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

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

### Scale Drawings

#### Related Links

- Scale drawing: An enlarged or reduced drawing that is similar to an actual object or place
- The scale is the ratio of the two

### Scale Drawings

- [2/50] = [x/200]
- 2 ·200 = 50x
- 400 = 50x
- [400/50] = [50x/50]
- [400/50] = x

- [3/30] = [x/300]
- 3 ·300 = 30x
- 900 = 30x
- [900/30] = [30x/30]
- [900/30] = x

- [2/10] = [x/300]
- 2 ·300 = 10x
- 600 = 30x
- [600/30] = [30x/30]
- [600/30] = x

- [l/3] = [x/72]
- 72 = 3x
- [72/3] = [3x/3]
- [72/3] = x

- [l/3] = [x/45]
- 90 = 3x
- [90/3] = [3x/3]
- [90/3] = x

- [l/10] = [x/120]
- 120 = 10x
- [120/10] = [10x/10]
- [120/10] = x

- [20 in/0.5 mm] = [x/5]
- 100 = 0.5x
- [100/0.5] = [0.5x/0.5]
- [100/0.5] = x

- [30in/0.6 mm] = [x/6 mm]
- 180 = 0.6x
- [180/0.6] = [0.6x/0.6]
- [180/0.6] = x

- [5/80] = [40/x]
- 5x = 3200
- [5x/5] = [3200/5]
- x = [3200/5]

- [7/100] = [x/2000]
- 7 ·2000 = 100x
- [14,000/1,00] = [1,00x/1,00]
- [14,000/1,00] = x

*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

### Scale Drawings

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
- Scale Drawing 0:05
- Definition of a Scale Drawing
- Example: Scale Drawings
- Extra Example 1: Scale Drawing 4:50
- Extra Example 2: Scale Drawing 7:02
- Extra Example 3: Scale Drawing 9:34

### Basic Math Online Course

### Transcription: Scale Drawings

*Welcome back to Educator.com.*0000

*For the next lesson, we are going to go over some scale drawings.*0002

*A scale drawing is an enlarged or reduced drawing that is similar to the actual object or place.*0007

*You are basically going to compare two things--the actual object or place and the drawing.*0016

*It could be something that is enlarged or can be something that is reduced.*0026

*We just went over similar figures.*0031

*It is the same concept where you are going to compare something huge and something small.*0035

*Or vice versa, something small with something big.*0044

*Again these two things are going to be similar,*0049

*meaning they are going to have the same shape but just different size.*0053

*The scale is the ratio of the two.*0057

*A lot of times for a scale drawing, we use maps.*0062

*A map is one of the main examples of a scale drawing.*0067

*If you have a map of the city that you live in, then that would be drawn to scale,*0071

*meaning every inch or so on the map is going to represent however many miles in real life, the actual place.*0077

*That is one example of a scale drawing.*0089

*If you have let's say a person and you draw a picture of that person,*0093

*but you draw it to scale meaning you are going to draw that person the same size but just on paper,*0101

*then that would also be a scale drawing because that drawing is going to represent the actual person or object.*0108

*For example, if I have a map of... go back to the map example... two cities.*0118

*Let's say this is city A; that is one city; here is another city B.*0125

*This map is going to represent the actual place, city A and city B.*0136

*If we say that from here to here on the map, let's say this is 2 inches apart.*0146

*We know that in actuality city A is not 2 inches away from city B.*0156

*But on the map, if this represents 1 inch... this is also 1 inch.*0161

*If I say that 1 inch on the map represents 10 miles in real life,*0168

*then the ratio, the scale, is going to be 1 inch on the map to 10 miles in real life.*0176

*It is going to be the ratio between the drawing and the actual place.*0187

*You are going to use that to find, let's say I ask how away is city A from city B?*0194

*On the map, since it is 2 inches, how will I know how far away it actually is in real life?*0205

*If this is a ratio, I can turn this into a fraction.*0217

*1/10, 1 to 10, that is the ratio.*0220

*Then I am going to create a proportion.*0225

*2 inches to X, that is what we are looking for.*0228

*If 1/10 equals 2/X, what does X equal?*0235

*You can either make this using this equivalent fraction,*0241

*meaning turn this into the same fraction as 1/10 to find X.*0249

*Or remember we can use cross products.*0255

*We can multiply this way, 1 times X equal to 2 times 20.*0258

*If you multiply across this way and use cross products, then 1 times X is 1X.*0263

*Equals... 2 times 10 is 20.*0271

*1X is the same thing as X; so we know that X is 20; 20 miles.*0275

*That means city A and city B, they are actually 20 miles apart from each other.*0283

*Let's go through some examples; the first example is the map.*0289

*On the map, it is 1 inch; 1 inch represents 50 miles in real life.*0296

*The ratio is 1 inch to 50 miles.*0303

*If I want to turn this into a word ratio, remember I can say that this is the map.*0309

*Then I can say that this is the place or actual.*0316

*This would be like the word ratio.*0326

*Your word ratio is in words the ratio of what is going to go on top and what is going to go on the bottom.*0328

