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

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

### Writing Proportions

#### Related Links

- When writing proportions, first create a ratio that you can base your proportion on

### Writing Proportions

8 pounds for $ 24, find the cost for 2 pounds

- [24/8] = [x/2]
- 2 ·24 = 8x
- 48 = 8x
- [48/8] = [8x/8]
- [48/8] = x

21 feet for every 5 minutes, find how many feet in 10 minutes

- [21/5] = [x/10]
- [(21 ×2)/(5 ×2)] = [x/10]

10 chocolate bars cost $ 20.50. Find the cost of 4 chocolate bars

- [10/20.50] = [4/x]
- 10x = 4 ·20.50
- 10x = 82
- [10x/10] = [82/10]
- x = [(82 ÷2)/(10 ÷2)] = [41/5] = 8.20

Sharon types 80 words per minute. Find how long it will take for her to type 120 words

- [80/1] = [120/x]
- 80x = 120
- x = [(120 ÷40)/(80 ÷40)] = [3/2] = 1[1/2]

- [8/1200] and [4/600]
- [(8 ÷8)/(1200 ÷8)] = [1/150]
- [(4 ÷4)/(600 ÷4)] = [1/150]
- [1/150] = [1/150]

2 pounds for $ 30, find the cost of 15 pounds

- [2/30] = [15/x]
- 2x = 30 ·15
- 2x = 450
- [2x/2] = [450/2]

12 feet for every 3 minutes, find how many feet in 9 minutes

- [12/3] = [x/9]
- 3x = 12 ·9
- 3x = 108
- [3x/3] = [108/3]
- x = [108/3]

6 chocolate bars cost $ 8.50. Find the cost of 3 chocolate bars

- [6/8.50] = [3/x]
- 6x = 3 ·8.50
- 6x = 25.50
- [6x/6] = [25.50/6]
- x = [25.50/6]

[80/1] = [200/x]

- 80x = 200
- [80x/80] = [200/80]
- x = [(200 ÷40)/(80 ÷40)] = [5/2] = 2[1/2]

- [12/15] = [20/x]
- 12x = 20 ·15
- 12x = 300
- [12x/12] = [300/12]
- x = [300/12] = 25

*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

### Writing 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
- Writing Proportions 0:08
- Introduction to Writing Proportions and Example
- Extra Example 1: Write a Proportion and Solve 5:54
- Extra Example 2: Write a Proportion and Solve 11:19
- Extra Example 3: Write a Proportion for Word Problem 17:29

### Basic Math Online Course

### Transcription: 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 have*0022

*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 top*0039

*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 bottom*0077

*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 miles*0109

*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

1 answer

Last reply by: Mary Pyo

Fri Feb 3, 2012 11:54 PM

Post by jeffrey breci on December 7, 2011

80/60 is 1.33, 1and 1/3 when you switch to an improper fraction is 4/3 and again switch to a decimal is 1.33. how do you get 1 min, and 20 seconds?

0 answers

Post by Siddharth Gupta on August 14, 2011

great video! you can learn a lot from this. she explains it nicely. she is amazing