Solving Proportions - Free Educational videos for Students in K-12

Solving Proportions - By Anywhere Math

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00:0-1	Welcome anywhere . Math . I'm Jeff Jacobson . And
00:01	today we're gonna talk about a few methods you can
00:05	use for solving proportions . Let's get started . Yeah
00:25	. All right , here's our first example , we've
00:28	got to proportions we're gonna solve . And the way
00:31	we're going to solve it is just using mental math
00:33	. We're not gonna do anything real fancy . Um
00:36	So for this first proportion 10/14 is equal to X
00:41	over 21 . I'm solving for X . Now I'm
00:45	not gonna use cross multiplication , we're not gonna do
00:47	that yet . That's gonna be the next method .
00:50	Right ? Now if I look at this I noticed
00:53	that 10/14 I can simplify that but I can make
00:57	that uh five over seven . Okay ? And now
01:03	I know that uh 5/7 has to be equivalent to
01:10	X over 21 . Right ? So basically I can
01:13	think to myself , well If my ratio is 5/7
01:18	, another equivalent ratio would be 10/14 . Right ,
01:23	add five , add seven , Another one would be
01:29	doing the same thing , add five and 7 would
01:32	be 15/21 . Well there we go . 21 21
01:39	that means X . has to be 15 . Now
01:42	obviously you don't want to have to do this every
01:45	time right at five at seven at five at seven
01:47	. That takes a long time . Uh So instead
01:50	you can hopefully think well From seven directly to 21
01:57	I can just multiply by three And if I'm multiplying
02:01	or dividing I do the same thing to the numerator
02:04	. Okay so then five to get to 15 notice
02:08	also multiply by three so we can use that information
02:13	. I'm just gonna race that and show you what
02:16	to do here . I can think well 7-21 again
02:21	just multiply by three . So to get from five
02:24	to my ex I multiply by three and 5 times
02:29	three is 15 so X . is equal to 15
02:34	. Nice and quick . Very simple . Not a
02:37	lot of not a lot of difficult calculations . Just
02:40	all mental math . Let's try the next 1 .
02:43	7/16 is equal to X over four . Now there's
02:48	nothing to simplify there and I don't need to if
02:53	I look over here remember I'm trying to get to
02:56	X . That's really key . So I'm trying I
02:59	have to go this way . I'm not going the
03:03	other way because I don't know what exes I'm going
03:05	from seven to get two X . So I got
03:08	to think well how do I get from 16 ?
03:10	16 to 4 ? Well that's simple . I just
03:14	divide by four Right 16 divided by four is 4
03:20	so seven divided by four will give me X .
03:23	So X is equal to 7 4th whoops at 7/3
03:30	seven Force . Or I could write that as a
03:34	mixed number one and 3/4 . And we're done so
03:41	very simple using methods using mental math , that's our
03:45	first method . Here's some to try on your own
03:54	. All right , here's example No . uh I've
03:57	got to proportions I'm gonna solve . And this time
03:59	the method I'm going to use is cross products or
04:03	cross multiplication , same thing . Um So for the
04:06	first one , X over eight is equal to 7/10
04:10	. Now the reason we're going to use cross products
04:13	is because first that's already simplified . And second if
04:19	I'm trying to go uh two X . From 10
04:23	to 8 , that's not easy , right ? You're
04:25	gonna be dividing but it's not divided by a whole
04:28	number . So it's not easy to use mental math
04:30	in this situation . Always try to use mental math
04:34	First , that's gonna be the easiest and quickest .
04:37	Uh And if it doesn't work then like this situation
04:40	we can use cross products . So cross products are
04:43	very simple , just like the name sounds you're find
04:47	the products of going across . So The products of
04:51	X & 10 , well product means multiplication , so
04:54	X times 10 is 10 X . That's going to
04:58	be equal to The products of eight and 7 which
05:03	is eight times 7 is 56 . So now we've
05:06	just set up an equation . Now all we need
05:09	to do is solve for X . So 10 x
05:12	equals 56 . I'm gonna divide by 10 to both
05:16	sides to get x alone and I get x equals
05:20	5.6 . Okay so it's a little longer than mental
05:26	math . You've got an extra step here where you've
05:28	got to solve your equation but still not too bad
05:31	. Let's try the next one Again . This is
05:34	already simplified . It's not easy to go from 4-14
05:39	, right ? It's gonna be multiplied by a decimal
05:41	. So this again is why we're gonna use cross
05:43	products . So I'm going to find the products going
05:46	across ah for and V . So that's gonna be
05:52	four . V is equal to three Times 14 ,
05:57	which is what 42 and then solve your equation ,
06:02	divide by four on both sides . So I get
06:05	V is equal to what's that going to be ?
06:08	Uh 10.5 , I believe . Yeah . Mm hmm
06:17	. So the is equal to 10.5 . So again
06:20	, this is solving proportions using cross products . Here's
06:24	some to try on your own . Here's our last
06:33	example , right ? And solve a proportion to complete
06:37	the statement . So 10 miles , that's abbreviation for
06:41	miles is approximately notice it's not an equal sign .
06:45	Okay , uh this sign kind of , the wave
06:48	looking one is means approximately is approximately how many kilometers
06:54	um well we need to know a little bit more
06:58	information to solve this and if you google um kind
07:02	of unit conversions or something like that , you'll be
07:04	able to find out that One mile is approximately 1.61
07:12	km , that's rounded , that's not an exact number
07:16	, that's why I wrote it approximately . Now ,
07:19	I'm gonna solve this using a proportion . Well I'm
07:23	gonna use this unit conversion here uh this conversion factor
07:27	in my proportion , so I'm going to say well
07:29	1.61 km to one mile , that's gonna be my
07:37	first ratio , it's going to be equal to ,
07:41	I'm trying to find kilometers , I don't know what
07:43	it is . So that's gonna be my ex kilometers
07:45	were in the numerator , so my ex is also
07:49	going to be in the numerator because that is representing
07:52	kilometers now in my denominator I had 100 miles right
08:01	miles miles kilometers kilometers , Okay , I can put
08:05	kilometers here if I want , but I'm just gonna
08:07	leave it as X . So that's the first step
08:10	. Here is my proportion now I need to solve
08:13	it . Uh and again , we we just learned
08:16	two ways right ? Mental math and cross products .
08:21	Always try to do mental math first . If it
08:24	works great , if not then you can go to
08:26	cross products . So if I look here , I'm
08:28	trying to get to X well from one mile to
08:32	100 miles , that's real simple . Just Multiply ,
08:36	I'll do it different colours , multiply by 100 .
08:39	So I do the same thing here to get to
08:44	X . I'm just gonna multiply by 100 So 1.61
08:50	km times 100 . That's very simple . Just move
08:53	the decimal .2 times to the right , So my
08:56	answer is 161 km . Okay , X is 161
09:05	km , so 100 miles is approximately 161 km .
09:10	Here's some more to try on your own . Thank
09:20	you so much for watching , and if you like
09:21	this video , please subscribe .

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