Solving Equations Using Multiplication or Division - Free Educational videos for Students in K-12

Solving Equations Using Multiplication or Division - By Anywhere Math

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00:0-1	Welcome anywhere . Math . I'm Jeff Jacobson . And
00:02	today we're going to kick it up a notch .
00:04	We're gonna be solving equations using multiplication and division .
00:08	Let's get started . Mhm . All right . Here's
00:28	our first example . But before we get to these
00:31	, I just want to go over what we learned
00:33	in our last video . When solving equations , remember
00:36	the whole goal of solving equations is to get the
00:39	variable alone . The variable equals something on the other
00:43	side . Right , get that variable . All alone
00:47	. Uh Another thing to remember is that anything you
00:50	do to one side , you have to do the
00:52	exact same thing to the other . If you don't
00:55	, the equation will not be balanced and you won't
00:57	have an equation because each side are not equal to
01:00	each other . So whenever you do one thing to
01:02	one side , you have to do the exact to
01:04	the other side . That's the other really , really
01:07	important thing to remember . And then also lastly when
01:10	you are solving equations , we use the inverse operations
01:16	with addition . If we're trying to get rid of
01:18	addition , we use the subtraction . If we're trying
01:21	to get rid of subtraction , we use addition .
01:23	We use the opposite operation to cancel out or undo
01:28	what's been done to the variable . So with that
01:31	in mind , let's solve these . So our first
01:35	equation w over four is equal to 12 . Well
01:39	, W is being divided by four . Remember I'm
01:42	going to focus on the variable first . Well what's
01:46	the opposite of division ? It's multiplication . Right ?
01:50	So to undo that divided by four , that division
01:54	, I'm gonna I'm going to multiply by four .
01:57	So I'm gonna show it like this w uh time
02:01	, I'm sorry four times W over four Is equal
02:06	to , I multiply this side by four . I
02:09	have to do the same thing over here . 12
02:12	times four . Okay , well , what happens when
02:16	we do that ? Well , I can put that
02:18	over one . And whenever you're multiplying with fractions ,
02:22	we always try to simplify that . Four would cancel
02:25	out with that for and I left with W over
02:29	one , which is just W . That's perfect .
02:33	That's what I wanted . I wanted w alone and
02:37	I have it . So w equals 12 times four
02:40	is 48 before I box that answer . I can
02:44	always check substituted back in at the top four .
02:49	W if W is equal to 48 let's check if
02:53	48 divided by four . Well , what's 48 divided
02:56	by four ? I can do that down here .
02:58	48 divided by 44 and four goes at once .
03:01	That's four . Subtract . I get zero . Bring
03:04	down the eight . four and 8 is two times
03:07	. So 48 divided by four is 12 . So
03:12	that is our solution . Okay , Uh let's try
03:17	the next one . Now we have 27 x equals
03:21	six . This 2/7 is right next to my variable
03:25	X . Which means they're being multiplied by each other
03:28	. So the opposite of multiplication is division . So
03:33	to get rid of this 2/7 , I can divide
03:35	by 2/7 . Well divided by a fraction . We
03:39	hopefully you remember is the same exact thing as multiplying
03:44	by , it's reciprocal . So what I'm gonna do
03:48	is I'm going to multiply this to seven X .
03:51	Times the reciprocal of two sevens . So I'm gonna
03:55	multiply it by seven half's seven half times to seven
04:00	X . Is going to be equal to . Well
04:04	if I multiply this side by 2/7 , I got
04:07	to do the same thing on the other side .
04:10	seven times 7/2 there . Okay well look what happens
04:15	here again simplify . Well the two's cancel out the
04:18	sevens cancel out basically you get one times X .
04:21	Which is just X . So your X . Equals
04:26	same thing here . I'm gonna try to simplify ,
04:27	I'll put that over one just so I know that
04:29	it's in my numerator . That would be one of
