Basic Math Solving Proportions

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For the next lesson, we are going to be solving proportions.0002

A proportion is when we have two equal ratios.0008

A ratio is a comparison between two parts, A and B.0014

Here this is a ratio comparing A and B together.0022

You read it as A to B.0028

You can also write ratios A to B like that.0030

But when you are taking two ratios and you are comparing them0036

to each other and you are saying that they are equal,0039

the ratio of A to B is equal to the ratio of C to D, then you have a proportion.0042

You are actually going to have to write it A to B like a fraction.0049

Proportion is when you have ratio equaling another ratio.0056

To solve proportions, let's say you are missing one of these.0062

You are missing A; or you are missing B; one of these.0065

To solve a proportion, you are going to use what is called cross products.0069

Cross products is when you multiply across.0075

You are going to go A times D equal to B times C.0078

You have the proportion A over B equal to C over D.0089

Then you are going to find the products AD.0096

Cross products, that is A times D.0100

When you write two variables next to each other like that, that means multiply.0103

A times D equal to B times C.0107

Be careful, this is not the same thing as cross cancelling.0113

Cross cancelling is when you are multiplying fractions0117

and you can cancel out numbers if they have common factors.0120

But this is cross products; this is for proportions.0126

This is only when they are equal to each other.0129

Then you can multiply across and make it equal to this across.0132

AD, A times D is equal to B times C.0140

Let's do an example; if I have let's say 1/2 equal to X/ 4.0145

This one is easy; we know we can do this in our head.0156

One half, 1/2, is the same thing as 2/4.0158

I know that X has to be 2.0163

But to solve it, just to use cross products, it will be 2 times X.0167

2 times X is 2X; same thing as 2 times X.0174

It is equal to 1 times 4 which is 4.0178

Then to solve this out, we are going to... remember one-step equation.0183

This is 2 times X or 2 times what equals 4?0188

2 times 2 equals 4; X equals 2.0193

Let's do a few examples; the first example, find two equivalent ratios for each.0200

We know that proportions are when we have two equal ratios.0207

Let's find two other ratios that are equal to this.0214

3/4, I can say that if I multiply this by 2, then this is 6/8.0218

This ratio is equal to this ratio.0228

To find another one, how about if I multiply it by 3?0232

3 times 3 is 9; 4 times 3 is 12.0235

Here are my two equivalent ratios.0241

Here I can also divide.0248

If I divide by 10, divide this by 10, because I know 10 goes into both, this becomes 1/2.0250

That is one equivalent ratio.0261

I can multiply this by 2; multiplied by 2; multiplied by 2.0266

This can be 2/4.0272

This and this, they don't look like they are equivalent.0276

But they actually are because if you simplify this, this is 1/2.0279

If you simplify this, this is 1/2; it is the same; it is equivalent ratios.0284

This one, you can multiply it by 2; you can divide.0294

I know that 11 and 33 have factors of 11.0301

11 divided by 11 is 1 over... 33 divided by 11 is 3.0308

Again you can just base it on this for the next one.0315

Multiply it by 2; it will be 2.0318

Multiply this by 2; it will be 6.0321

There are actually many, many different ratios or fractions that you can write out to make them equivalent.0327

There is going to be many, many; these are not the only answers.0336

These are not the only fractions that are equal to this fraction.0339

If you want, you can multiply this by 10, multiply it by 20.0344

As long as you do it to both numbers, you are going to have equivalent ratios.0347

Let's solve these proportions; but we are going to use mental math.0354

Meaning we are going to try to solve these out in our head.0358

For the first one, I want to solve for X; 3/4 equals X/12.0362

If this fraction is going to have to equal this fraction, 4 times what is 12?0371

4 times 3 is 12; that means I have to multiply the top number by 3.0376

X has to be 9; X equals 9.0382

Same thing here; this is 1 times 5 which gave me 5.0388

Then I have to multiply 5 to this; A is going to be 25.0394

Same thing here.0404

If you look at the bottom numbers, this is 6 times 1 equals 6.0406

Something times 1 is going to equal 4; isn't this 4 times 1?0414

This is going to be the same fraction; 4/6 has to equal 4/6.0418

D is going to be 4.0424

The next one, this one is a little bit different0428

because I can't divide and multiply a number 15 to give me 12.0433

What I can do is I can just simplify this ratio because I have both the top and bottom number.0441

I want to simplify this ratio to help me solve for this ratio.0449

If I simplify this, I know that 4 goes into both numbers.0454

Divide this by 4; this is 3/2; this ratio is equivalent to that ratio.0459

I just have to base this one on this then.0473

3 times 5 is 15; to go from here to here, it is times 5.0480

To go from here to here then, it will be times 5.0489

Z has to be 10.0493

Tell whether the two ratios form a proportion.0503

That just means that they have to be equal.0508

It is just a yes or no.0511

Are they equal or are they not equal?--because proportions have to be two equal ratios.0512

