hi folks looks like I'm recording now Trang keep my volume to minimum looks like we're down to two more left in operations this is the B section of Algebra one we are going to evaluate numerical expressions involving rational numbers basically we're going to deal with order of operations with fractions and maybe mixed numbers we'll take a look when we get there I hear this let's take a look what they got for us oh we've got a multiplication of some fractions and we're subtracting that from one that's how you say that so I'm going to go ahead and write it down that's 1 sorry 1 plus negative 2/3 and I'm gonna write my multiplication with a dot instead of an ax 3/4 now we have to do according to order operations we have to do the multiplication before we can add and I'm gonna go ahead and simplify this a bit 3 goes into 3 once and I also have this negative 1/2 here I could just multiply these together and get negative 2 or 4 and then reduce it if you do reduce these be careful when you reduce this you're dividing by 2 and you're dividing by 2 and a lot of people are gonna put the 1 and forget all about their negative it is important to include that negative so now I've got 1 plus negative negative 1/2 which happens to be 1/2 and I think I'm just gonna leave it at that and if you need any further help we'll be doing more example soon let's take a look ok now we're doing a division first so I'm going to write rewrite my division as a multiplier 3/4 multiplied by the reciprocal of 1/5 which is 5 and then we're going to add a negative 1/2 so I did two things I changed the division to multiplying by the reciprocal and I change the subtraction to adding the opposite now I have to do my multiplication first which is 15 over Thor and I'm adding negative 1/2 but I'd like a common denominator since I have a 4 in my denominator I'm going to change it to negative 2/4 which is equal to 13 before and I'm all done it looks like we have a mix of quite a bit of stuff going on here I think I am going to multiply first not because it goes multiplication and division but because multiplication and division are on the same level and we have to go left to right now if I take 9 times 1/10 or times point 0.1 I get 0.9 or 9/10 I can write it like this or I can write it as 9 over 10 it's being divided by 1 but that's not going to change anything dividing by 1 keeps everything the same so I'm just gonna write it as 0.9 and be done hopefully we'll get more examples and I was wondering if I had to put the 0 in wasn't sure all right now we've got division and then multiplication it's really easy to make a mistake here be very careful you have to do the division first then you can do the multiplication because you have to go left to right the last thing we do is the addition not because it's farthest over but because addition comes after multiplying dividing I'm going to rewrite this as 0.2 over 0.4 that is the division and it's being multiplied by 2 and then we're adding 4 I want you to notice something 0.2 / 0.4 is really 1/2 this is the same as 2 / 4 you can multiply by 10 on the numerator in the numerator and denominator and that's 1/2 times 2 which happens to be 1 plus 4 which is 5 I could go into more detail but I think that that one is pretty obvious and you'll do it over here 0.2 / 0.4 what I did is I simplified this by multiplying the numerator and denominator by 10 that moves your decimal over and then simplified it now when I multiplied that 1/2 times 2 I got the 1 anymore there it is alright we've got another division which is negative 1/5 this time and then we're adding 1 but we're multiplying it by negative 0.3 why lots of stuff going on here I think I'm gonna go ahead and I have to do this division and I have to do this multiplication and then I can do the subtraction need to be a little bit careful here that double negative acts like a multiplication as well so I could do it first or I could wait I think it's probably more it's probably clearer if I go ahead and leave the subtraction in place so I'm gonna rewrite this as a fraction this is 0.1 over and I like to put my negative my numerator 0.5 and the subtraction I'm going to leave it for now and I have a negative 1 times a negative 0.3 which is 0.3 over 1 if you like lots of ways to go here and I think I'm gonna do it the other way as well so this is negative 1/5 plus negative 3/10 and times 2 so we've got negative two tenths plus negative three tenths which is negative five tenths or zero negative 0.5 or if you like a negative 1/2 any one of these is fine let me show you another way to think of this I'm just gonna go straight forward I'm just gonna say this right here is negative one-fifth and that double negative makes that plus 1 negative 1 times negative 3/10 and because that plus because I made it positive that's really a positive 1 times negative 3/10 which is negative 3/10 and when we add those together we get our negative 5 over 10 and you can see that this seems maybe a little quicker so negative 0.5 Oh negative Oh lots of stuff going on here let's okay that I don't like that negative if you can see it I'm like a little arrow here I don't like