WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to go over some scale drawings.
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A scale drawing is an enlarged or reduced drawing that is similar to the actual object or place.
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You are basically going to compare two things--the actual object or place and the drawing.
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It could be something that is enlarged or can be something that is reduced.
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We just went over similar figures.
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It is the same concept where you are going to compare something huge and something small.
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Or vice versa, something small with something big.
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Again these two things are going to be similar,
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meaning they are going to have the same shape but just different size.
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The scale is the ratio of the two.
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A lot of times for a scale drawing, we use maps.
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A map is one of the main examples of a scale drawing.
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If you have a map of the city that you live in, then that would be drawn to scale,
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meaning every inch or so on the map is going to represent however many miles in real life, the actual place.
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That is one example of a scale drawing.
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If you have let's say a person and you draw a picture of that person,
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but you draw it to scale meaning you are going to draw that person the same size but just on paper,
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then that would also be a scale drawing because that drawing is going to represent the actual person or object.
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For example, if I have a map of... go back to the map example... two cities.
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Let's say this is city A; that is one city; here is another city B.
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This map is going to represent the actual place, city A and city B.
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If we say that from here to here on the map, let's say this is 2 inches apart.
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We know that in actuality city A is not 2 inches away from city B.
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But on the map, if this represents 1 inch... this is also 1 inch.
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If I say that 1 inch on the map represents 10 miles in real life,
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then the ratio, the scale, is going to be 1 inch on the map to 10 miles in real life.
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It is going to be the ratio between the drawing and the actual place.
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You are going to use that to find, let's say I ask how away is city A from city B?
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On the map, since it is 2 inches, how will I know how far away it actually is in real life?
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If this is a ratio, I can turn this into a fraction.
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1/10, 1 to 10, that is the ratio.
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Then I am going to create a proportion.
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2 inches to X, that is what we are looking for.
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If 1/10 equals 2/X, what does X equal?
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You can either make this using this equivalent fraction,
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meaning turn this into the same fraction as 1/10 to find X.
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Or remember we can use cross products.
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We can multiply this way, 1 times X equal to 2 times 20.
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If you multiply across this way and use cross products, then 1 times X is 1X.
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Equals... 2 times 10 is 20.
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1X is the same thing as X; so we know that X is 20; 20 miles.
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That means city A and city B, they are actually 20 miles apart from each other.
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Let's go through some examples; the first example is the map.
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On the map, it is 1 inch; 1 inch represents 50 miles in real life.
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The ratio is 1 inch to 50 miles.
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If I want to turn this into a word ratio, remember I can say that this is the map.
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Then I can say that this is the place or actual.
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This would be like the word ratio.
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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.
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Again the ratio is 1 to 50.
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This next part, if it is 100 miles between two cities, how many inches is it apart on the map?--the 100 miles.
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Is that going to go on the top or the bottom of this next ratio?
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Remember you have to keep the ratio according to the word ratio.
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It is actually 100 miles.
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That would be on the bottom because that is the actual place.
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100 goes on the bottom.
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Then the map, how many inches is it apart on the map?
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The map number is going to go on the top.
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That is what we are looking for; you can call that X.
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Now we can solve this.
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If we are going to use cross products, 50 times X is 50X.
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Remember number times letter, you just put them together like that.
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Equals... 1 times 100 is 100.
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Here remember to solve for X.
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50 times X equals 100; 50 times what equals 100?
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I know that X is 2 because 50 times 2 is 100.
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That is inches; X is 2 inches; on the map, it is 2 inches apart.
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The next example, the scale of a drawing of king kong is 1 inch to 3 feet.
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If king kong is 54 feet tall, how tall is he in the drawing?
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Again we have this ratio.
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We are going to say drawing of king kong over the actual height of king kong.
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This is our word ratio; this is what we are going to base it on.
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The drawing is 1 inch over 3 feet.
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You don't have to put these here because we are not going to use that to solve.
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If you want, you can just put 1/3; that is fine.
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Equals... king kong is actually 54 feet tall.
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That is going to go on the bottom because that is the actual; 54 feet.
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How tall is he in the drawing?
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That is the top number; that is X; that is what we are looking for.
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Again I can use this, cross products; 1 times 54 is 54.
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Equals... 3 times X, 3 times X.
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You can just write that as 3X as long as you know that that represents 3 times X.
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To solve for X, remember if I want to get rid of this, I select the variable, get rid of the 3 by dividing.
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I can divide this by 3; then I can divide this by 3.
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Here to do 54 divided by 3, put 54 the top number inside.
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3 goes into 5 one time; this is 3; subtract it; you get 2.
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Bring down the 4; 3 goes into 24 eight times; X is 18.
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That means 3 times 18 is 54.
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Since that is the top number, that is the drawing number, I know that that is in inches.
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King kong is 18 inches tall in the drawing.
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The third example, a toy car is made to scale with the actual car.
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If the ratio of the car to the toy is 15 inches to 0.5 millimeters,
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and the toy is 6 millimeters long, what would be the length of the actual car?
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The ratio of the car to the toy; that means my word ratio is going to be car over the toy.
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The car to the toy is 15 inches to 0.5 millimeters.
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I am going to create a proportion; the toy is 6 millimeters.
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That is the toy number; I am going to put that on the bottom.
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What would be the length of the actual car?
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That is going to go on the top, X.
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Again I am going to cross multiply.
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Here 0.5 times X is 0.5 times X or just 0.5X.
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Equals 15 times 6; we are going to have to solve that out.
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15 times 6; this is 0; 6 times 1 is 6; plus 3 is 9; this becomes 90.
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Again I want to know what I have to multiply to 0.5 or 0.5 to give me 90.
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Then I would have to divide 0.5.
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If I make this into a fraction, this is the same thing as divide; 0.5.
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Again this is 90 divided by 0.5.
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I am going to do that right here; 90 divided by 0.5.
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Make sure that this top number is inside the house or inside this.
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To divide this, if you have a decimal on the outside, remember you have to move it to the end.
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I moved it one space.
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That means from here, this end of the number, since I don't see a decimal, it is always at the end.
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I have to move this number one space.
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Then I have to fill this space with something; that will be 0.
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This is my new decimal point right here; I am going to bring that up.
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Then I have 3 spaces on top right here; now I can divide.
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05 is the same thing as 5; 5 goes into 9 one time.
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This is 5; subtract it; I get 4; bring down the 0.
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5 goes into 40 eight times; that becomes 40.
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If I subtract it, I get 0; then I have to bring down this 0.
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5 goes into 0 zero times; that is just 0 and 0.
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My answer becomes 180; X equals 180.
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0.5 times X equals 90; that means 0.5 times 180 equals 90.
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Again my car then because that is the top number, my X.
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That represents the car length; that is going to be in inches.
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My car is 180 inches long.
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That is it for this lesson; thank you for watching Educator.com.