Percent, Ratios, and Rates using the box method - By tecmath
Transcript
| 00:0-1 | Good day . Welcome to Tech Math channel . What | |
| 00:01 | we're going to be having a look at in this | |
| 00:02 | video is a method of working out a whole bunch | |
| 00:06 | of things , ratios , rates , percentages , currency | |
| 00:08 | conversions . It's called the box method . So I'll | |
| 00:11 | show you how to do this . I think I've | |
| 00:13 | just looked straight into an example . All right . | |
| 00:15 | The first question , $6 is equal to $4.50 us | |
| 00:19 | . How many us dollars would I get for ? | |
| 00:21 | $25 . So the way that we do this method | |
| 00:25 | is we draw up a box and Tsarnaev the box | |
| 00:28 | method . Okay . And We break it up into | |
| 00:32 | four like this . All right . The first thing | |
| 00:35 | we do is we're just going to start putting in | |
| 00:37 | our values here . So this is $6 and for | |
| 00:41 | this we're going to get $4.50 us lighting this up | |
| 00:49 | . We're after To find out what for $25 . | |
| 00:52 | So I'm keeping the Australian dollars in a line here | |
| 00:55 | and I want to know what I'm going to get | |
| 00:57 | in U . S . Dollars . Okay or not | |
| 00:59 | . These us dollars are this is the unknown . | |
| 01:01 | Now it's fairly simple . What we do now , | |
| 01:03 | what we're gonna do is going to multiply these diagonals | |
| 01:06 | here , the ones that are filled in . So | |
| 01:08 | we're gonna multiply those and divide by the other one | |
| 01:11 | . So we're going to multiply these guys . All | |
| 01:14 | right , this is 25 times 4 50 and then | |
| 01:20 | we divide by this one . Okay , divided by | |
| 01:26 | six . And the nss pattern repeated a fair bit | |
| 01:29 | . So when we do this , $4.50 times 25 | |
| 01:33 | is 100 and 12 $50 , divided by six . | |
| 01:37 | This is 1875 . US . dollars . And that's | |
| 01:41 | how this method works . It's fairly simple and it | |
| 01:44 | works for a whole variety of things . Let me | |
| 01:46 | show you another one . Okay for the next question | |
| 01:49 | , 85% of what number is 34 ? Or you | |
| 01:52 | get 85% for a test ? 34 questions correct ? | |
| 01:55 | How many questions on the test ? So when you | |
| 01:57 | look at this you might think , Okay , here | |
| 02:00 | is 85 out of how much percent out of 100 | |
| 02:05 | ? Yeah , This is 85 over 100 . And | |
| 02:08 | we want to know he's here . 34 out of | |
| 02:14 | how many ? Okay , so with this , the | |
| 02:18 | first thing we do is we draw up our box | |
| 02:20 | here . All right , so what do we have | |
| 02:26 | here ? We have 85 out of 100 And I | |
| 02:34 | would know at 34 out of how many years . | |
| 02:37 | Okay , so this is the one laughter . So | |
| 02:39 | what do we do ? First off , what you | |
| 02:41 | remember is you might remember we multiplied the diagonals , | |
| 02:44 | so 34 times , 100 Which is 3400 . And | |
| 02:51 | then we divide by this one here , so once | |
| 02:54 | again multiplied by these , divide by this , so | |
| 02:58 | this Divided by 85 . How many questions are on | |
| 03:03 | the test ? There were 40 so that's another example | |
| 03:08 | , how you might is this , we'll go through | |
| 03:09 | a couple more of these . Okay , for the | |
| 03:11 | next question , a car goes 100 and 60 kilometers | |
| 03:14 | in three hours . How far did it go ? | |
| 03:16 | Therefore , in 45 minutes . So I will draw | |
| 03:20 | up this box to work this out and you might | |
| 03:24 | notice what this just something we might have to be | |
| 03:26 | aware of . Which is this , this particular time | |
| 03:29 | unit is in ours , in this particular time . | |
| 03:31 | In it is in minutes , we're gonna have to | |
| 03:32 | make them into the same . I'll show you what | |
| 03:35 | I mean in a second , so this is 100 | |
| 03:37 | and 60 kilometers and it is in three hours . | |