*Again the ratio is 1 to 50.*0334

*This next part, if it is 100 miles between two cities, how many inches is it apart on the map?--the 100 miles.*0343

*Is that going to go on the top or the bottom of this next ratio?*0353

*Remember you have to keep the ratio according to the word ratio.*0356

*It is actually 100 miles.*0362

*That would be on the bottom because that is the actual place.*0363

*100 goes on the bottom.*0367

*Then the map, how many inches is it apart on the map?*0369

*The map number is going to go on the top.*0374

*That is what we are looking for; you can call that X.*0376

*Now we can solve this.*0380

*If we are going to use cross products, 50 times X is 50X.*0384

*Remember number times letter, you just put them together like that.*0390

*Equals... 1 times 100 is 100.*0393

*Here remember to solve for X.*0399

*50 times X equals 100; 50 times what equals 100?*0402

*I know that X is 2 because 50 times 2 is 100.*0406

*That is inches; X is 2 inches; on the map, it is 2 inches apart.*0412

*The next example, the scale of a drawing of king kong is 1 inch to 3 feet.*0423

*If king kong is 54 feet tall, how tall is he in the drawing?*0430

*Again we have this ratio.*0437

*We are going to say drawing of king kong over the actual height of king kong.*0440

*This is our word ratio; this is what we are going to base it on.*0449

*The drawing is 1 inch over 3 feet.*0452

*You don't have to put these here because we are not going to use that to solve.*0459

*If you want, you can just put 1/3; that is fine.*0464

*Equals... king kong is actually 54 feet tall.*0467

*That is going to go on the bottom because that is the actual; 54 feet.*0474

*How tall is he in the drawing?*0480

*That is the top number; that is X; that is what we are looking for.*0483

*Again I can use this, cross products; 1 times 54 is 54.*0488

*Equals... 3 times X, 3 times X.*0501

*You can just write that as 3X as long as you know that that represents 3 times X.*0507

*To solve for X, remember if I want to get rid of this, I select the variable, get rid of the 3 by dividing.*0513

*I can divide this by 3; then I can divide this by 3.*0522

*Here to do 54 divided by 3, put 54 the top number inside.*0529

*3 goes into 5 one time; this is 3; subtract it; you get 2.*0538

*Bring down the 4; 3 goes into 24 eight times; X is 18.*0544

*That means 3 times 18 is 54.*0554

*Since that is the top number, that is the drawing number, I know that that is in inches.*0558

*King kong is 18 inches tall in the drawing.*0563

*The third example, a toy car is made to scale with the actual car.*0576

*If the ratio of the car to the toy is 15 inches to 0.5 millimeters,*0582

*and the toy is 6 millimeters long, what would be the length of the actual car?*0591

*The ratio of the car to the toy; that means my word ratio is going to be car over the toy.*0600

*The car to the toy is 15 inches to 0.5 millimeters.*0610

*I am going to create a proportion; the toy is 6 millimeters.*0620

*That is the toy number; I am going to put that on the bottom.*0627

*What would be the length of the actual car?*0632

*That is going to go on the top, X.*0634

*Again I am going to cross multiply.*0640

*Here 0.5 times X is 0.5 times X or just 0.5X.*0647

*Equals 15 times 6; we are going to have to solve that out.*0655

*15 times 6; this is 0; 6 times 1 is 6; plus 3 is 9; this becomes 90.*0661

*Again I want to know what I have to multiply to 0.5 or 0.5 to give me 90.*0674

*Then I would have to divide 0.5.*0683

*If I make this into a fraction, this is the same thing as divide; 0.5.*0686

*Again this is 90 divided by 0.5.*0694

*I am going to do that right here; 90 divided by 0.5.*0698

*Make sure that this top number is inside the house or inside this.*0705

*To divide this, if you have a decimal on the outside, remember you have to move it to the end.*0712

*I moved it one space.*0718

*That means from here, this end of the number, since I don't see a decimal, it is always at the end.*0721

*I have to move this number one space.*0727

*Then I have to fill this space with something; that will be 0.*0732

*This is my new decimal point right here; I am going to bring that up.*0739

*Then I have 3 spaces on top right here; now I can divide.*0744

*05 is the same thing as 5; 5 goes into 9 one time.*0750

*This is 5; subtract it; I get 4; bring down the 0.*0756

*5 goes into 40 eight times; that becomes 40.*0761

*If I subtract it, I get 0; then I have to bring down this 0.*0768

*5 goes into 0 zero times; that is just 0 and 0.*0773

*My answer becomes 180; X equals 180.*0779

*0.5 times X equals 90; that means 0.5 times 180 equals 90.*0788

*Again my car then because that is the top number, my X.*0796

*That represents the car length; that is going to be in inches.*0801

*My car is 180 inches long.*0813

*That is it for this lesson; thank you for watching Educator.com.*0819

0 answers

Post by Jeanette Akers on October 23, 2012

Now I get it. I did not get it before. How easy this is. You explain things very well. Thanks.

1 answer

Last reply by: Mary Pyo

Sat Oct 29, 2011 11:08 PM

Post by Denis Ivanov on September 23, 2011

Why 15 inches were not converted to mm?