Solving Equations with Rational Numbers - Free Educational videos for Students in K-12

Solving Equations with Rational Numbers - By Anywhere Math

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00:0-1	Welcome anywhere . Math . I'm Jeff Jacobson . And
00:02	today we're gonna be solving equations with rational numbers .
00:06	Let's get started . All right . Let's get into
00:26	our first example part A negative three equals m minus
00:30	eight . Now , just a quick reminder about solving
00:33	equations . We're always trying to get the variable alone
00:36	. That's our goal . And anything you do to
00:39	one side you have to do to the other side
00:42	to make sure that it stays equivalent . Now ,
00:44	if this is your first time solving equations , check
00:46	out this video up here . Those are going to
00:49	show you the basics today we're dealing with rational numbers
00:52	as well . So there's going to be fractions ,
00:54	decimals and both positive and negative numbers . Let's get
00:57	started . Them . We're trying to get the variable
00:59	alone . Here's the variable M I'm not even going
01:02	to worry about this side . I'm focusing here .
01:04	Well M is being subtracted by eight so to get
01:07	rid of that minus A . I do the inverse
01:09	operation which is plus A Anything I do to one
01:13	side and do the other plus a . To both
01:16	sides that goes away I'm left with m equals negative
01:20	three plus eight would be five . And always remember
01:23	the nice thing about equations is that you can always
01:26	check your answer . So if I want to check
01:30	, all I do is substitute this five back in
01:34	for em because I'm saying m is equal to five
01:37	. So my check I'm saying is negative three .
01:40	It's my question , is it equal to five minus
01:45	eight ? And five minus eight is negative three which
01:48	is equal to negative three ? So we're happy about
01:53	that . Okay so there is my solution to that
01:56	equation . Let's try B w plus three halves equals
01:59	one half . Again I'm gonna focus where that variable
02:02	is . We're adding three halves to it . So
02:04	to get rid of that three halves I'm gonna subtract
02:07	three halves from both sides . Those go away and
02:11	I'm left with W equals one half minus three halves
02:15	. If I want to show that work , if
02:17	you're a little unsure one half minus three halves they
02:22	already have common denominators which is really nice . So
02:25	it basically is just one minus three in the numerator
02:29	which is negative 2/2 Which is the same as -1
02:35	. So there is my solution . Here's something to
02:38	try on your own . Get example to a company
02:45	has a profit of $750 this week . This is
02:49	$900 more than the profit P . Last week write
02:54	an equation that can be used to find P .
02:56	So when we have a word problem like this and
02:58	we're trying to write an equation , the first thing
03:01	we're looking for our keywords , right ? So if
03:03	you look here hopefully more than jumps out at you
03:07	. You also want to think , well we write
03:09	an equation what's my variable is going to be ?
03:12	Well they tell us the profit P . P .
03:14	Is going to be the variable . So I'm gonna
03:15	write P . Is my variable , and it's always
03:18	important to know . Well what does that variable represents
03:20	the profit P . Last week . So P .
03:23	Represents the profit last week we know it's going to
03:27	be an equation , so we're going to have an
03:28	equal sign . Let's start to fill in the pieces
03:31	. So company has a profit of $750 this week
03:34	. This is $900 more than the profit P .
03:38	From last week . Well more than is a keyword
03:42	. And that means addition . So $900 plus P
03:46	. Right ? More than means plus edition plus P
03:49	. This is the profit last week , right ?
03:52	Plus $900 is going to be equal to the profit
03:56	from last week . 750 . So there is our
04:01	equation . It didn't ask to solve it . So
04:03	we're done there . Here's another problem to try on
04:04	your own . Okay example three . We've got a
04:08	couple more equations to solve . Let's get after it
04:11	uh negative X over three equals negative six . Now
04:16	with this when they write the negative in front it's
04:19	hard to tell . Well is that negative on the
04:21	X . The numerator or is it on the denominator
04:25	? And the truth is it doesn't matter . I
04:28	can write this as a negative X over three or
04:33	X over negative three . When I saw it I
04:37	would get the same thing and I can prove it
04:39	to you real quick . If I had it like
04:41	this negative X . Over three equals negative six .
04:45	Well then I would multiply both sides by three to
04:49	get the X alone . But I have negative X
04:53	. Still because that was a negative X . In
04:55	the numerator equals negative 18 . Well then how do
05:00	I make this chest X . Remember negative X .
05:03	Is like a negative one X . So I could
05:06	either multiply by negative or divide by a negative one
05:10	to both sides . Either way it's basically just changing
05:13	the side X equals 18 . If I did it
05:17	where the negative is in the denominator I would get
05:21	X over negative three equals negative six . And then
05:25	I would do it in one step . Multiply both
05:27	sides by negative three to get excellent . And I
05:29	get X equals 18 . If you noticed there was
05:32	one way that was one step quicker and that's this
05:36	way when we do this problem just put the negative
05:39	in the denominator so that when I multiply by negative
05:43	three , the X . Is gonna be alone ,
05:45	there won't be a negative X . So again I'm
05:48	trying to get the variable alone . So it's being
05:50	divided by negative three . So to undo that division
05:54	, I use the inverse operation which is multiple multiplication
05:57	. Multiply both sides by -3 to keep it equivalent
06:01	those cancel each other out . And I'm left with
06:04	X equals negative times . Negative is going to be
06:07	a positive 18 . And if I substitute that back
06:10	in 18 divided by three is six . With that
06:13	negative negative six equals negative six . Let's try the
06:16	other one , 18 equals negative four . Why ?
06:19	Again I'm concentrating on the variable Y . Is being
06:23	multiplied by negative four . So to undo that I
06:26	divide by negative four to both sides , those cancel
06:31	out and I get why equals 18 divided by -4
06:36	. Just like we did here , We took the
06:39	negative out from here and put it in the denominator
06:42	. I can go the other way I can just
06:44	take this negative and put it out front because I
06:46	know that my answer is gonna be negative and then
06:49	I can just worry about this 18/4 so I know
06:53	it's gonna be negative 18/4 . We could simplify to
06:58	nine halves but again that's an improper fraction . I
07:01	don't want that . So I've got two options .
07:04	I could write it as a mixed number or as
07:07	a decima . Uh Me I'll just write it as
07:10	a mixed number . So why equals 4.5 . Again
07:14	you could have said why equals negative 4.5 . Here's
07:17	something to try on your own . Alright example for
07:24	it , this is our last example solve negative for
07:27	fist . X equals negative eight . Same rules apply
07:31	. I'm trying to get the variable alone X .
07:33	Is being multiplied by negative four fists . So I
07:36	should divide by negative four fist . But with fractions
07:40	we know that divided by a fraction . It's the
07:43	same thing as multiplying by its reciprocal so you can
07:48	skip that dividing step and just multiply by the reciprocal
07:52	. Reciprocal of negative for fist would be negative five
07:56	. Force you just flip it so if I do
07:58	that to both sides negative five fours times negative four
08:03	fists X equals negative eight . Have to multiply this
08:08	side by -5 . Force that cancels with that and
08:13	that cancel that I'm left with x equals here .
08:18	I would just make that as a fraction . Put
08:19	it over one so it looks like a fraction I
08:22	can remember that . This is in the numerator Simplify
08:26	, that becomes one that becomes too so negative two
08:30	times negative five would give me positive 10 . And
08:35	that is my solution . Here's some to try on
08:38	your own . Thanks so much for watching . And
08:45	if you like this video please up scott . Mhm
00:0-1	.

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