what is the value of s in the equation 3r = 10 + 5s, when r = 10? This is a topic that many people are looking for. amritsang.org is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, amritsang.org would like to introduce to you How to do Algebra Part 1 Simplifying Expressions. Following along are instructions in the video below:
And welcome to the part one of the how to do algebra. There is a a star. There is a introductions and basics.
Which i explained the idea of the and why im doing them. And just introduce very simple algebra and this is really part one where we look at expressions. But its worth looking at that first video.
If any of this you dont understand okay so were going to look at expressions. We can split up into a number of videos. So were going to start off by just looking at simplifying expressions.
Then were going to go on to factorizing and canceling and then look at quadratics completing a square and algebraic fractions. So its going to be quite a lot in this and this series videos and theyll be then a separate set of videos on equations. Inequalities and then well try and clear up some graph work okay remember this is good start at the basics.
But by the end. Well get up to grade a star and first part of a level so as i said in my first video. I expect you to do some work when you watch these so.
If you have a piece of paper and a pen handy that will help you and heres your first exercise. I want you to simplify this expression. Now a lot of students would think that means give me the answer what does this equal.
Which is it is the right way of thinking about it when its just simple numbers like this but what i want you to think about is that thats animal matter expression and i want you to write it in a more simple way so pause your video copy that down and see if you can write that in a more simple way okay. So one way of doing. It is to say 10 plus.
5. Is 15 take away. 10 is 5.
And so on and other ways to look for numbers. Which can subtract from each other to make 0. So 10 take away 10 is 0 2.
2 8 2 take away. 2 is 0. So youre left with 5 plus.
4. And depends on how you prefer to do it. But the simplest way of writing this expression is just the number 9.
So these two expressions are identical size valley. This is more complicated and this is more simple so we have simplified that expression. So we can also go the other way we can start with an expression.
Something is well lets something as simple as the number two and we can make it more complicated. We can make it less simple now you do that but you have to keep the expression. The same size so for instance.
I could say well 2 plus 10 take away. 8.
Take away. 2. They are the same size expression they are both the same value.
Its just this one is more simple than that one so we have this is a simple version of that theyre the same value theyre the same expression numerically. But theyre just written this is more complicated and thats what were doing when were simplifying algebraic expressions will algebraic with unknowns in or and variables. In all if we write them down to a plus.
3a plus. 2a thats a mathematical expression. Thats to lots of a plus 3 lots of a plus 2 lots of a and what i want you to do now is see if you can simplify that support your video.
Okay so weve got 2 lots of a and another 3 lots of a which is 5 lots of a plus that lots of a there and then weve got 5 lots of a plus 2 lots of a is 7 lots of a or 7. A remember we dont put the multiply symbol between that is the same as a plus a plus a plus a plus a 7 times. So thats a plus a thats a plus a plus a and thats a plus a so if you add all those days.
Together you have seven of them theres seven lots of the unknown. A now we dont have to go by this intermediate step. We can just work out and we.
All whitney will just work out with two two as plus. 3. As is 5 as and then add another two lots of a seven lots of a in total or seven as so we have simplified that expression.
These three expressions. All have the same value theyre all the same math mathematically. They just look different they look less more complicated as you move up the rows.
So i could also make these more complicated. I could add a two but if i add a 2. I must also will take away a two otherwise the expression.
It hasnt got the same value i could add a b. But if i add a b. Ive got to take away a be okay.
These are the same just this is more complicated than that so thats all were doing when were simplifying expressions. Were taking an expression and were writing it in the most simple way possible without changing the value of it right so weve looked at one unknown lets look at two unknowns now 2a plus 3a plus 2b oops b. Lets cross that out do a plus 3.
A plus 2b plus 3b again pause your video and see if you can write that in a more simple way without changing the value of the overall expression. Okay well weve got to lots of a in three lots of a which is five lots of a and weve got to lots of b. And three lots of b.
