during your 9 in this video I'm going through questions 22 239 from the practice algebra test so these are relational thinking questions and you have to link skills together so they're a bit of a step up on the first 21 questions you definitely need to make sure you've got the individual skills down easily first so in question 22 we have to simplify and the big idea here is like terms and that's because I'm looking at adding and subtracting different terms so if the letters match up they can go together so that means that the 7p squared goes with negative 4p squared or the takeaway for P squared C takeaway 11 P goes with take away another P and then we've got this leftover one just sitting on the end so my answer for this one will be 7 take away 4 is 3 so 3p squared I've got negative 11 P minus P so minus 12 P plus 1 in the next one we're multiplying we're not adding so this has got nothing to do with like terms now and I think this is one place that unites often can get really confused as when we start to put the different skills together so that's what's happening to you go back through your notes or your worksheets and just go over the separate skills and then see how they're different so here I'm multiplying the numbers the coefficients so 6 to 12 and then I've got a squared times a cubed when I got the same base I just need to add the powers so that's my answer now it's just in case you've forgotten why they were all works it's because 6a squared means 6 times a times a times 2 times a times a times a and we can reorder that because the order of multiplication doesn't matter but we don't want to have to go through all of that drama every time so we want you to get pretty comfortable with knowing that we're just going to add the powers when we've got the same base ok on to the next one so here we have to remember our business rules because we've got multiplication here and here we've got some addition so the first thing we do is we do our multiplication we never write five times B in algebra we write five B then we're going to have plus B plus B squared so all of that early work we did on bidness is coming in here so now we can put the five B and the B together because they're like terms and we get six B plus B squared right number 25 is a division problem and this is the skill that I think is the hardest out of the four operations so we have 15 V to the 6 over 3 B squared first we work with the coefficients what's 15 divided by 3 well it's 5 next we look at the powers we've got B to the power of 6 divided by B squared the base is the same so we can subtract 1 power from the other here I've got B to the power of 6 in the numerator and B squared in the denominator 6 minus 2 is 4 so we get 5 B to the power of 4 so let's again write that out just once with what that means B to the power of 6 means B times B times B and so on 6 times and it can really help to do this because we remember that anything divided by itself is equal to 1 right so if I had 17 divided by 17 that's equal to 1 so here B divided by B is 1 B divided by B is 1 and that leaves me with the B to the power of 4 and then 15 divided by 3 is where 5 comes from the number 26 has a couple of ways to do it we're multiplying fractions just like we did with numbers so we can multiply the numerator and get 8x and we can multiply the denominator in 3 years but I'm not finished yet because I've got a common factor first look at the numbers and look for a common factor there isn't one so that's good we're going to end up with an 8-3 but look at the XS we've got X divided by X X divided by X is just 1 so the answer is 8/3 okay so this is not sort of quite but this is simplified on to the next one this is a division problem and it works just like number fraction division this is quite good like that right so when I see a fraction and I'm dividing by a fraction I multiply by the reciprocal that's that's to C over 5 times 4 over 3 D now I can multiply the numerators make it 8c and I multiply the denominators and they get 15 D but I'm not finished I have to stop and I have to look I look at my coefficients I've got 8 and I've got 15 is there a common factor nope there's no common factor so that's good what about the C in the D is there a common factor no there's not so this answer is finished that's as far as it can go now I just want to show you one other way that we can do question 26 because we've got often have several different ways of working when we're doing algebra so I'm just going to give myself a little bit of space to do that so remember back when we did fractions with numbers and we had things like this so let's suppose we've got that when we first learn to do that we might have multiplied the top and multiplied the bottom right and then we'd find the common factor and the common factor in here is 2 so we'd get 14 over 5 and that's fine it works but if the numbers big it's a big pain so a better way to do that is to look at the floor and look at the 2 and look for common factors between those two and the common factor there is 2 so that means that we can do this right simplify within the fraction and then we get straight to my answer now the same idea works I mean I'm dealing with this here I've got 2x over 3 times 4 over and you can see that I've got a common factor here it's the X and the X here so X divided by X it's just 1 so that gets me to my final answer of 8 thirds it's a little bit more efficient but it takes a while to see that so we don't really