Basic Math 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