How to Simplify Ratios - Free Educational videos for Students in K-12

How to Simplify Ratios - By tecmath

Transcript


00:01	Good day . Welcome with the Tech Math channel .
00:03	What we're going to be having a look at in
00:04	this video is how to simplify ratios . Very easy
00:07	technique , um , and something you'll be able to
00:09	do really , really quickly now , a ratio just
00:12	for a bit of a recap . We looked at
00:14	in other videos , but ratio is a way of
00:18	comparing two different quantities or even more quantities . Okay
00:22	. And we write these generally as one number compared
00:26	to another number . So an example of this ,
00:29	say I was comparing The amount of petrol to oil
00:33	in a petrol oil mix . I could compare the
00:36	amount of petrol to the amount of oil . Say
00:38	I needed 40 parts petrol to one part oil .
00:41	We would look at it like this . Okay ,
00:43	so it's a it's a way of comparing these two
00:45	numbers . Now , when I talk about simplifying ratios
00:49	, what we're talking about is reducing it to its
00:52	lowest terms . Now , a couple of things to
00:55	understand with this . And these are pretty simple ideas
00:58	. First off ratios can be multiplied or divided the
01:02	numbers and ratios can be multiplied or divided to give
01:05	equivalent ratios . What do I mean by that ?
01:07	Well say I was talking about 80 parts petrol I
01:11	was using as you'll see with this . I've just
01:14	doubled this number of just times it by two .
01:17	Okay , well I can multiply this by two And
01:22	keep the ratio the same by multiplying this other part
01:25	also by two . Okay , so I will multiply
01:28	this by two to get 80 . I multiply this
01:30	one here to get to and that's an equivalent .
01:35	Okay , it's an equivalent ratio there . Okay ,
01:37	we're still this number is still This number is still
01:40	40 times the amount of this number . Okay ,
01:43	so 40 is still Is 40 times 1 , 8
01:47	years , 40 times two . Okay , so we
01:49	can multiply or divide numbers and the numbers in a
01:53	ratio and we can keep the ratio equivalent and therefore
01:56	we can play around with it . And when we're
01:58	saying about simplifying it , all we're doing is we're
02:00	making it like this one and it's most reduced form
02:03	. So we've divided it down to its most reduced
02:05	form . So I'll give you a couple examples of
02:09	doing this . In fact the examples I'm going to
02:11	give you are as follows . Okay , Because these
02:14	are the most likely one you'll encounter where we're asked
02:16	to simplify ratios such as 16 to 40 . Okay
02:21	. And turn that into its most simple form .
02:24	Or say we were asked to simplify uh ratio or
02:28	make a ratio . And then simplify where we had
02:30	to say something like um 60 cm And 1.8 m
02:38	and putting that into a ratio and then simplify it
02:40	. Or say we were asked to simplify ratio where
02:44	we're looking at fractions and we're saying 3/5 is to
02:49	8/10 . And here we would simplify this ratio Or
02:53	say we would ask to simplify a decimal type ratio
02:56	. Where it was like to say something like 2.1
02:59	is two , So these are the examples we'll have
03:03	a look at , okay I'll go through these in
03:06	Each turn . So look at the example , 16
03:10	is 2:40 . Now when we're simplifying this particular ratio
03:15	here , what we're doing is we're just taking it
03:18	down to its lowest terms once again . So we're
03:20	looking for a number that divides into both of these
03:22	numbers . Okay , so a number that divides into
03:25	both 16 and 40 and you might look at it
03:27	and go hey four goes into both . So I'm
03:29	gonna divide four into both of these numbers . 16
03:33	divided by four is four , 40 divided by four
03:36	is 10 . Okay , so with this and you
03:42	might look at this now and say is this at
03:44	its lowest terms ? It could this be reduced any
03:46	further ? Is there a number that goes into four
03:49	and 10 divides into both ? Four and 10 ?
03:51	To reduce it further ? And there is a common
03:53	number that both goes into four and 10 . 2
03:55	goes into it . So I can reduce this further
03:57	to goes into 42 times and it goes into 10
04:01	five times . Is there a number that goes into
04:04	both of these ? That divides into both of these
04:06	? To reduce it further ? Well there's not .
04:08	So this is said to be simplified . It's at
04:11	its most simple . Okay , It's most reduced form
04:17	. Okay , We'll go through the next example ,
04:20	Say what we were looking at now is we're looking
04:23	at putting 60 centimetres and 1.8 m into a ratio
04:32	and then reducing it into its simplest form . Now
04:35	, when we do this , first off , what
04:38	we need to do is if you get something like
04:40	this , you need to make sure the units are
04:42	the same , we need to make sure we're comparing
04:44	the same things . So I'm going to make both
04:46	of these inter centimeters . So we're comparing 60 centimeters
04:49	, which doesn't need to change but 1.8 m ,
04:53	I'm going to change into centimeters 100 centimeters in a
04:55	meter . This is 180 centimeters . Okay , So
05:00	as a ratio this is 60 is to 180 ,
05:04	And we look for a number now that both goes
05:07	into both of these 60 goes into both of these
05:09	, 60 goes into this one Once and 60 goes
05:13	into 183 times . And then we look at this
05:16	and we think is there a number that goes into
05:18	both of these that can reduce it further ? And
05:20	the answer is going to be no , because this
05:22	is the one . We're not going to reduce this
05:23	one down any further . So this is at its
05:26	most simplified version . Okay , The next one we're
05:32	going to have a look at was that fraction one
05:34	, wasn't it ? That was 3/5 is To 8/10
05:41	. Now , when you get one like this ,
05:43	these aren't that bad . They look a bit scary
05:45	to start off with , but pretty much the way
05:47	that you do this is the first goal that we
05:50	have , is we're just gonna get these bottom numbers
05:52	, these denominators the same . Okay . And you
05:55	might need to stuff around or mess around with both
05:58	. Uh , either that both fractions or just one
06:01	of the fractions with this one . You're gonna notice
06:03	that we have a five at the bottom number here
06:05	, in a tent on the bottom number here .
06:06	So if I double This and make an equivalent fraction
06:09	here , but I can change this . Bottott number
06:12	starts at 10 . Okay , so To do that
06:14	, I'd have to multiply this bottom number by two
06:17	. Okay , five times two , it's 10 ,
06:24	two times 3 is six . And then this number
06:28	is going to stay the same because I don't need
06:30	to mess with that one . So now our ratio
06:33	has been changed to this . Now this is a
06:35	really good bit of this part . Now we can
06:37	just get rid of this bottom part . So we
06:40	end up with six years to eight , we get
06:44	rid of those denominators and now we reduce it as
06:46	normal . Is there a number that goes into both
06:48	? Yeah , two goes into both . Two goes
06:51	into this 13 times and two goes into this 14
06:55	times . It's been simplified . There's no other number
06:58	that will reduce us any further . Okay . And
07:02	the last one in which I have given the example
07:04	of is where you would get a decimal . Say
07:07	you were asked to simplify a ratio of 2.1 is
07:14	two , Now if you get something like this the
07:18	easiest way straight away is to get rid of these
07:22	decimals and if we multiply both of these numbers by
07:24	10 This will turn into 21 and this number will
07:28	turn into three and now we reduce these as normal
07:32	. So a number that goes into both of these
07:34	is three , it goes into this 17 times it
07:36	goes into this 11 times can't be reduced any further
07:40	. This is at its most simple . Okay ,
07:42	so this is the way that you simplify ratios fairly
07:46	simple . Okay , I'll see you next time .
07:50	Thank you for watching . Bye .

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