Math Antics - Ratios And Rates - By Mathantics
Transcript
00:03 | Uh huh . Hi , welcome to Math Antics . | |
00:08 | In this lesson we're going to learn about ratios what | |
00:11 | the world's ratio . Well let's look it up in | |
00:13 | a math book to find out . It says here | |
00:17 | that a ratio is a comparison of two numbers by | |
00:20 | division . Well that's true but it's also a little | |
00:24 | confusing and it's confusing because most of us think of | |
00:28 | comparing numbers is trying to decide if a number is | |
00:31 | greater than less than or equal to another number . | |
00:34 | But with ratios were not trying to compare numbers like | |
00:37 | that . Instead we're really trying to see how to | |
00:41 | numbers relate to each other . And so at Math | |
00:43 | Antics we like to think of ratios as a relationship | |
00:47 | between two numbers by division . Okay , but how | |
00:50 | do you compare or show how to numbers are related | |
00:53 | by division ? Well , to see what the by | |
00:56 | division part really means . Let's look at an example | |
00:59 | of a ratio . Excuse me . That's not a | |
01:04 | ratio . That's a fraction . Oh it's a ratio | |
01:08 | . Alright . Mathematically , ratios and fractions are basically | |
01:12 | the same thing . It's just that when we use | |
01:14 | a fraction in a particular way , we call it | |
01:17 | a ratio . Well , sure everybody knows that . | |
01:21 | Well . Like I was saying , ratios are basically | |
01:24 | just like fractions . The difference is how we use | |
01:27 | them to describe things in the real world to see | |
01:31 | what I mean . Let's look at examples of how | |
01:33 | we could use the fraction 1/2 and the ratio 1/2 | |
01:37 | . Mathematically , these are both the same thing . | |
01:40 | They're just the division problem , one divided by two | |
01:44 | . But in the case of the fraction , we | |
01:45 | usually treat it as if it's just a single number | |
01:48 | . For example , at lunchtime you might eat one | |
01:51 | sandwich or if you're really hungry you might eat two | |
01:54 | sandwiches . But if you're not very hungry you might | |
01:56 | just have half a sandwich . We can use the | |
02:01 | fraction one half just like we use one or two | |
02:04 | to show how many sandwiches you eat . It's just | |
02:06 | that in the case of one half , we know | |
02:08 | that it's only part of a sandwich . Just a | |
02:10 | fraction of one . Mhm . Now let's see how | |
02:13 | we can use the ratio 1/2 with the ratio we | |
02:16 | don't treat it as if it's just a single number | |
02:19 | . Instead we pay close attention to the top and | |
02:22 | bottom numbers because we use them to refer to different | |
02:25 | things . For example , let's say we're planning to | |
02:28 | go on a picnic and for every two people that | |
02:31 | are going on the picnic , we're only bringing one | |
02:34 | sandwich . In that case we would say that the | |
02:36 | ratio of sandwiches to people is 1-2 or one sandwich | |
02:42 | for two people . Do you see the difference between | |
02:45 | our fraction and our ratio ? The math part of | |
02:48 | each of them is the same but with a fraction | |
02:51 | , both the top and bottom numbers are referring to | |
02:54 | the same thing the sandwich , however , with the | |
02:57 | ratio the top and bottom numbers are referring to different | |
03:00 | things , sandwiches and people . The fraction shows a | |
03:05 | part of something but the ratio shows a relationship or | |
03:09 | a comparison between two different things . And you can | |
03:13 | see that they're the same thing mathematically because if you | |
03:16 | did have the ratio of one sandwich for every two | |
03:19 | people on a picnic , guess how much of a | |
03:21 | sandwich each person would get , yep , half a | |
03:25 | sandwich . Mhm . All right . So now , | |
03:30 | you know that fractions and ratios are basically the same | |
03:33 | thing but since they're used differently in math sometimes are | |
03:37 | also showing differently once in awhile . Instead of seeing | |
03:40 | , the standard division form ratio might be represented with | |
03:44 | this symbol . When you see a ratio written this | |
03:46 | way , it just means 1-2 or one per two | |
03:51 | . For example , in this picture , you can | |
03:54 | say that the ratio of dogs two cats is 3-2 | |
03:58 | , three dogs , 2 two cats . And you | |
04:01 | can also write it in the standard division form three | |
04:03 | dogs over two cats . They're just different ways to | |
04:07 | write the same ratio ratios are used all the time | |
04:11 | to represent all sorts of things in real world situations | |
04:15 | . So let's see a few more examples to help | |
04:17 | you really understand what ratios are . Have you ever | |
