Oh [Music] [Music] okay so share 240 pounds in the ratio five to seven so if we're splitting this in a ratio and some luck we've gotten total here five plus seven equals twelve parts okay so if we split this into twelve parts we could do 240 and divide it by twelve and tune in 40 divided by twelve is twenty so in each part is twenty pounds now there was five parts and seven parts so those five parts are going to be five lots of 20 which would be a hundred pounds and the other part there were seven parts and that times twenty would give us 140 pounds so splitting in the ratio five to seven gives us a hundred 240 and the last little check you can do here is just to add these two together just to make sure you do get that 240 pound that you started with so we're happy with that as a final answer so Craig Annie and share somebody in the ratio 8 to 3 Craig receives 32 pounds how much does Ian receive of c2i Crater Ian was in the ratio 8 to 3 and it said that Craig receives 32 pounds so that is this first number 8 here that is 32 so we've got to think about is how do we get from 8 to 32 so 32 divided by 8 which we can do to the side 32 divided by 8 is 4 so we must have times by 4 to get there so if we do the same to the other side times by 4 3 times 4 is 12 so there we go how much does he and receive in receives this 12 so I just say 12 pounds final answer Emily and James share some money in the ratio 4 to 7 James receives 21 pounds more than Emily how much do they share between them so Emily - James is in the ratio 4 to 7 now it says that James receives 21 pounds more and if we look at these two numbers here from 4 to 7 is an extra 3 parts you go as an extra 3 so that extra 21 pounds is three parts so three parts of this ratio equals 21 pounds then one part must be to divide that by 3 must be 7 pounds and from there we can work out how much they both receive if it was four to seven let's get rid of this little bit down here and each part is now worth seven pounds or four times seven gives us 28 pounds for Emily and seven times seven gives us 49 pounds for James so Emily Emily receives 28 and James receives 49 it says how much does did they share between them so if we can add these together it gives us the total amount so 49 plus 28 gives us seven and seven so 77 pounds there we go to this that they share 77 pounds between them a 2 B is in the ratio 3 2 5 and B 2 C is in the ratio two to one workout the ratio a to B to C so if you're right out A to B to C and starts right what we've got so far now it says A to B is in the ratio three to five and then it gives us B to C so there's an overlap in these there's a B in both so I can't put another number just over the top of the five so I'm going to start a new level I'm gonna write the other one underneath so B to C is two to one now looking at this if I can make these middle numbers the same I can merge these ratios together I can squish them together essentially so let's think 2 & 5 can make 10 so if we times the top one by 2 that would make that 5 or 10 and we'd have 2 times the bottom 1 by 5 so if we times the top 1 by 2 3 becomes a 6 and the 5 becomes a 10 looking at the one below times and up by 5 2 times 5 makes 10 which we've already got in the middle and 1 times 5 is 5 and there's my ratio a 2 B 2 C 6 to 10 to 5 just have a look to see if you can simplify in there in any of these questions but it doesn't actually ask us to simplify it there so our mobile phone cost 480 pounds in the UK in the same thing for 600 dollars in America the exchange rate is 1 pound to $1 29 where offers the cheapest price so have two options here we could put them base into pounds or I could put them both into dollars I'm gonna decide to put them both into pounds so as we can see we've already got the cost in the UK is 480 pounds that were gonna have to convert this $600 so looking at our exchange rate the actual number itself we get a bigger number in dollars so we know that our answer here is gonna have to get smaller so we only have one decision to make and that is either we times or we divide by this 1.29 okay so it's times or divide okay but we know logically we're gonna get a smaller number in pounds so let's go for this when we do convert back we are going to divide so it's gonna be 600 divided by one point two nine more doing it on the calculator 600 divided by one point two nine gives us not very nice number here 465 pounds and 12 P to the nearest penny now it doesn't matter about all the decimals after that because at the end of the day we're looking at which offers the cheapest value and as you can see there 465 pound 12 is cheaper than 480 obviously there is another way of doing this we could convert them both into dollars so instead of doing that what I could do is times this number here by one point two nine and 480 times one point two nine if again we work that on the calculator gives us an answer of in dollars six hundred and nineteen dollars and 20 cents and again that's more than six hundred dollars so again we would stay that it's cheaper in America the ingredients to make 16 biscuits are 150 flour 100 but 275 sugar and twelve Alma grams of almonds Alice has 140 grams of butter and it's gonna make enough biscuits for 24 people does she have enough well whenever we're doing this look this is a recipe for 16 and we can start to break this down particularly an on calculator way here if we want to get half of that that's going to be 8 1/2 of all of those would be 75 grams of flour be 50 grams of butter it'd be not a very nice number here 75 divided by 2 it's thirty seven point five grams of sugar and half of 12 is 6 grams of almonds now we could keep going we could have this again for a recipe for four we could have it again for a recipe - four - we could have it again for a recipe for one or we could have just divided all of these by 16 if we had a calculator to straight away get recipe for one I'm going to assume this is an on calculator though but it says we want a recipe for 24 people and if we have a look 16 people nope didn't mean to erase out there we go so 16 people in this recipe and 8 people in this recipe 1 in total 16 plus 8 is 24 people so if we combine these together the recipe for 16 the recipe for 8 they'll give us a recipe for 24 so for 24 people we got these together so 150 plus 75 is 225 grams of flour 100 plus 50 150 grams of butter 75 plus 37.5 not very nice one there gives us one hundred and twelve point five and twelve plus six gives us 18 grams for that last one now it says we're actually only looking at the buzzer here but I've got I've gone ahead and done the whole recipe but it says Alice has 140 grams of butter and if we have a look at the actual amount of butter that we have or we got a need is 150 grams so if she only has 140 grams we can say no okay she needs 150 but there's a little process there for working out any any sort of recipe there that we