Basic Math Writing Proportions

Welcome back to Educator.com; for the next lesson, we are going to continue proportions.0001

We are going to actually write proportions and then solve them.0005

When we write proportions, it is easier if you first create a ratio that you can base your proportion on.0011

I like to call it a word ratio because you are going to look at what you have0022

and then create a word ratio meaning a part to a part.0033

You are going to find out what you are going to leave on the top0039

and what you are going to put on the bottom of your ratio.0043

Here I have my example, 2 miles in 20 minutes.0048

I want to find out how many miles it will be in 30 minutes.0053

I want to create my word ratio; for example, I could put miles over minutes.0059

That means all the numbers that have to do with miles is going to go on the top.0071

All the numbers that have to do with minutes is going to go on the bottom0077

because when we write a proportion, remember a proportion has to be two ratios that equal each other.0081

The first ratio I am going to write is going to have to do with this part right here.0091

2 miles in 20 minutes; remember ratio, I am comparing two things.0096

I am comparing the miles and I am comparing the number of minutes.0103

All the miles is going to go on the top.0106

That means I am going to write 2 miles... mi for miles0109

Over 20 minutes because that is on the bottom; 2 miles in 20 minutes.0116

Then I have to create my next ratio.0126

Remember I am making a proportion; I am making this ratio equal to this ratio.0131

That way I have a proportion, I can solve for whatever is missing, my X, my variable.0138

Again the miles is going to go on the top because that is what I set.0147

That is my word ratio; it is going to be X miles over... 30 minutes.0154

That is minutes; that is going to go on the bottom.0162

As long as I keep all the miles on the top and all the minutes on the bottom, I can create my proportion.0169

Let's say I created my word ratio so that it was minutes over miles.0175

That is OK.0180

As long as you keep all the minutes on the top and all the miles on the bottom,0181

you are still going to get the same answer.0186

You are still going to get the correct answer.0189

Again this ratio is equal to this ratio; that is how I get my proportion.0192

That is how I am going to write my proportion.0198

From here, I need to solve this out; I can cross multiply.0200

If I can solve it in my head, then I want to do that instead so I don't have to do all the work.0208

2/20 is going to equal X/30.0214

I just rewrote the proportion without all of the units so you can see it a little bit easier.0223

Here I can create an equivalent ratio; remember equivalent ratios from the previous lesson.0232

2/20 is the same thing as 1 over... because here I divided this by 2.0241

2 divided by 2 is 1.0250

If I want to do 20 divided by 2, then it is going to equal 10.0253

I can also do the same thing here.0260

I want to make this ratio the same as 1/10.0263

I can multiply this by 3 to get 30.0269

Then I have to multiply this top by 3 to get 3.0273

My X is going to be 3.0279

Here I just used mental math to solve for X.0285

I just made this equivalent ratio, 1/10, and then turned this into the same thing, 1/10.0289

If you want, you can use cross products instead; that is another method.0297

You are going to multiply all this together; make it equal to this.0302

2 times 30... actually let's go this way first.0309

It doesn't matter which way you go first.0311

20 times X is 20X; equal to... 2 times 30 is 60.0313

If I double 30, it is 60; 20 times what equals 60?0325

20 times 3 equals 60.0331

20, 40, 60; that is 3; X will become 3.0335

That is the same thing; it doesn't matter which way you solve.0340

As long as you make it so that this ratio is equal to this ratio.0347

Let's do a few examples.0354

We are going to write a proportion and then solve them out.0358

5 pounds for $15; find the cost for 4 pounds.0362

I want to first create a word ratio; word ratio, what am I comparing?0369

Or what am I using?--I am using pounds and I am using money.0380

I can say money or dollars on the top.0385

Then I am going to keep the pounds on the bottom.0391

It doesn't matter if you do pounds over money; that is fine too.0395

Here is my word ratio; that means when I create my proportion,0398

I am going to keep all the dollars on the top and then all the number of pounds on the bottom.0402

