Comparing and Graphing Ratios - By Anywhere Math
Transcript
00:0-1 | Welcome to you where Math . I'm Jeff Jacobson . | |
00:01 | And today we're gonna be comparing and graphing ratios . | |
00:07 | Let's get started . Alright , for example one , | |
00:27 | we're gonna talk about one of my all time favorite | |
00:30 | afternoon snacks and that's chips and salsa . Now a | |
00:34 | lot of people can't handle spicy foods and so they | |
00:38 | usually by the mild salsa , but for me , | |
00:40 | I love spicy food , so I actually like to | |
00:43 | add extra hot sauce into the salsa . So if | |
00:47 | I'm having salsa with some friends , I'll make a | |
00:49 | batch for me and a batch for my friends . | |
00:52 | So for this we're gonna do two bowls of salsa | |
00:55 | . In the first bowl , we're gonna put five | |
00:58 | tablespoons of hot sauce with three cups of salsa . | |
01:02 | In the second bowl , we're gonna do seven tablespoons | |
01:06 | of hot sauce and four cups of salsa . Now | |
01:10 | the question is which bowl is gonna be hotter . | |
01:13 | Okay , so example one , Which mixture is harder | |
01:16 | . That's what we're trying to figure out . So | |
01:18 | basically we're comparing two different ratios we're comparing with hot | |
01:24 | sauce and salsa . So those are gonna be my | |
01:27 | two rows . So again bowl one we had five | |
01:30 | tablespoons of hot sauce for every three cups of salsa | |
01:36 | . Okay now over here I'm gonna write bowl too | |
01:42 | . And that again I'm gonna have my I'll just | |
01:46 | call it hs hot sauce . And my salsa . | |
01:50 | And this one again was seven tablespoons of hot sauce | |
01:54 | for every four cups of salsa . Now to be | |
02:00 | able to compare these uh it helps to be able | |
02:05 | to compare having the same quantity . I can't compare | |
02:09 | which one is harder because this has only three cups | |
02:13 | of salsa but this has four cups of salsa . | |
02:15 | So yeah we have more hot sauce but there's also | |
02:18 | more salsa to kind of absorb all that hot sauce | |
02:22 | . Right ? So I want to compare with the | |
02:24 | same amount of salsa in each and then see which | |
02:28 | one has more hot sauce . And now tell me | |
02:30 | which one's hotter . So , if I'm looking at | |
02:33 | three and four , well , what's the least common | |
02:39 | multiple of three and four ? Well , hopefully you | |
02:41 | realize 12 , 12 would be my least common multiple | |
02:45 | of three and four . So that's where I want | |
02:49 | to go for both of those . Really . I | |
02:52 | want both of them at 12 . So , I | |
02:53 | can compare Well , to get from 3 to 12 | |
02:58 | . I just times four . So 4 hot sauce | |
03:02 | . I'm gonna do the same thing . I'm going | |
03:03 | times that by four to make it equivalent . Right | |
03:06 | ? I want equivalent ratios five times four gives me | |
03:10 | 20 tablespoons of hot sauce in this mixture with 12 | |
03:15 | cups of salsa . Now over here , bull to | |
03:18 | how do I get from four cups of salsa to | |
03:21 | 12 cups . The easiest way is times three . | |
03:25 | So for my hot sauce , I'm gonna triple The | |
03:29 | amount of hot sauce seven times 3 is 21 tablespoons | |
03:34 | of hot sauce . Now that they both have the | |
03:38 | same amount of cups of salsa . I can compare | |
03:42 | which one is hotter . 20 tablespoons of hot sauce | |
03:47 | in bo one but 21 tablespoons of hot sauce in | |
03:52 | bold to that one extra tablespoon of hot sauce means | |
03:56 | bold to is the hotter mixture . Bull to . | |
04:04 | Let's try another example . Okay , example to which | |
04:07 | bag of dog food is the better buy . So | |
04:10 | if we look over here , we see two different | |
04:12 | amounts of dog food for two different prices , we | |
04:16 | have to see which one is the better buy . | |
04:19 | So we have a £20 bag of dog food for | |
04:23 | $17.20 . We also have a £30 bag for $25.20 | |
04:30 | . Now obviously the £30 bag is more is going | |
04:33 | to be more expensive but that doesn't necessarily mean it's | |
04:37 | the better by now to compare them . We're gonna | |
04:40 | do the same thing . Let's make a ratio table | |
04:42 | . This is the same thing as before . I've | |
04:45 | got two different amounts . I can't compare which one | |
04:48 | is the better buy unless I'm comparing the same amount | |
04:53 | . So one thing I could do is I could | |
04:55 | find just like we did before the least common multiple | |
04:59 | which in this case would be 60 . But I'm | |
05:02 | not gonna do it that way . Instead I'm going | |
05:05 | to compare their unit rates . So I want to | |
05:08 | get to one . What does it cost for just | |
05:11 | £1 of dog food for each bag ? So to | |
05:15 | do that from 20 to 1 . Well I'm divided | |
05:19 | by 20 . So here I also want to divide | |
05:22 | by 20 , so that cost 86 cents per pound | |
05:30 | from 30 to 1 . I need to divide by | |
05:33 | 30 . So I'm going to divide by 30 year | |
05:38 | . I want to make sure I'm keeping an equivalent | |
