Comparing and Graphing Ratios - Free Educational videos for Students in K-12 | Lumos Learning

Comparing and Graphing Ratios - Free Educational videos for Students in k-12


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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