For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

### Solving Proportions

#### Related Links

- Portion: An equality of two ratios

### Solving Proportions

[3/5]

- [(3 ×2)/(5 ×2)] = [6/10]
- [(6 ×2)/(10 ×2)] = [12/20]

[11/44]

- [(11 ÷11)/(44 ÷11)] = [1/4]
- [(1 ×2)/(4 ×2)] = [2/8]

[3/5] = [x/10]

- [(3 ·2)/(5 ·2)] = [x/10]

[1/8] = [x/24]

- [(1 ·3)/(8 ·3)] = [x/24]

[3/z] = [12/16]

- [(3 ·4)/(z ·4)] = [12/16]

[4/40],[8/80]

- [(4 ×2)/(40 ×2)] = [8/40]

[12/24],[24/47]

- [(12 ×2)/(24 ×2)] = [24/48]

[13/26],[25/52]

- [(13 ×2)/(26 ×2)] = [26/52]
- [26/52] ≠ [25/52]

[5/x] = [2/20]

- 2x = 5 ·20
- 2x = 100
- [2x/2] = [100/2]
- x = [100/2]

[2/4] = [y/16]

- 4y = 2 ·16
- 4y = 32
- [4y/4] = [32/4]
- y = [32/4]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Solving Proportions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Proportions 0:05
- An Equality of Two Ratios
- Cross Products
- Extra Example 1: Find Two Equivalent Ratios for Each 3:21
- Extra Example 2: Use Mental Math to Solve the Proportion 5:52
- Extra Example 3: Tell Whether the Two Ratios Form a Proportion 8:21
- Extra Example 4: Solve the Proportion 13:26

### Basic Math Online Course

### Transcription: Solving Proportions

*Welcome back to Educator.com.*0000

*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 them*0036

*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 fractions*0117

*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 different*0428

*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

2 answers

Last reply by: Ana Chu

Sun Feb 1, 2015 11:21 AM

Post by mohamed bulhan on July 3, 2014

PROPORTIONS are confusing to me. what is the easiest way to solve proportions?