| 03:41 | Now we're gonna put in there 45 minutes here , | |
| 03:44 | but I need to convert this across the hours . | |
| 03:46 | So this is not just a matter of saying it's | |
| 03:48 | .45 hours because let's face it times out of 60 | |
| 03:54 | , so this is 45 minutes out of 60 minutes | |
| 03:58 | , which is 0.75 hours , Okay , 60 minutes | |
| 04:03 | in an hour . So 0.75 hours . And then | |
| 04:08 | what we're going to do is where it's going to | |
| 04:10 | treat this exactly like every other one we've done . | |
| 04:13 | We're going to multiply the diagonals and divide by this | |
| 04:16 | one here . So we're going to get 160 , | |
| 04:19 | We're gonna times it by 0.75 they were going to | |
| 04:23 | divide . So we multiply , these were divided by | |
| 04:26 | this three here , so 160 times 0.75 or three | |
| 04:32 | quarters of 100 and 60 a quarter , 160 is | |
| 04:35 | 43 quarters is 100 and 2100 and 20 divided by | |
| 04:40 | three . This is 40 kilometers . Pretty cool . | |
| 04:47 | Right ? So in here 40 km . All right | |
| 04:53 | , Okay . Let's have a look at this next | |
| 04:55 | one . Okay , for the last question , the | |
| 04:57 | school has a girl boy ratio of 5-4 . That | |
| 04:59 | is to say for every five girls , there's four | |
| 05:02 | boys . So first off , if it's 205 girls | |
| 05:05 | in school , how many boys are there ? And | |
| 05:08 | the second question , Gonna have a look at it | |
| 05:09 | . There's 972 kids altogether . How many boys are | |
| 05:13 | there ? So for both of these were going to | |
| 05:16 | draw up our box . All right . So I'll | |
| 05:19 | draw it up here and this will be good because | |
| 05:24 | I'll keep everything nice and ordered . So we have | |
| 05:27 | a five girls , two for boys ratio . And | |
| 05:35 | then we have over here 205 Girls . Right , | |
| 05:39 | so everything's nice and lined up . And what we | |
| 05:42 | do is we're just going to multiply these and divide | |
| 05:44 | by this . So 205 times four And then we'll | |
| 05:49 | divide that by five . All right . So what | |
| 05:53 | do we get ? 205 times four ? That's going | |
| 05:56 | to be 820 divided by five . That's going to | |
| 05:59 | be 164 . Okay ? So this is 100 and | |
| 06:03 | 60 for boys . Okay . 164 . All right | |
| 06:11 | . What about part two here ? Okay . If | |
| 06:14 | there are 972 kids altogether . How many boys are | |
| 06:17 | there ? So , I'm going to draw up my | |
| 06:20 | box once again . And what I'm gonna do is | |
| 06:24 | this a slight tweak now , and that's this We're | |
| 06:27 | looking at how many boys are ? So how many | |
| 06:30 | boys are this ? four boys ? This is out | |
| 06:34 | of What we're looking at ? 5-4 . This adds | |
| 06:37 | up to nine altogether . So , for every nine | |
| 06:41 | kids . All right . So there's For every four | |
| 06:44 | boys there's nine kids . All right . So when | |
| 06:47 | we know that there's 972 kids altogether , And I | |
| 06:52 | want to know how many boys are . Okay , | |
| 06:54 | so this is fairly simple because we're just going to | |
| 06:56 | now multiply 972 . These diagonals here , Times four | |
| 07:03 | divided by nine . So , if you could do | |
| 07:05 | that , we're going to get 432 . Okay , | |
| 07:09 | this is 432 boys in this particular circumstance . Anyway | |
| 07:17 | , that's a box method of how to do a | |
| 07:19 | whole bunch of things , percentages , ratios . There's | |
| 07:22 | a whole bunch of things you can do with this | |
| 07:24 | . It's a really , really good little method . | |
| 07:26 | So anyway , call me and tell us what you | |
| 07:28 | think . Hope . This video was also help to | |
| 07:30 | you see you next time . Bye . |
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Percent, Ratios, and Rates using the box method is a free educational video by tecmath.
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