04:33	the six . Uh Simplifies to a 33 times seven
04:37	is 21 . And again before I box that answer
04:42	I can substitute it back in 27 times 21 .
04:46	Well 27 times 21 . Put that over one .
04:53	That would simplify . That becomes what 32 times three
04:58	is six . So 21 is my solution . Okay
05:04	here's some to try on your own For example to
05:14	solving another equation 5B is equal to 65 Now uh
05:20	five b . When you see it like that you
05:23	see a coefficient next to the variable . That means
05:27	multiplication , This is five times b . So to
05:31	undo that multiplication , I'm going to do the opposite
05:34	, I'm going to divide . So I'm going to
05:37	divide this side by five right ? And anything I
05:42	do to one side I have to do to the
05:43	other . So right away I'm gonna also divide that
05:46	side by five , divide both sides by five .
05:50	Well hopefully you notice This five in this five we'll
05:54	cancel each other out . Okay so I'm left with
05:58	B Which is perfect . That's my goal . Get
06:01	the variable alone is equal to 65 divided by five
06:05	while six or five and the six goes once that's
06:08	15 . So three . So I get B is
06:12	equal to 13 before I bought it . I'm gonna
06:14	check substituted back in five times 13 is 65 .
06:20	So that is my solution . Okay so here we
06:25	were using division to solve this equation and write it
06:30	like this , right ? It like a fraction .
06:32	It makes a lot more sense when you write it
06:34	like a fraction because you can see cancelling out there
06:37	. And if you're running well , how does that
06:39	leave us with B . Five B again Means five
06:46	times b . Excuse me ? So if I'm dividing
06:51	that by five , Well I could separate that as
06:56	5/5 times b . Uh And if you're wondering how
07:03	how does that work ? Just go the other way
07:06	. Right ? If you had five or 5 times
07:08	b . Well this is like be over one .
07:13	I can always do that with a with a variable
07:16	or a whole number or whatever . So then I
07:18	would go okay well five times B is five B
07:23	. five times 1 is five . Right ? So
07:27	I should put that down there . Okay so it's
07:30	the same . And what do you get there ?
07:34	5/5 just becomes one . That's why I kind of
07:37	cancelled out with looks kind of like a big one
07:40	and then your left would be over one which is
07:41	just be Okay . So that does work . You
07:45	get be alone is equal to 13 . Let's try
07:48	one more example . Here's our last example . The
07:51	area of the parallelogram shaped playground right over here Is
07:58	2730 ft squared or square feet . How long is
08:01	the sidewalk ? Okay well if it's a parallelogram ,
08:06	well then we know the area for a parallelogram is
08:09	equal to base times height . And if you look
08:13	at our picture you can see that the base Is
08:17	65 ft . So I can make an equation already
08:22	. I know the area of it . Area is
08:24	2730 sq ft . sold me to substitute that in
08:28	for area 2730 Is equal to I also know the
08:34	base was 65 ft . So I'm going to substitute
08:36	that in for B 65 . H . Is what
08:42	I'm trying to solve the length of that sidewalk .
08:44	Noticed that's going perpendicular to my base , which means
08:48	it is the height . That's what I'm solving for
08:52	. So that's why I'm leaving that as H as
08:54	my variable . So here's my equation . 2007 and
08:58	30 is equal to 65 h . Well , how
09:01	am I going to solve that ? Focus on the
09:03	variable 65 is being multiplied by H . to undo
09:09	that multiplication . I need to divide right ? I'm
09:14	going to divide both sides by 65 . Yeah .
09:19	Okay , 65/65 just becomes one that goes away .
09:25	Right ? So I'm left with H . 2730 divided
09:30	by 65 . If you do that on your paper
09:33	, you should get 42 . Okay , so my
09:38	final answer , How long is the sidewalk ? Well
09:42	, it's 42 ft . Okay , that's our last
09:50	example . Here's some to try on your own .
10:00	Thank you so much for watching , and if you
10:01	like this video , please subscribe . Yeah .

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