Which is plus plus five lots of b. Now. Youll hear a lot of people saying collect like terms here.
And what were saying is anything. Which has the same unknown in the term. So this is the unknown.
A and this is the unknown a so these two have the same unknown. Were collecting them together produce one term with that unknown so thats what people have mean when they say collect like terms that to weigh in at 3a make 5a in total five lots of a and that to be ii and that 3b makes five lots of b in total.
We could have also written the answer as 5b plus 5a so if you ever get the questions and you think theyre wrong. Because theyre the wrong way round. Then just just think about it and think about whether its adding or multiplying.
It doesnt matter. Which order you do the adding and multiplying. But it does matter.
Which order you do the subtraction and division. Okay so these two are also the same okay if we have 5a plus 5b take away for a plus 4b. See.
If you can simplify that expression for me. Please pause. The video.
Okay got 5a and if we take away for as from that 5a. Were left with 1a and weve got five b. And if we add four bs to that we get nine bs so thats 5a plus 9b.
Now lets look at it. I said 1a when i did five a takeaway for a and you can write a 1 in front. If you want but we dont need to okay.
We dont need to so we dont tend to write the 1a in front. We just write it as a that is 1a plus 9b. But if you want one at gcse.
Its not going to be a problem. Although as you get up through the grades and you understand more about your mathematics you should try and avoid writing the ones in to begin with now if we just make them more complicated now a plus b. Plus.
Two minus a minus 2b okay. Try simplifying that now think about it carefully try simplifying that one pause it again okay well. Weve got a and if we take away a.
Were left with no as now we could write that as zero a. But we dont because wed have to write zero everything else. There is and then that would take forever.
So if we have none of an airman unknown. We dont have to write it down thats what we mean no as so theres nothing to write down. So be take away two bs is minus b.
And then just left with this ad. So weve got minus b or negative b. Plus.
Two or you could write that as to take away b. Both of those answers are the same mathematically and it just depends on what you prefer to write down so again if you wrote negative b. Plus.
Two youre correct. And if youd wrote to take away b.
Youre correct. So thats simple expression simplifying that confuses some students when you come to simplify that type of expression. Now theres a tendency to think that well thats an x and thats an x so x.
Is are the same so theyre like terms so we can add them together. But an x is not the same number as an x squared. Okay.
There are a couple values. Where x. And x.
Squared are the same you might want to try. And think about what values they are in your own time. But in mathematics and algebra they are not the same number so we cannot simplify them in that way we can only collect we can only add together things are absolutely the same so this x squared and the x squared.
Theyre the same number. So theres two of those so we can write that down is 2x squared and then this x. And this 2x are the same so we can write that down as 3x.
If youve got an x. And you add another 2 x.s to it youve got 3 lots of that x.
So that is also now simplified. I want you to think about that one can you simplify that any further so pause your video and give it a bit of thought and then come back with an answer of whether or not you can simplify that one any further. Okay well.
The answer is yes you can because a b is the same number as b. A. If you think about it.
Two threes are the same as three twos look at my first video. The basics and introductions to see a little bit more on that so we could rewrite this question. As a b.
Plus a b because b a. Is the same as a b. Which means we have to a b to lots of a b.
So thats basic simplification collecting like terms. Give you a few questions at the end here that id like you to do and then you can pause your video and check whether youve got them right or not at the end okay so try these four questions and then when youre ready for the answers start your video. Again okay.
So they are the answers to those four questions hopefully you got them right if not look back you might wonder where the x squareds have gone well. If you have an x squared. And you take away an x squared.
Youve got no x. Squareds left. And you may have got this bit wrong here.
If you try to add a d to a cd. You cant do that see they use a different number to d. But a b and ba were the same number which is why you can combine these two together okay so theyre the answers hopefully got those right if not perhaps you watch a video again and dont forget that you can always come and ask for help during a lunch time if youre still finding this difficult.
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