the way they wrote that negative I'm gonna write this as negative 3/4 plus 1/2 parentheses since I have to do that first and it's being divided by little needs of vision I have a negative 1/3 plus negative 2/3 and now I've got a I need a common denominator here so multiply by 2 and that is negative 1/4 divided by and this happens to be negative 3 over 3 well negative 1/4 divided by negative 1 is just 1/4 and I'm done that's that's it oK we've got all editions here except for that subtraction right on the end but that really is an addition if I change it to plus five over one I'm gonna do this all in fractions see what happens so I've got a 1/4 I've got a twenty 1/4 20 21 fifths I've got a 2/5 and I've got plus a negative 5 over 1 now to get a common denominator it's going to be 24 all of these um don't see any other easier way to go although decimals would be pretty easy in this particular case I'm gonna go ahead and go with common denominator which is xx so I'm gonna multiply by 5 x 4 x 4 x 20 and that is 5 plus 84 plus 8 plus negative 100 all over 20 and I think you're gonna see why I chose to do this 8 + 84 is 92 and five makes 97 plus negative 120 which is negative 3 over 20 if you like you can write that as negative 0.15 either one of these is perfectly acceptable a lot of people are gonna want to grab their calculator on this now I'm gonna go ahead and write the decimals just so you can see them that's 1/4 that is 4.2 that is 0.4 and that is minus a negative 5 so home- fires and when you add these together you can see that if you add this piece together right there you get four point eight five and when you take away the negative five you get negative five so either way doesn't really matter I'm gonna go ahead and leave it as a fraction negative three but I had the negative negative three over 20 all right that lots of fractions going on here be careful you've got that division right in the middle I can go ahead and change that to a positive 3/4 I have a negative 1/2 again I like putting my negative with the numerator plus 3/4 times 1/5 or 1 I'm changing the division to multiplying by the reciprocal plus a negative 1/4 now it is a very very common mistake to want to do this addition before you do anything else you have to do the multiplication first so we've got 15 over 4 plus negative 1/4 and I really need to make this fourths as well so I'm gonna multiply by 2 and get negative 2/4 and when we add these together you get negative 3 and 15 is 12 over 4 just 3 okay we have an addition inside parentheses then we have to square it and then we have to subtract it be careful the subtraction is the last thing you do a lot of people are going to be tempted to try and put that negative inside that parenthesis and you can't this is a lot like multiplying by a negative 1 I'm I've got one minus I'm going to leave my parentheses in place and this is 2/4 that's my 1/2 plus my negative 3/4 squared all I did has changed this 1/2 right here to 2 over 4 we have 1 minus this is negative 1/4 squared and again a very common mistake is to want to cancel out those negatives and you can you have to square the negative 1/4 which is 1 over 16 and the subtraction is still in place and if you like you can change this to 16 over 16 bit helps and that's 15 over 16 you're done well good almost done all right we've got a mixed number which I'm going to change to a fraction the negative 3 and 1/2 is negative 7 over 2 this is inside parentheses so I can this would all you want I'm gonna change that subtraction to adding a negative 2/5 there this is being multiplied I don't have to put the dot but I think that it's nice to do that that's negative 22 over 5 plus 4 over 1 now I have 2 additions that are inside parentheses so I need a common denominator in this case I have to multiply by the 5 and in this case I have to multiply by the 2 and we end up with sorry - there we go negative 35 plus negative 4 which is negative 39 over 10 and we're multiplying that to get it a common denominator I need to multiply by 5 and that is negative 22 plus 20 which is negative 2 over 5 and we're multiplying these now there's no simplifying excepts of the 10 and negative two and I can go ahead and do that that's a five sorry negative one don't forget your negatives negative 39 continue to be 39 over five times five yes that's a common denominator but we are multiplying that is 25 and you're done 39 over 25 whole lots of stuff going on here I'm gonna do a couple of things at one time one thing I have to be careful of is that subtraction if you if you look at it right there that subtraction has to be one of the last things I deal with I have to square see that squared term there before I can deal with that negative I also have to cube because that cube is inside parentheses and I have to do the addition inside parentheses before I deal with that square I've got 1/4 - now I'm gonna go ahead and cube that negative 1/2 and I'm gonna do this on the side just so you can see what I'm doing and I would normally just do this in my head but that's a negative 1/2 times negative 1/2 times negative 1/2 which happens to be negative 1 over 8 so