Algebra Basics: Solving Basic Equations Part 2 - Math Antics - Free Educational videos for Students in K-12

Algebra Basics: Solving Basic Equations Part 2 - Math Antics - By Mathantics

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00:03	Uh huh . Hi , I'm rob . Welcome to
00:07	Math antics . In our last video we learned how
00:10	to solve basic algebraic equations . That only had one
00:13	addition or one subtraction operation in this video will focus
00:17	on equations that have only one multiplication or one division
00:20	operation . Now before we see some examples , do
00:24	you remember the key strategy for solving an equation with
00:27	an unknown value in it ? Yep . We have
00:30	to use arithmetic to rearrange the equation so that the
00:33	unknown is all by itself on one side of the
00:36	equal sign . And the most important thing to keep
00:39	in mind will rearranging equations is that whenever we do
00:42	something to one side of an equation we have to
00:45	do the same thing to the other side or else
00:47	the other side might get jealous . Hey how come
00:52	he got a cookie And I didn't actually . It's
00:58	to keep the equation in balance . Now remember from
01:01	the last video in equations where a number was being
01:04	added to an unknown , we had to subtract that
01:07	number from both sides . But when a number was
01:10	being subtracted from the unknown , we had to add
01:12	that number to both sides . And that makes sense
01:15	because as we learned in the video called what is
01:18	arithmetic ? Addition and subtraction are inverse operations . They
01:23	undo each other . Well , guess what ? Multiplication
01:26	and division are also inverse operations so we can use
01:30	them to undo each other to If an unknown is
01:33	being multiplied by a number to undo that we need
01:37	to divide both sides by that number . But if
01:40	an unknown is being divided by a number to undo
01:43	that we need to multiply both sides by that number
01:46	. Now don't worry if that sounds a little confusing
01:49	right now it will make it a lot more sense
01:51	. After you've seen a few examples , let's start
01:53	with this 13 X equals 15 . Excuse me .
01:57	Thank you forgot something . I mean didn't you say
02:00	that these equations we're going to have multiplication or division
02:03	in them ? But I don't see any arithmetic operator
02:06	at all in this equation actually . I think you
02:09	forgot something that we learned in the video . What
02:11	is algebra ? You did watch that ? Right ?
02:14	Oh sure sure . Of course . But I you
02:18	know I I just remembered I have something I gotta
02:20	do . I'll be right back . Well I'm sure
02:23	you remember that multiplication is the default operation in algebra
02:28	. So when you see a number and assemble right
02:30	next to each other like this with no operation between
02:33	them . It means they're being multiplied . So three
02:37	X . Is the same as three times X .
02:39	O . And just a side note since in multiplication
02:43	the order of the numbers doesn't matter . You could
02:46	switch the order and right X . Three . But
02:49	it's customary to always list the known number first and
02:52	the unknown number . Second . All right . But
02:55	we need to solve this equation . Right ? That
02:57	means we need to get the unknown X all by
03:00	itself on one side of the equal sign . Right
03:03	now , the X is not by itself because it's
03:05	being multiplied by three . So to undo that operation
03:10	, we need to divide that side by three .
03:12	In algebra , we almost always right , division infraction
03:16	form . So to divide this side by three ,
03:19	we just write a fraction line under it and we
03:21	put a three below the line There . This means
03:25	three times x divided by three . Ah But don't
03:29	forget our rule for rearranging equations . We have to
03:32	do the exact same thing to the other side to
03:35	keep the equation balanced . That's better now both sides
03:39	are being divided by three . The next step is
03:42	to simplify the three on the top and the three
03:44	on the bottom on this side cancel because three divided
03:47	by three would just be one . This is just
03:50	like canceling common factors when you're simplifying a fraction .
03:54	That leaves us with just X . On this side
03:57	. And on the other side we have 15 divided
04:00	by three which simplifies to five . There we've solved
04:04	our equation by changing it into the simplified form x
04:07	equals five . Let's try another one just like that
04:10	. 12 x equals 96 . In this problem the
04:14	unknown is being multiplied by 12 . So to get
04:17	the X . All by itself , we're gonna need
04:19	to divide both sides of the equation by 12 On
04:22	the first side . The 12 on top and the
04:25	12 on bottom cancel out , leaving just X .
04:27	On that side . And on the other side we
04:30	need to divide 96 x 12 . You might be
04:33	able to do that by memory , but if not
04:35	you can use a calculator to divide 96 , divided
