# Math Antics – Ratios And Rates

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“Welcome to math antics in this lesson. We re gonna learn about ratios. Well what what in the world is a ratio well let s look it up in a book to find out it says here that a ratio is a comparison of two numbers by division well that s true. But it s also a little confusing.

It s confusing because most of us think of comparing numbers as trying to decide if a number is greater that less than or equal to another number. But with ratios. We re not trying to compare numbers like that instead we re really trying to see how two numbers relate to each other and so at math antics. We.

Like to think of ratios as a relationship between two numbers by division okay. But how do you compare or show. How two numbers are related by division well to see what the by division part really means let s look at an example of a ratio uh excuse me that s not a ratio that s a fraction oh it s a ratio alright mathematically ratios and fractions are basically the same thing. It s just that when we use a fraction in a particular way we call it a ratio well sure everybody knows that well like i was saying ratios are basically just like fractions.

The difference is how we use them to describe things in the real world to see what i mean let s look at examples of how we could use the fraction 1 over 2 and the ratio 1 over 2 mathematically. These are both the same thing they re just the division problem. 1 divided by 2. But in the case of the fraction.

We usually treat it as if it s just a single number for example at lunch time you might eat 1 sandwich. Or if you re really hungry you might eat 2 sandwiches. But if your not very hungry you might just have 1 2 sandwich. We can use the fraction 1 2.

Just like we use 1 or 2. To show how many sandwiches you eat. It s just that in the case of 1 2. We know that it s only part of a sandwich just a fraction of one now.

Let s see how we can use the ratio.. 1 over 2 with a ratio. We don t treat it as if it s just a single number instead we pay close attention to the top and bottom numbers. Because we use them to refer to different things for example. Let s say we re planning to go on a picnic and for every two people that are going on the picnic.

We re only bringing 1 sandwich. In that case we d say that the ratio of sandwiches to people is 1 to 2 or 1 sandwich. Per 2. People do you see the difference between our fraction and our ratio.

The math part of each of them is the same but with the fraction both the top and bottom numbers are referring to the same thing. The sandwich however with the ratio. The top and bottom numbers are referring to different things sandwiches and people the fraction shows a part of something. But the ratio shows a relationship or a comparison between two different things.

And you can see that they re the same mathematically because if you did have the ratio of 1 sandwich. Per. Every 2 people on a picnic. Guess how much of a sandwich each person would get yep half a sandwich alright.

So now you know that fractions and ratios are basically the same thing. But since they re used differently in math sometimes they re also shown differently once in a while instead of seeing the standard division. Form. A ratio might be represented with this symbol.

When you see a ratio written this way it just means 1 to 2 or 1 per 2. . For example. In this picture.

You could say the ratio of dogs to cats is 3 to 2 3 dogs.. To 2 cats and you could also write it in the standard division form. 3. Dogs over 2 cats they re just different ways to write the same ratio ratios are used all the time to represent all sorts of things in real world. Situations.

So let s see a few more examples to help you really understand what ratios are have you ever wanted to compare apples to oranges. But someone told you you couldn t well you can with a ratio. Let s say a fruit stand sells 5 apples for ever. 3 oranges.

They sell the ratio of apples to oranges would be 5 to 3 or have you ever helped someone bake cookies the recipe might tell you that for every 2 cups of flour you need 1 cup of sugar that means that the ratio of flour to sugar is 2 to 1 or. What about your tv screen or your computer monitor have you ever hear someone say that the size or aspect ratio is 16 to 9 16 to. 9. Is the ratio of the screen s width to its height.

So if the screen is 16 inches. Wide. Then its height would be 9 inches. Tall.

Ah. Here s another good ratio. That you might use in your car. 40.

Miles per hour. Ah ha. Didn t you said that a ratio was a relationship between two numbers. But 40 miles per hour is just one number looks like someone s got some explainin to do actually there are two numbers do you remember how any number can be written like a fraction just by writing 1 as the bottom number well 40 miles per hour is the ratio 40 miles per.

One hour well.. I guess you have an answer for everything don t you 40 miles per 1 hour. Is a type of ratio that we call a rate. A rate is just a ratio that usually involves a period of time here are some common examples of rates 10 meters per second 12 per hour 3 meals per day 50 games per year notice that the bottom numbers in each of these ratios relate to a period of time seconds hours days years. And that s why we call them a rate alright.

So that s simple enough. But you might be wondering why are the bottom numbers of all these rates 1 couldn t you have a rate like 90 meters per 9 seconds. Or 60 per 5 hours. We sure could but most of the time when we have rates like that we want to convert them into an equivalent rate that has 1 as the bottom number that s because whenever the bottom.

Number represents. Only one unit of time like one hour or one day it makes comparing different rates much easier for example imagine two cars driving at two different rates. The first car s rate. Is 120 miles per 3.

Hours. And the second car s rate. Is 150 miles per 5. Hours.

Which car is going faster. Well. It s not all that easy to tell when the rates have different bottom numbers. Fortunately it s really easy to change a rate.

So that it has 1 as the bottom number all you have to do is divide the top number by the bottom. Number the answer you get is the top number of the new equivalent rate and the bottom number is just 1 rates like. This are called unit rate because. Unit means one alright.

Let s convert the rates of speed for our two cars into unit.. Rates. So that we can compare them easily. The first car s rate. Was 120 miles per 3.

Hours. So if we take 120 and divide. It by 3. We get 40 that means that the unit rate for the first car is 40 miles per hour.

The second car s rate was 150 miles per 5. Hours. So if we divide 150 by 5. We get 30.

So the unit rate for the second car is 30 miles per hour. And now you can easily tell that the first car is going faster and you can tell why unit rates are so helpful okay. So that s it for this lesson. We ve learned that a ratio is basically just like a fraction.

But instead of showing what part of something you have it shows the relationship between two different things. We also learned that when one of those two things is time we call the ratio a rate and last of all we learned how to convert a rate into a unit rate for easy comparison. As always thanks for watching math antics and i ll see ya next time. ” .

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