that's what I'm doing there now I'm gonna put this inside parentheses my negative 3/4 is right there I just moved this particular negative right there to the up to the numerator plus my negative 1/2 cubed is negative 1/8 and I am squaring the whole thing I now need a common denominator inside my parentheses which is times 2 that's negative 7 over 8 make that negative a little bit bigger negative 7 over 8 but it's being squared okay here's a problem that you really need to be careful of that double negative looks like you can maybe cancel it out but you can't because the square is more and multiplying by that negative now what that does is it takes seven eighths and squares it so I've got a 1/4 it's gonna be minus that subtraction stays negative 7/8 times negative 7/8 is 49 over 64 and you have to multiply by 16 to get a common denominator 16 minus forty-nine is negative 33 over 64 and there's no reducing it and you're all done some people are going to insist on grabbing their calculator for this it's really not that much easier and your calculator is going to have problems with all those fractions in parentheses so I think you're better off doing it by hand that is negative 33 over 64 okay we've got some decimals going on here let's go ahead we have to do the multiplication first and then do the division if I want I could rewrite this with a big fraction I've got 2.8 times negative 3 now rewrite it with a big fraction here this is all inside parentheses and we've got the negative four point six plus two point six squared well because this is separated by this this division here oh wait I'm sorry the only way that this would be true is if this piece was in parentheses but because I have to do this first before I do the division it does work out it really isn't exactly correct unless this were in parentheses so my room my rewriting isn't exactly right but it's close let's go ahead and multiply the negative three times a two point eight which happens to be negative eight point four yeah and negative four point six plus two point six is negative two and when you square that you get four and four goes into negative eight point four negative two twenty-one times all right we've got some decimals going on here on they made those decimals work out kind of nice they're that negative one point one four and that's 0.214 are going to simplify pretty nice when I had I'm going to go ahead and add these in my head if you need to you can do them on the side zero point two one four minus zero point one one four happens to be zero point one that is one tenth cubed you could also write it as point one cubed it's the same thing now I still got that minus point eight six six and then I've got plus point one eight one one eight I'm gonna write it as a negative zero twenty eight six six plus zero point one one eight my reason for doing that is because you if you leave the subtraction you have to do the subtraction in order and then do the addition if I change it to adding negative then I can do this addition in any order I choose now it just so happens that one tenth times itself three times 1/10 times 1/10 times 1/10 is one one thousandth and if you like that happens to be 0.001 and since these are in decimal form it might be nice to leave it in decimal form by the way I have to do the cube first zero point zero zero one plus negative zero point eight six six plus zero point one one eight and however you want to do it I know that that the negative is going to be affected by this positive and that I'm looking at a difference here so I really have to do that eight sixty six minus two one eighteen and get a difference aid from sixteen it's eight one four five is four one from a to seven and so this is plus negative zero point seven four eight plus the zero point zero zero one and it just makes one more which is negative zero point seven four seven negative zero seven four seven I'm not sure if I can put that zero okay we've got some fractions now now I have to be careful of this negative out here there that's the only one I have to be really careful I'm going to change this to a fraction that's a negative nineteen over five I multiply the 3 times the five plus four is 19 plus my negative four over five and then I am subtracting I do have to leave the subtraction in place I've got negative two plus one and a half happens to be negative one half now negative 1/2 cubed is negative one-eighth negative 1/2 cubed is negative one half times negative 1/2 times negative 1/2 which is negative 1/8 so I've got minus negative 1 8 which is negative 19 over 15 by the way I can add these together that's negative 23 over 5 plus and this was negative 1/8 and when I do that double negative I get 1/8 I'm almost done I just need a common denominator now I'm going to multiply by 8 and multiply by 5 to get in fortieths and I've got 184 maybe 184 plus 5 over 40 which is negative 179 over 40 nothing nice there and we're done that was kind of a tough one you can see that in some cases it might be helpful to have a calculator handy to check your work but as much as possible do it in your head as usual and good luck folks hope you do well