0 here.0409

Let's go over more examples.0414

Convert from fraction to decimal or decimal to fraction.0417

Here we have a decimal; I am going to convert it to a fraction.0421

If I look at this, if I have 25 cents, I have 1 quarter.0429

1 quarter would be having 1 quarter out of... how many quarters equal a dollar?0438

4; so having 1 quarter, 25 cents or 0.25, is the same thing as 1/4.0446

Another way to do this, I take this number, 25.0457

I am going to make that into my numerator.0465

Then I am going to count how many numbers do I have after the decimal place?0468

I have two numbers; I have one, two.0475

I am going to put that many 0s after my 1 as my denominator.0479

This becomes 25/100.0487

I have to simplify this because this fraction... I know that 25 can go into 100.0491

I am going to take this 25; I am going to divide by 25.0499

Then I have to divide the bottom number by the same number.0503

25 divided by 25 is 1; 100 divided by 25 is 4.0509

0.25 is going to be the same thing as 1/4.0518

The next example is a fraction 3/10; I can convert this into a decimal.0527

Again let's relate it to money.0536

If I have 10 as my denominator, then what do I have?0538

10 parts to make a dollar would be 10 dimes.0546

I know that I am working with dimes here.0553

If I have 3 dimes, then how much do I have?0556

How can I write that into a decimal?--I would have 30 cents.0561

Having 3 dimes is the same thing as 30 cents.0569

Or 3/10 is the same thing as 0.30 or 0.3 because again this is the same thing.0576

I can put a 0 here because it is after the decimal place.0585

Another way you can do this, just divide; 3 divided by 10.0592

I have to add 0s at the end of it.0601

10 goes into 30 three times; but I have to write it over the 0.0605

Then I have to bring up my decimal; this becomes 30.0612

If I subtract, I get 0.0617

3/10 or 3 divided by 10 is going to be 0.3.0621

This next example, 0.77, I am going to convert this into a fraction.0630

If I have 0.77 or 77 cents, I have the same thing as 77 pennies.0637

Again I can write that number at the top.0653

How many pennies are equal to a dollar?0659

I know that 100 are equal to a dollar.0662

This is the same thing as saying I have 77 pennies.0665

0.77 is the same thing as 77/100.0671

Again without thinking of money, I can just take this number, 77, as my numerator.0677

Count how many numbers I have after my decimal place which is 2.0685

That means I am going to add two 0s which is 100 as my denominator.0690

It is the same thing.0697

This fourth example here, I have a fraction and I am going to convert this into a decimal.0704

This top number tells me how many I have.0712

This bottom number tells me how many out of 100 I have or how many out of a dollar I have.0716

If I have 100 parts to make a dollar, what do I have?0722

I have the penny because 100 pennies equals 1 dollar.0727

I know that I have 9 of them.0732

9 out of 100 would be the same thing as having 9 pennies.0734

In order to write this as a decimal, if I have 9 pennies, how much do I have?0743

I have 9 cents which is written like that.0748

9 out of 100 is the same thing as 0.09.0753

You can also think of this as 9 divided by 100.0761

You can take 9 divided by 100.0768

But since this is 100, I can do a shortcut here.0771

Whenever my denominator is 10 or 100 or 1000, any number that is a multiple of 10,0779

all I am going to do is take that top number... let's write that out; the top number is 9.0787

I am going to count how many 0s I have here.0794

I have one; I have two 0s.0796

Since I have two 0s, I am going to take that number 2.0800

I am going to place this decimal point right there.0806

The decimal point always goes after the number.0812

I am going to move the decimal point two places because again there are two 0s here.0815

If I had a 10, I only have one 0.0822

I would only move it one place value.0826

If I had 1000, I would have three 0s.0828

I would have to move it three place values.0833

Again I am going to take this decimal point.0837

I am going to move it two place values going to the left.0839

I am going to go one and two.0844

There is where my decimal point is going to go.0848

Then I have a space right here; I have to put a 0 right there.0852

For this shortcut, you can only do that if the denominator is a multiple of 10.0856

It has to be 10, 100, or 1000, and so on.0861

Otherwise you are going to have to do 9 divided by 100.0866

Again this sign right here means divide.0870

We can do 9 divided by 100 to change that into a decimal.0872

But I also knew that this bottom number right here, it takes 100 pennies to make a dollar.0878

Since it takes 100 pennies to make a dollar and I have 9 of them,0888

I would have 9 cents; I can just write that as 0.09.0892

That is it for this lesson; thank you for watching Educator.com.0898