5 pounds for $15, here is my first ratio, comparing these two things.0410

$15, that is the dollars; that is going to go on the top; 15.0415

Over 5 pounds; that is going to go on the bottom because that is what I made my word ratio.0420

Find the cost for 4 pounds.0429

4 pounds, does the 4 go on the top or the bottom?0432

It is pounds; it is going to go on the bottom.0435

I want to find the cost; that is what I am looking for.0440

I am going to make that my variable; I can say X.0442

That is the money part; find the cost; cost is money.0446

That is going to go on the top.0451

Here I am going to solve for X; again you can solve this two ways.0454

You can find the equivalent ratio; I am going to simplify this.0462

This is going to become... divide this by 5.0468

15 divided by 5 is going to be 3.0474

5 divided by 5 is going to be 1; there was my equivalent fraction.0478

Same thing here; I want to make this the same as 3/1.0487

How did I go from 1 to 4?--this was multiplied by 4.0498

Or I can just do 4 divided by 4 is 1.0502

Same thing here; 3 times... whatever I do to the bottom, I have to do to the top.0505

X becomes 12; or again you can just do cross multiplying.0511

You can do 15 times 4 equal to 5 times X.0520

Then you can see what you have to multiply by 5 to get this number.0524

My X is going to be 12 because 12/4 is going to be 3/1.0531

That is the same thing as 15/5.0538

I have to look back and see what am I looking for?0543

I know that X is 12; but it is asking for the cost.0546

We know cost is money.0551

How much is it going to cost for 4 pounds? $12.0555

The next one, 15 feet for every 4 minutes; find how many feet in 10 minutes.0562

My word ratio, I am going to make it 50 over minutes.0570

My 16 feet is going to go on the top.0581

My 4 minutes is going to go on the bottom.0584

Equal it to how many feet?--find how many feet.0588

That is what we are looking for; feet, that is the top number.0591

That is X; over the number of minutes is 10.0595

Again you can look for equivalent fraction.0606

This is going to be the same... 16/4 is going to be the same as...0610

If you divide this by 4, divide this by 4, you are going to get 4/1.0615

I am going to use that fraction to help me solve for X.0626

1 times 10 equals 10; it is 4 times 10 is 40.0635

That means X has to be 40.0640

Again these two have to be equal; this is the same as 4/1.0647

That means this has to be the same as 4/1.0653

1 times 10 is 10; 4 times 10 has to be 40.0659

How many feet?--X is going to be 40 feet.0667

Example two, write a proportion and solve.0680

5 chocolate bars costs 7.50; find the cost of 2 chocolate bars.0684

My word ratio, chocolate bars; you can do money on the bottom.0689

Or you can just do money on the top and then the number of chocolate bars on the bottom.0698

It doesn't matter; there is my word ratio.0702

Chocolate bars; 5 chocolate bars; 5 on top; over money; 7.50 on the bottom.0708

Equal to chocolate bars... that is 2 on the top; over the amount of money on the bottom.0717

For this one, I can solve this proportionally.0730

You can also use this as a ratio.0739

Remember 7.50 for 5 chocolate bars; you can make that as a ratio.0746

Then find the unit rate; find how much it costs per chocolate bar.0751

If you remember from a couple of lessons ago, you can use unit rate also for the same problem.0758

Let's just go ahead and solve this using cross products.0766

I am going to multiply this and this; that is going to be 5X.0770

Again if you are multiplying number times variable, then you can just put it together like that.0776

