Percentage Change - Free Educational videos for Students in K-12

Percentage Change - By tecmath

Transcript


00:0-1	Good day . Welcome to the Tech Math channel .
00:01	What we're going to be having a look at in
00:02	this video is how to work out the percentage change
00:05	between two numbers . Pretty simple to either give me
00:08	an increase or a decrease . So we're going to
00:10	start off and have a look at a couple of
00:12	these . Then what we're going to have a look
00:14	at is the formula which you can use for these
00:16	. Then finally , what we're going to have a
00:18	look at is a bit of a tricky thing ,
00:20	which is actually not too bad once you've shown ,
00:22	which is how to actually reverse the percentage change .
00:25	And it's not as simple as you might think .
00:26	Okay , it's not as direct as you might think
00:29	. So there is a bit of a trick behind
00:30	that , but lets us launch into these and we'll
00:32	start by having a look at just working out the
00:34	percentage change between two numbers with a couple of examples
00:38	. So this is our first example , a shirt
00:40	cost $10 last year and now a cost $12 .
00:43	Disgraceful prices going up like that . What is the
00:47	percentage change ? So the way that we're going to
00:49	work this out is fairly simple . What we're going
00:51	to do is we're going to work out how much
00:53	has changed and then we're going to work this out
00:55	as a percentage of the original price . See how
00:58	complicated it's not too bad . So first off let's
01:00	work out what the actual change is . So how
01:04	much have we changed ? We've gone from $10 to
01:08	$12 . And so you can see there's been an
01:10	increase of $2 . 12 take away 10 is equal
01:15	to two . The next thing we do is we
01:17	work this out as a percentage . And what I
01:20	mean by this this $2 out of the original price
01:24	. So the original price was $10 , so two
01:26	out of 10 . This is a fraction of what's
01:29	happened . But we can now work this out as
01:31	a decimal and then as a percentage . So to
01:34	work this out as a decimal would go to divided
01:36	by 10 And that would be equal to 0.2 .
01:41	We then multiplied by 100 . To turn that into
01:44	a percentage . 0.2 times 100 . We have had
01:48	a 20% increase . That's pretty simple . Right ?
01:51	So just a couple of steps , we work at
01:53	the difference between these , how much things have changed
01:56	? We put that over the original amount and multiplied
01:58	by 100 . We'll go through another example and then
02:01	what I'll do is I'll show you the formula for
02:03	this . So for a second example a bag and
02:06	35 lollies in it , but now it only has
02:08	27 . What is the percentage change ? So we
02:11	go through the same process to work out this percentage
02:14	change . The very first thing we work out is
02:16	the difference between these two numbers here , so we
02:18	can see the change is how much . Well if
02:22	we get 27 and we take off 35 we can
02:24	see we've decreased eight . Okay , the number of
02:27	lollies has decreased . eight . So this amount which
02:29	is going to be negative is over the original amounts
02:33	of eight Over 35 . And we can see what
02:37	this is . So 8/35 is 0.23 . Remembering that
02:42	this is a negative change , would multiply this by
02:45	100 and that would turn that into a percent .
02:48	So this is a 23 decrease because it is negative
02:54	. Okay , pretty simple . Right , So that's
02:57	a fairly simple thing to work out . So what
02:59	about we have a look at the formula for this
03:00	and then what we're going to do is we're going
03:02	to look at how much we need to increase .
03:05	Say for instance , here this 27 to go back
03:08	to 35 to get to that original statement by the
03:10	way , it's not increasing it by 23% . There's
03:13	a bit of a trick with us . Let's summarize
03:15	this all in a formula now . So , what
03:17	happened is the very first thing we did is we
03:19	got the new amount and we subtracted the old amount
03:23	to work out how much things had changed . All
03:26	right . So , let's just write that down the
03:29	new amount . Take away the old amount . Then
03:31	what we did is we put the entire amount over
03:35	In a fractured the original amount . That old amount
03:38	. Then after a bit of chewing and throwing .
03:40	What we did is we got this amount divided by
03:42	this . We end up multiplying by 100 . And
03:45	this is the formula you can use to work out
03:48	percentage change . It's pretty simple . Right ? What
03:51	about we have a look at an example with this
03:53	? Okay , so we used the formula to solve
03:55	this particular question . There were 150 customers yesterday ,
03:59	but there were 200 today . What is the percentage
04:02	change ? So what we're going to do is going
04:04	to get the new amount and subtract that old amount
04:06	. The very first thing that we did before .
04:08	So The new amount 200 take away 150 , Take
04:14	away . 150 . And this is going to go
04:17	over The old amount . That original amount , that
04:21	150 We're gonna multiply by 100 Now . What is
