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

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



Transcript
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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