04:39	by 12 is eight . So in this problem x
04:42	equals eight . That's pretty easy , isn't it ?
04:45	Are you ready to try a division problem ? Now
04:47	, here we have X divided by two equals three
04:51	. Now when you see division written like this from
04:54	left to right , with the traditional division symbol ,
04:56	I want you to rewrite it using the fraction form
04:59	for division . And that's because it's much easier to
05:03	cancel common factors and simplify your equation . When you
05:06	use the fraction for now that we haven't rewritten ,
05:10	let's solve it . We can see that the unknown
05:12	is not by itself because it's being divided by two
05:16	. How can we get rid of or undo that
05:19	division , yep , we can undo division with multiplication
05:23	. So we need to multiply both sides of the
05:25	equation by two . Instead of writing the multiplication sign
05:29	. I'm using the parentheses notation that we learned about
05:32	in the video called What is algebra ? Remember the
05:35	multiplication is just implied now to simplify it On the
05:39	first side , the two on top cancels out the
05:42	two on the bottom . Since two divided by two
05:45	is just one . And I know what some of
05:47	you are thinking . How is there a two on
05:49	top ? The two looks like it's really in the
05:51	middle . Kind of like how it makes number looks
05:54	That's true . But don't confuse this with a mixed
05:57	number . Mixed numbers involve addition . But the parentheses
06:01	let you know that the two and the X .
06:03	Over two are being multiplied since multiplication is the default
06:07	operation . Okay , so it's not a mixed number
06:10	, but how is the two on top ? Well
06:13	do you remember how you can turn any number into
06:15	a fraction ? Just by making one the bottom number
06:19	? That means that too is the same as to
06:21	over one . Ah Now you can see that the
06:24	two really is on top . It's just that we
06:26	don't usually show the one on the bottom . All
06:29	right then . So the two's cancel leaving the X
06:32	all by itself on this side . And on the
06:34	other side we have three times two , which is
06:37	just six . So in this problem x equals six
06:41	. That's not too hard either . Let's try another
06:43	one . X over 10 equals 15 In this problem
06:48	. Since the X is being divided by 10 To
06:51	get it by itself , we're going to need to
06:52	multiply both sides of the equation by 10 . On
06:56	the first side , the tense cancel leaving X all
07:00	by itself . And on the other side we have
07:02	15 times 10 , which is 150 . So our
07:06	answer is x equals 150 . Great . That's how
07:11	you solve simple equations where an unknown is being multiplied
07:15	by a number or divided by a number . But
07:18	just like with subtraction in the last video with division
07:22	, there's a tricky variation that I need to tell
07:24	you about . What if you have an equation where
07:27	a number is being divided by an unknown since division
07:31	does not have the community of property X over four
07:35	is not the same thing as four over X .
07:39	So what do we do if the unknown is on
07:41	the bottom ? Like in this problem for over X
07:44	equals two . Well , your first thought might be
07:48	to multiply both sides by four , but that won't
07:51	help us here because both of the fours would be
07:53	on top so they wouldn't cancel each other out instead
07:57	what we need to do is multiply both sides by
08:00	ex watch what happens then the X . Is on
08:04	this side of the equation will cancel yep you can
08:07	cancel unknowns and variables exactly like you can regular numbers
08:12	. That will leave us with just four on this
08:14	side of the equation . And on the other side
08:17	we have two times X . Or two X .
08:21	True . That didn't solve the equation but it did
08:24	get rid of the tricky X on the bottom and
08:26	it changed our equation into a problem that we already
08:29	know how to solve . Now to get the X
08:31	. All by itself we just need to divide both
08:34	sides of the equation by two . On the first
08:37	side we have four divided by two which is two
08:40	. And on the other side the 2/2 cancels and
08:43	we're left with just X . So now we know
08:46	that x equals two . Okay , So now that
08:50	you've watched these first three mathematics algebra videos , you
08:53	should be able to solve any simple one step equation
08:56	involving addition , subtraction , multiplication or division . Right
09:00	. Well not unless you practice to really learn how
09:03	to solve equations , you have to try a lot
09:06	of problems on your own to make sure that you
09:08	really understand how to do it . And if you're
09:10	still confused , try re watching these videos a few
09:13	times since they cover so much information as always .
09:17	Thanks for watching Math Antics and I'll see you next
09:19	time . Learn more at Math Antics dot com .
09:24	Hey , I watched that video . You mentioned .
09:26	Hello ? Hello ? Where am I ?

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