04:21 | wanted to compare apples to oranges ? But someone told | |
04:24 | you you couldn't ? Well you can with a ratio | |
04:27 | . Now let's say a fruit stand sells five apples | |
04:29 | for every three oranges . They sell the ratio of | |
04:32 | apples to oranges would be 5-3 . Or have you | |
04:36 | ever helped someone big cookies ? The recipe might tell | |
04:39 | you that for every two cups of flour you need | |
04:42 | one cup of sugar . That means that the ratio | |
04:44 | of flour to sugar is 2-1 . Or what about | |
04:49 | your T . V . Screen or your computer monitor | |
04:51 | ? Have you ever heard someone say that the size | |
04:54 | or aspect ratio is 16-9 . 16 - nine is | |
04:59 | the ratio of the screen's width to its height . | |
05:02 | So if the screen is 16 wide then its height | |
05:06 | would be nine taller . Uh Here's another good ratio | |
05:10 | that you might use in your car . 40 mph | |
05:13 | . Ha ha didn't you say that a ratio was | |
05:17 | a relationship between two numbers ? But 40 MPH is | |
05:20 | just one number . Looks like someone's got some explaining | |
05:24 | to do . Actually there are two numbers . Do | |
05:28 | you remember how any number can be written like a | |
05:30 | fraction just by writing one as the bottom number ? | |
05:33 | Well 40 mph is the ratio 40 miles per one | |
05:37 | hour . Well I guess you have an answer for | |
05:40 | everything , don't you ? 40 mph is a type | |
05:45 | of ratio that we call a rate . A rate | |
05:47 | is just ratio that usually involves a period of time | |
05:52 | . Here are some common examples of rates 10 , | |
05:56 | m/s $12 per hour , three Meals per day . | |
06:00 | 50 games per year notice that the bottom numbers and | |
06:04 | each of these ratios relate to a period of time | |
06:08 | , seconds , hours , days , years . And | |
06:11 | that's why we call them a rate . All right | |
06:14 | . So that's simple enough . But you might be | |
06:17 | wondering Why are the bottom numbers of all these rates | |
06:20 | one Couldn't you ever rate like 90 m per nine | |
06:24 | seconds or $60 per five hours ? We sure could | |
06:29 | . But most of the time when we have rates | |
06:31 | like that , we want to convert them into an | |
06:33 | equivalent rate that has one as the bottom number . | |
06:37 | And that's because whenever the bottom number represents only one | |
06:40 | unit of time , like one hour or one day | |
06:44 | it makes comparing different rates much easier . For example | |
06:49 | , imagine two cars driving at two different rates . | |
06:52 | The first cars rate is 120 mph three hours And | |
06:57 | the second cars rate is 150 miles per five hours | |
07:01 | . Which car is going faster ? Well , it's | |
07:04 | not all that easy to tell when the rates have | |
07:06 | different bottom numbers . Fortunately it's really easy to change | |
07:11 | a rate so that has one as the bottom number | |
07:14 | . All you have to do is divide the top | |
07:16 | number by the bottom number . The answer you get | |
07:20 | is the top number of the new equivalent rate . | |
07:23 | And the bottom number is just one Rates like this | |
07:27 | are called unit rates because unit means one . All | |
07:32 | right , let's convert the rates of speed for our | |
07:34 | two cars into unit rates so that we can compare | |
07:37 | them easily . The first cars rate was 120 mph | |
07:42 | three hours . So if we take 120 and divide | |
07:46 | it by three , we get 40 . That means | |
07:48 | that the unit rate for the first car is 40 | |
07:52 | mph . The second cars rate was 150 miles per | |
07:56 | five hours . So if we divide 150 x five | |
08:01 | , we get 30 . So the unit rate for | |
08:04 | the second car is 30 mph . And now you | |
08:08 | can easily tell that the first car is going faster | |
08:12 | and you can tell why unit rates are so helpful | |
08:15 | . Okay , so that's it for this lesson . | |
08:18 | We've learned that a ratio is basically just like a | |
08:21 | fraction , but instead of showing what part of something | |
08:25 | you have , it shows the relationship between two different | |
08:28 | things . We also learned that when one of those | |
08:32 | two things is time we call the ratio or rate | |
08:35 | . And last of all , we learned how to | |
08:37 | convert a rate into a unit rate for easy comparison | |
08:40 | as always . Thanks for watching Math Antics and I'll | |
08:43 | see you next time learn more at Math Antics dot | |
08:48 | com . |
Summarizer
DESCRIPTION:
OVERVIEW:
Math Antics - Ratios And Rates is a free educational video by Mathantics.
This page not only allows students and teachers view Math Antics - Ratios And Rates videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.