mind which way you do it as long as you're working is really clear okay I'm gonna go on to the last ten questions now so number 28 is a substitutional question the key word here is evaluate which means work out the value of one thing to notice is that I'm gonna have to think about bit mess so when I see this a fraction line this is how we do division with algebra that's like having invisible brackets around whatever is in the numerator so we're gonna start like this and we're going to substitute in my numbers so 3 times 4 plus B is negative 2 let's see what if we got past negative 2 divided by 2 times negative 2 cleaning that up gives me this 12 takeaway 2 divided by negative 4 which gives me 10 over negative 4 so that's not simplified yet so we're gonna write that as negative 5 over 2 now there's a pretty strong convention of nets that we always write the negative sign with the with the numerator okay so that's how you should be writing that answer or you could also write negative 225 remember we don't want to use decimals at least they're an exact value so it's usually better to stick with fractions so that's that one done next question this is a good use of algebra right so often in life and we're using algebra whenever we do formulate so if you're doing baking and you have to convert things as we do in this question you're using algebra without ever having known at before so we've got a formula that tells us how to convert the temperature in degrees Fahrenheit to the equivalent temperature and degrees Celsius so it's have a look at what we've got this is my formula and we're told if it is 77 degrees and degrees Fahrenheit what's the temperature in degrees Celsius so that means that F is equal to CB seven so we're going to substitute that in here and that will give me C is equal to 5/9 of 77 minus 32 so that's five nights of 45 and we know one night the 45 is five so that gives me five nights 25 degrees C okay on to questions 32 36 right so here we've got some expanding hands and factorizing and I've done separate videos on these skills so I'm going to go reasonably quickly through these ones here we have to multiply the 3 by each term in the brackets so we get 3x plus 3y minus 3z we do the same thing in this one we multiply each term in here by the 2x squared and we get 2x cubed minus 6x squared next up we have to factorize so when we factorize we're working backwards first we look at the coefficients we look for common factors and the numbers finding the highest common factor of 3 and 12 gives me 3 next we look at the variables we've got x squared here and we've got X here what's the highest common factor well that's it now we just work backwards and we see what do I have 2 times this by to get back to 3x squared well I have 2 times it back by X now what do I have 2 times 3x by to get minus 12x and it will be minus 4 let's look at number city 3 5 X minus 10y minus 15 the only common factor here is 5 so my answer is going to be 5 times X minus 2y minus 3 now we've just got a few questions left and see if I can get through in 15 minutes this is another example number 34 of like terms the thing to notice here is that the order in which we multiply doesn't matter so 9 a B and take away 6 be a are like terms I've got minus 6 here in minus 2 here so they also are like terms so cleaning all of that up give us me 3 baby plus for ABC take away 8 number 35 with vector multiplication right we want you thinking about which skill you have to use in distinguishing between these two situations first we multiply the numbers and we get 3 times 6 then we look for all of the P terms in here so we've got a P here in P here so that gives me P squared next we look for the Q tunes I've got Q squared times Q so I get 6 P squared Q cubed this one is another bidness question for checking out whether you can apply the business rules that seemed really easy when you had them a number 2 algebra so we do what's in the brackets first this is equal to 5 times 3 B times B then equals 15 B squared right two minutes left I wonder if I can get through the last three questions well hopefully so I'm gonna go a little bit faster guys just ask me questions in the comments if you're not sure so looking here I'm looking at the 24 on the 10 and I'm looking for the common sector and in the numbers and it's too so I'm gonna have 12 over 5 now here I've got X cubed and here I've got X so X cubed over X leaves me with x squared here now I look at the Y's I've got Y over Y to the power of 5 it's just think what that looks like Y over Y why why why well I've got a common factor of the Y's and this is really y times 1 so here I've got Y cubed sorry should have been Y to the power of 5 I've got Y to the power of 4 in the denominator but there's lots of good practice of those on education perfect if you need it and lots of you probably do next up I've got another of these ones where I have to multiply the fractions so let's see what we get here so if I look I'm going to do this the way where I look for common factors across the fractions the C's will simplify out and then 10 divided by 5 is 2 so here I've got 4 d squared e over 7 you could also do that by multiplying the numerator multiplying the denominator and then simplifying and this next one we've got 32 x over 15 why is it divided by 8 X is the same as x 1 over 8 X so now we're going to simplify here here and here that leaves me with four over 15 why is it thanks for watching that's all I've got time for now