05:43 | equivalent rates here . I've heard so much . So | |
05:48 | that 0.84 or 84 cents per pound . Sorry about | |
05:56 | that . Any first cents per pound here . Well | |
06:00 | , now that we're comparing both as unit rates , | |
06:03 | how much it costs per pound . You can see | |
06:06 | that the better by is obviously going to be the | |
06:09 | £30 bag and it's actually two cents cheaper per pound | |
06:15 | . Okay , here's some to try on your own | |
06:22 | . Okay , example , three hot air balloon rises | |
06:25 | nine m every three seconds . A blimp rises seven | |
06:30 | m every two seconds , which rises faster . Use | |
06:35 | the ratio table to compare . So , let's see | |
06:37 | . Let's just continue . So every three seconds we're | |
06:40 | adding another nine m . So next would be six | |
06:43 | seconds . Is that 18 m ? nine seconds would | |
06:48 | be at 27 m . uh 12 seconds would be | |
06:53 | at 36 m and I'll stop there . Um Next | |
06:59 | four seconds Would be at 14 m . Six seconds | |
07:07 | would be at 21 m , I'll go . Another | |
07:09 | 1.8 seconds would be at uh 20 eight m . | |
07:16 | So with this , hopefully you can see that there | |
07:18 | is a time . That is the same in both | |
07:23 | . Okay , I'll just circle here at six seconds | |
07:30 | . The balloon was 18 m high Here at six | |
07:34 | seconds . The blimp was 20 m high . So | |
07:42 | the question is , which rises faster ? Well , | |
07:46 | given the same amount of time , the blimp is | |
07:49 | higher up . So that would mean the blimp Rises | |
07:54 | faster . That was part eight . Now , let's | |
07:56 | try part B . All right , here's our last | |
07:58 | example . So part B . Same example , three | |
08:01 | graft the ordered pairs the time and then the height | |
08:05 | from part A . That we already did . Uh | |
08:07 | And what can you conclude if we think about an | |
08:10 | ordered pair . Time is going to represent my X | |
08:13 | coordinate . That's going to go along my X . | |
08:15 | Axis time . And then height is gonna be my | |
08:18 | Y coordinate . Uh Here is my coordinate plane . | |
08:23 | I need to label it . So like I said | |
08:25 | , my X axis is going to be time reliable | |
08:29 | that here , time and most of the time . | |
08:32 | Most of the time anytime you have time , it | |
08:35 | does tend to go on your X . Axis . | |
08:37 | Uh my Y . Axis . I'm gonna label as | |
08:40 | height just like that . And again , time . | |
08:45 | I should also add that in seconds . Height is | |
08:50 | in . Let's see what was it meters ? So | |
08:53 | now we've got to think , well what do I | |
08:55 | want to be counting by the second was pretty simple | |
08:59 | . I think we can easily just count by one | |
09:02 | . Now , the height is a little trickier if | |
09:04 | you remember we were going nine m every three seconds | |
09:09 | And the blimp was I think seven m every two | |
09:13 | seconds . So that was kind of jumping quite a | |
09:15 | lot . Maybe we'll go by 4s instead just because | |
09:19 | it's gonna take us a while if we went just | |
09:21 | by once . Now let's graph it . Uh both | |
09:27 | of these are going to start at 00 Right ? | |
09:29 | When you think about it , zero time happens there | |
09:32 | on the ground , right ? They haven't gone anywhere | |
09:34 | in the area . So they're both gonna start at | |
09:36 | 00 I'm going to have two lines , one for | |
09:39 | the for the hot air balloon and one for the | |
09:41 | blimp . So , I would suggest using two different | |
09:44 | colors . Let's do the hot air balloon first . | |
09:46 | So again , every three seconds it was climbing nine | |
09:50 | m , right ? Three seconds nine years . So | |
09:53 | we're starting at 00 that's here . three seconds . | |
09:57 | It was at nine m . Okay , I can | |
10:01 | label that . That's at 3 9 . The next | |
10:05 | one again , six seconds is gonna be at 18 | |
10:09 | , 6 , 18 . Whatever you do , whatever | |
10:14 | you like . Just pretend that's a straight line . | |
10:19 | I'm gonna have a key right here . The black | |
10:24 | is the hot air balloon Next with the blue . | |
10:32 | We're gonna do the blimp and the blimp every two | |
10:36 | seconds rose seven m . So two seconds again , | |
10:40 | we're starting here . 00 two seconds went up to | |
10:44 | seven and that's gonna be 2 7 p . A | |
10:55 | . Blue was the blunt . There's our graph , | |
11:04 | the question . What can you conclude ? Well , | |
11:07 | we can conclude that because this blue line , the | |
11:10 | line for the blimp is steeper . That's the slope | |
11:14 | . We're talking about . The slope . You'll figure | |
11:15 | that out later , but it's deeper . That means | |
11:18 | the blimp rises faster than the hot air balloon , | |
11:22 | which is exactly what we talked about in part a | |
11:26 | here's one more to try on your own as always | |
11:33 | , Thank you so much for watching , and if | |
11:34 | you like this video , please subscribe . |
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