Equals 7.50 times 2; 7.50 times 2.0782

If you want, you can just multiply it out like that.0790

0; 5 times 2 is 10; 2 times 7 is 14; add the 1; 15.0796

You know that this is 7.50; that is money; 7 times 2 is 14.0808

If you have 50 cents and you double it, that is a dollar.0815

You can think of it that way too; 5X equals $15.0818

I am not going to put the 0.00 because that is just change.0825

This is my whole number, $15; I can now find X.0829

5 times... I know 3 equals 15; X is going to be 3.0836

That means if for 5 chocolate bars, it costs 7.50,0845

for 2 chocolate bars, it is going to cost me $3.0850

I need to write my dollar sign here to give me the answer.0855

The next one, Sharon types 60 words per minute.0864

Find how long it will take for her to type 80 words.0869

My word ratio could be words over minute; 60 words per minute.0874

That is over 1 because the number of minutes is 1.0886

How long will it take... they are asking how long it will take.0894

They are asking for words or minutes?--they are asking for minutes; how long.0899

This will be X down here; then they are asking for 80 words.0903

Again you can use proportions; you can use cross products.0911

60 times X is 60X; equal to 1 times 80 is 80.0919

Remember if you want to find what 60 times X is and what X is, then you can divide the 60.0929

Anytime you have a number times 60, you have a number times a variable,0939

you can just divide that number to find X.0942

X is going to equal... I am going to cross out these 0s.0947

I am going to have 8/6; but then here I can simplify that.0951

Divide this by 2; divide this by 2; it is going to be 4/3; 4/3.0957

If I want to change this to a mixed number, this will be... 3 goes into 4 one whole times.0971

How many do I have left over?--1; my denominator is 3.0982

It will be 1 and 1/3 of a minute.0988

If you have a problem like this on your homework or at school,1001

it depends on how your teacher wants it, but you can change this to a decimal.1008

Or since it is minutes, you can take this fraction.1012

It is 1 whole minute and then some seconds; 1/3 is part of a minute.1016

You can just figure out how many seconds that would be by doing 60 divided by 3.1022

60 divided by 3; that is going to give you 20.1030

That means this is going to be 1 minute and 20 seconds.1036

Or you can just leave it like this if your teacher doesn't mind.1040

Then it is 1 and 1/3 of a minute.1045

The third example, Susanna estimates that it will take 4 hours to drive 600 kilometers.1051

After 3 hours, she has driven 500 kilometers.1058

Write a proportion to see if she is on schedule.1064

Basically they are asking if you make a ratio of this and you make a ratio of the next part,1068

are they the same?--that is all it is asking.1076

My word ratio, hours over kilometers.1083

It is going to be 4 hours over 600 kilometers.1091

We are going to see if this equals the same as 3 hours over 500 kilometers.1102

Let's see here; let's simplify these.1117

Here I can say that if I simplify this, 4 goes into 600 how many times?1124

Here is 1, 4, 2; I am just dividing it.1141

That is 5; 20; bring down this 0; 150.1146

If I divide this by 4 and I divide this by 4, I am going to get 1/150.1155

That means every hour, Susanna should drive 150 kilometers.1167

If 4 hours, she estimates she is going to be driving 600 kilometers,1178

that means every 1 hour, she is going to be driving 150 kilometers.1184

Is that the same thing as this?1191

If 1 hour, 150 kilometers, does she get this in 3 hours?1193

This is 1 times 3 equals 3 hours; 1 hour times 3 is 3 hours.1203

Does that mean 150 times 3 is 500?--let's see.1210

This times 3; 0; 5 times 3 is 15; add that; that will be 450.1219

No, if she drives 150 kilometers for every hour,1234

then in 3 hours, she should be driving 450 kilometers.1240

But she drove 500 kilometers; that means she is not really on schedule.1246

I mean, she is a little bit faster.1252

But according to what she has estimated, it is not the same.1256

So this one is no; she is not on schedule.1260

She is actually a little bit early because she drove more than what she thought she would be at.1264

This is not the same ratio.1273

If it is 4 hours for 600 kilometers, then in 3 hours, she should be driving 450 kilometers.1276

Because 1 hour is 150 kilometers; this needs to have the same ratio also.1292

1 hour is 150; this has to equal this too.1304

This one is no; she is early.1311

That is it for this lesson; thank you for watching Educator.com.1318