Is this ratio equal to this ratio?0519

2/3, multiply this by 10 to get 20; multiply this to 10 to get 30.0525

Is it equal?--yes, this one is equal.0533

The next one, are these equal ratios?0539

This one, you had to multiply this by 7 to get 35.0543

How about this one?0548

If you multiply this by 7, you have to multiply it by the same number.0549

Does it give you that?--this one is yes.0552

This one here, again I can't multiply or divide this number to get this number.0560

I can find another equivalent ratio to base both of these on.0566

I know that 5 goes into both of these.0572

5 goes into 25 five times; I am dividing by 5.0577

70 divided by 5 is going to be...0584

Again if you want to just divide it out, it is going to be 70 divided by 5.0589

Otherwise it is going to be 14.0594

I know that because... I will just solve it out.0598

Let's do it right here; 70 divided by 5.0602

1 is going to give you 5; subtract it; 2; 5 times 4 is 20.0608

That means to get from 5 to 35, I have to multiply this by 7.0617

What is 14 times 5?--it is 70; I know it is not 70.0626

This has to be 70; so I am going to say no.0636

The next one, here 42/21, this also is going to be equivalent fraction.0651

This will be 2/1 because 42/21... 21 is half of 42.0666

Again I can just divide this by 21 to get 2; and then 21 to get 1.0680

To get from here to here... or see if this one equals the same thing.0687

This one, divide this by common factor; is this 12?0693

This becomes 2; this becomes 1.0703

See how this was equal to this?--and then this also equal to this?0707

That means these are the same; so this one is yes.0712

You can do the same thing for this one.0716

I know that this simplified to get that.0720

Here 35 divided by 5 because a common factor between this one and this one is 5.0724

This one is 7 over... 75 divided by 5.0740

75 divided by 5 is going to be 15.0751

That will just be 5, 2; bring down the 5; this is 15.0757

Automatically because these are different, I know that it is a no.0765

Again if you want to figure out if two ratios are equal, you can either multiply, see if it is the same factor.0772

Or can just simplify each one of them and see if those simplified fractions are the same.0783

Like the bottom one right here, this last one, you simplify this; it became 2/1.0791

You simplify this; it became 2/1.0796

Since they simplify to become the same fraction, you know that these are the same.0798

So that is yes.0804

For the next example, we are going to solve the proportion using cross products.0807

Just practice using these cross products.0814

You are going to multiply these across.0816

You are going to make it equal to those two multiplied.0822

This becomes 2 times X; I am just going to write that as 2X.0828

Remember whenever you multiply a number with a variable, you can write it together like that.0832

Then equals 5 times 10 which is 50.0838

Again be careful, cross products is not the same thing as cross cancel.0843

You are not cancelling anything out.0849

This 5 and this 10, they have a common factor of 5.0850

But you are not cross cancelling out.0856

You only cross cancel when you are multiplying the fractions.0858

But here you are solving proportions where it is an equal, not a multiplication.0863

You are going to multiply them together and you are going to make it this side.0867

From here, I have to find out what X is; 2 times something equals 50.0874

2 times 25 equals 50; think of 50 cents.0880

2 times 2 quarters... that is 25 cents... equals 50 cents.0888

Or you can also just divide this 2; X is going to equal 25.0895

If you want, you can just use division like this.0906

2 goes into 5 two times; 4; subtract it; you bring down the 1.0910

Bring down the 0; 2 times 10 is 6; X is 25.0917

Same thing here; let's cross multiply; cross products.0927

3 times M would be 3M; just write them together like that.0939

Make sure you don't do it with numbers.0945

If it was 3 times 4, then you can't put 34 because it looks like the number 34.0946

This means 3 times M; then 4 times 21; 4 times 21 is 84.0952

21 times 4; 1 times 4 is 4; 4 times 2 is 8.0968

From here, 3 times something equals 84.0976

That means I have to divide this 3.0979

I need to divide the 3 to get my answer; 84 divided by 3.0984

How many times does 3 go into 8?--two times; that becomes 6.0993

I am going to subtract and get 2; bring down the 4.0998

3 times 8 equals 24; 24, 0; my M is 28.1002

Make sure you write what the variable is; the variable equals 28.1018

Don't forget, when you are solving proportions, if you can do it mentally, then go ahead and do that using mental math.1023

Otherwise you are going to just multiply this.1030

These two across equal these two across; then solve for your variable.1032

That is it for this lesson; thank you for watching Educator.com.1038