04:25	this equal to ? So this is pretty simple .
04:28	200 take away 150 . Well this is equal to
04:33	50 50 divided by 100 and 50 is equal to
04:37	0.333 times 100 . This is 33% . That's nice
04:43	and easy . Right ? If you like this by
04:45	the way , please really hit the like button .
04:47	But what we're going to have a bit of a
04:48	look at right now , you may not like so
04:50	much . It's not too bad . What we're gonna
04:53	have a look at is okay , so we've had
04:55	to Increased by 33 to get from 150 to 200
04:59	. But how much would we need to reduce ?
05:00	200 by To get back to 50 in terms of
05:04	percentage and it's not 33% . You may be a
05:07	bit surprised to see this . So I'm going to
05:09	show you this first off in an example . So
05:13	consider this example . We earned $120 yesterday but only
05:17	$90 today . So we're going to work out a
05:20	couple of things for this particular statement . What we're
05:23	going to work out is first off what percentage change
05:26	has occurred from yesterday till today , But then when
05:29	we're going to work out and this is a new
05:31	thing , we're going to work out how much we
05:32	need to increase $90 to get back . 220 .
05:36	How much we need to increase it in terms of
05:38	percentage . So let's just go through and work out
05:41	this first part . What is the percentage change ?
05:44	Okay , so the first part , the% 90 and 120
05:50	. So we've gone down $30 and this is out
05:54	of the original amount . 120 . We would multiply
05:57	this by 100 according to our formula . And if
06:00	we do that we will see that we have actually
06:01	gone down 25 percent . Okay , pretty simple .
06:07	So how much would you need to increase $90 to
06:10	go back to 120 now ? It is not 25%
06:13	. You wouldn't increase it by 25% . And I'll
06:15	show you why this is the case . 25 Of
06:19	90 is not 30 . of 90 is in fact
06:24	$22.50 . So we're going to be $7.50 short .
06:30	Okay . How much do we need to change ?
06:32	Well , it's just a bit of a tweaking of
06:34	what we have here because we're not after $22.50 .
06:38	How much we're trying to actually increase ? We're trying
06:40	to increase Back $30 . So let's put that there
06:45	. The other thing we actually have to change here
06:46	is we don't know what this particular percentages that's the
06:50	percentage of 90 but we don't know how much that
06:53	percentages and that's what we're trying to work out .
06:55	So the way I think about this is I would
06:57	think about this in terms of a decimal . OK
07:01	so a lot easier to work with a decimal here
07:03	. So what decimal would you multiply by 90 to
07:07	get 30 Now ? How would you go about working
07:10	out ? Well the opposite of multiplication is division .
07:14	So we could divide this side by 19 , divide
07:17	this by side by 90 . And pretty much what
07:19	we can get is we would say the amount we're
07:21	after is equal to this amount divided by 90 .
07:25	So 30 divided by 90 . It's going to be
07:28	as a percentage though , so multiply our answer by
07:32	100 because this will give it as a decimal .
07:35	So 30 divided by 90 is how much ? Well
07:39	that is 900.33333333 times by 100 . This is 33%
07:46	. So we would need to increase $90 x 33%
07:50	to get back to 120 . Okay , pretty simple
07:54	. Right , what about to give you one more
07:56	example of this ? So consider this , the cost
07:58	of a pair of pants fell from $70 to $62
08:03	. We're going to work out first off how much
08:05	it's fallen in terms of percentage and they were going
08:07	to work and how much it would need to be
08:08	increased to get back to that original price . So
08:12	let's just through those right now . So what has
08:14	been the percentage change ? So you can see here
08:18	that the initial percentage has gone from eight ? Okay
08:22	, there's a change of eight and it's gone downwards
08:24	so it's going to be a decrease Out of 78
08:27	, out of 70 multiplied by 100 . We have
08:31	this change of 11.4% . Pretty crazy . Right ?
08:37	No problems . Okay the second thing I want to
08:39	ask you now then , it's okay to get from
08:41	60 back to 70 . How much do we need
08:45	to increase 62 in terms of a percentage ? So
08:48	how do we do that ? Well once again ,
08:50	what we're going to be doing is we are going
08:52	to be getting trying to work out a certain percent
08:55	of an amount which we're going to work out as
08:56	a decimal uh and work out that amount of 62
09:02	which is equal to eight . Okay , so how
09:05	do we go about doing that ? Pretty simple .
09:07	We're gonna get eight , we're going to divide it
09:09	by 62 we're gonna multiply By 100 . Okay ,
09:14	so eight divided by 62 times 100 , we would
09:17	need to increase By 12.9% to get back to that
09:22	original $70 amount . Anyway . Hopefully you like that
09:26	video if you did pleasure ever hit the like Button
09:29	comment and big shout out to my patrons . Okay
09:32	? Big thank you to you guys . Uh and
09:34	I hope everybody's keeping Well anyway , thank you for
09:37	watching . We'll see you next time . Bye .

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