E38: FTCE | General Knowledge | Mathematics | Ratios and Proportions

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Welcome to episode 38 of FTCE seminar, a teacher certification podcast. I'm your host Mercedes Musto. Today we'll be talking about some mathematical concepts that help you prepare for the FTCE general knowledge mathematics subtest. More math. That's right.

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And today we're going to dive into the world of ratios and proportions. Aren't proportions and ratios kind of like the same thing? No. Hey, yeah, keep listening because we've got some concepts to cover. Okay, let's get started. Concept number one, ratios, and concept number two, proportions. Ratios and proportions are cool concepts in mathematics that we can apply to like cooking recipes or for constructing scaled models of buildings.

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The funny thing is that on the FCC practice test, you might see a math problem about the height of a building and the length of a shadow casted by a nearby statue. I know it sounds silly, but more on that later. Ratios, definition. A ratio is a comparison of two quantities. For example, if we have a bowl containing three red apples and four green apples,

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the ratio of red apples to green apples is three to four. But how do we write that mathematically? Ratios often are expressed in colon form, such as three colon four, or in fraction form, which would be three over four. Explanation, we have three red apples for every four green apples. Hmm, I love apples.

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Okay, wait, wait, where were we? Ah, yes, proportions, proportions, definition. Now that we understand ratios, we can explain proportions because basically proportions involve two ratios that equal each other.

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What?

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Okay, okay, get this. If we have two bowls with the same ratio of red to green apples, say three to four, then they are in proportion. And we would express this in a fraction form, meaning three over four is equal to three over four, signifying bowl one is equal to bowl two. Why is this important?

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Let's try an example. Let's apply our knowledge of ratios and proportions to ingredients to a real world problem like cooking. Let's say you have a recipe that serves four people, but you're cooking for eight people. So you've got to double the recipe, right? Well, I mean, how do I do that? You can use proportions to scale up the ingredients. Okay. Like this.

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If the original recipe calls for two cups of flour to serve four people, that's two cups to four people. The question we're asking ourselves is how many cups for eight people? We don't know yet, so we'll let x equal the unknown amount of cups and 8 equal the total amount of people. Therefore, set up a proportion using the fraction form 2 over 4 equals x over 8. That's 2 over 4 equals x over 8. Solving for x, you will cross multiply. That looks like

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this. Four times x equals two times eight. This simplifies to 4x equals 16. Next, solve for our unknown x by dividing both sides by four and you're gonna get x equals x equals four. Therefore you'll need four cups of flour to double the recipe. Now, there are a few different ways to set that up, but what we did was keep it equal by having the cups to people equals the cups to people proportion

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when we're solving for our unknown. I know, I know, stay with me now. You seem a little unsure. So let's try the example I was talking about earlier with the building and the statue from the FTCE mathematics practice test. The problem states, a building 51 feet tall casts a shadow 48 feet long.

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Simultaneously, a nearby statue casts a shadow of 16 feet. How tall is this statue?

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What?

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Where do I even start? Wait, wait, wait, I know. We can set this up using a proportion. So we have a building that is 51 feet tall with a 48 foot shadow. I'm gonna go ahead and set up this ratio as 51 to 48 using the fraction form 51 over 48. Next, I have a statue that is, I don't know how tall

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and a shadow of 16 feet. Well, what do I do with the unknown? Hmm, yes, that's right. I assign it as X. Now that I can set up this ratio as X to 16 or in the fraction form X over 16. Let's set up these two ratios using a proportion to solve the height of the statue.

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This is gonna look like the building height over shadow length equals statue height of X over statue length. The numbers for this are 51 over 48 equals X over 16. 51 over 48 equals X over 16. Solving for X, you will cross multiply. 48 times X equals 51 times 16. This simplifies to 48x equals 816. Next, solve for our unknown x by dividing both sides by 48 and you get x equals 17. Therefore, the height of

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the statue is 17 feet. Basically, the statue is 17 feet tall. Wow, that's really really well done. It's not as hard as I thought. Let's review. Remember that a ratio is a comparison of two quantities and ratios are often expressed in colon form, such as three colon four, or in fraction form, which would be three over four. Next, proportions involve two ratios

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that are equal to each other. We set up proportions using two equal ratios when we were solving for an unknown quantity, you know, like such as height. Being able to identify and understand when to use the ratio and proportions to solve problems will definitely help you on the FTCE Mathematics Subtest. For more practice with math concepts, visit ftceseminar.com to study for the test. The important thing is to start studying and start studying today so you can pass the teacher certification exam. Well, what are you waiting for? Check us out on YouTube at FTCE Seminar and start studying today.

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This podcast was recorded at the Pickens Multimedia Studio at the University of West Florida. This podcast is listener supported. Contributions can be made via the listener support link on Spotify or hey, you can buy me a coffee at ftceseminar.com. This is your host, Mercedes Musto. Join me again on FTCE Seminar, a teacher certification podcast, a teacher certification podcast, so you can pass the FTCE.

Transcribed with Cockatoo