can make combinations of those smaller amounts of recipes in a store you can buy two kilograms of washing powder for three pound for tea or five kilograms of washing powder for seven pound 20 web sizes best value for money as two ways of doing this I always like to split the page up so we've got two kilograms or we've got the five kilograms okay and the two kilograms is three pound 40 and the five kilograms is seven pound 20 now we can either build this up to the same amount of kilograms for each so we could think actually well what if we bought 10 kilograms of each or that would be five of these would be 10 kilograms so if we times three pound 40 by five we get 17 pounds or we can have two of these and that would be 14 pounds and 40 pence and it's quite clear to see there that if we buy 10 kilograms of each the five kilogram one is our cheaper option there so we just make that statement five kilograms is cheaper there is another way of doing this as well so if we think along the lines of something easy let's imagine two apples cost a pound so to our apples equals one pound but to work out the cost of one Apple we would do the amount of apples divided by the cost sorry the cost there divided by two so we would do one pound the cost and we divide it by two apples that will give us 50 P per Apple we can apply this same logic up here so we can do the cost of each divided by the amount so for the first one looking at the two kilograms and three pound forty Lisa we can do three pound forty divide it by two and that gives us 1 pound seventy per kilogram okay per kilogram we can also have a look at the next one in the same way so seven pounds 20 and we can do seven pounds 20 divided by 5 and that gives us so I look one pound forty four so one pounds forty four pence per kilogram and again you can see which one's cheaper there per kilogram it's the one pound 44 again the five kilogram box so two different ways one non calculator one with a calculator to work out a better value three tins of beans and four jars of jam way 2080 grams and a total weight of five tins of beans is 1800 workout the weight of wanting a beans on one jar of jam or straightaway we can work out the weight of wanting a beans from this because it says five tins of Eanes is 1800 so if we do 1,800 and divide it by five we get the answer 360 there we go master bus stop for that but we can do that fives into 1805 into 18 goes three remainder three fives into 30 goes six and then zero so 360 grams a nice for the tin of beans 13 of beans there we go it then says three tins of beans and four jars of jam wait 2080 back in the first line so if we workout with weight of three tins of beans now well three of those would be 360 360 and 360 if we have those all up we get 910 1080 so that's the weight of those tins of beans so if we subtract that away from this original amount so 208 a takeaway 108 a that leaves us with a thousand grams so those four jars of jam say four jars equals a thousand grams and we want to know the cost of one so we can divide that by four and it gives us one jar equaling 250 grams so there we go one jar is 250 and one tin of beans was 360 right so 180 grams of copper is mix with 105 grams of zinc to make an alloy the density of copper is 9 grams per centimeter cubed and the density of zinc is 7 grams per centimeter cube work out the density of the alloy which is which is just a mixture of metals don't ever we've got this sort of mixture going on with mass density in volume I like to tidy it up in a two way table first things first we definitely need to make sure we write down our formula so density equals mass over volume okay and you can stick that into a formula triangle if you want which I'm gonna do so density mass volume there we go so join us I was a little too weight able to tidy this up let's have a look now for each thing we're gonna need a density we're gonna need a mass I'm going to need a volume we have the copper we have the zinc and we have the alloy I'm gonna split this all up into a table right so let's fill in what we've got we've got a mass of the copper 180 we've got a mass of the zinc of 105 it also gives us a density of the copper which is 9 and identity of the zinc which is 7 and wants us to work out the density of the alloy just here now can't add these densities together because the density is gonna change as they're mixed together so if one's nine and one seven the density is gonna be somewhere in between there but we can work out is the volume of the copper and the volume of the zinc so looking at a formula to get volume we would do mass divided by density so mass divided by density so I'm gonna do 180 divided by nine for this one which gives us volume of 20 and for the zinc I'm gonna do 105 divided by seven and 105 divided by seven is 15 now masses and volumes can be added together so gab these together we've got 20 and 15 so $0.35 meter cubed is gonna be the total volume of this alloy and we can add masses together so adding these two together as well we can do 180 plus hundred and five which is 285 grams and we can finish this question off it wants the density remember in density over here is mass over volume so 285 divided by the volume which is 35 285 divided by 35 gives us not a very nice number here but we get eight a point one four two eight five seven it's actually a little recurring them are there as well now this question would normally ask you to write that to one or two decimal places so he would just round it however the question actually asked but it doesn't ask us we write down the full number there which is eight point one four two five seven with those little recurring dots so a karosta travel 30 miles on a motorway in 24 minutes will the car have to travel faster than 70 miles an hour to get there in 24 minutes I'm gonna do this as an on calculator one name I'll have a look at one that's maybe a little bit more calculator based but about stat travel at 70 miles an hour or more now 70 miles an hour means that we go 70 miles in 60 minutes so 70 miles equals 60 minutes not we can do is we can actually start to break this down so have a look what can I divide both sides by so I can divide both sides by 10 that would mean I would go 7 miles in 6 minutes okay dividing up by 10 as well so you can have a look to see if you can ever break these down this way so 60 divided by 10 gives us 6 minutes there we go now he says we've got to go 30 miles and we gotta go there in 24 minutes now just having a look at this speed here seven miles equals six minutes so traveling at this speed if I wanted to get to 24 minutes look 24 minutes we would times that by 4 so if I do the same to the other side and times up by 4 that gives us 28 miles so traveling at 70 miles an hour in 24 minutes we would go 28 miles and the question said a car faster travel 30 miles so it's not actually going to be able to make that 30 miles in 24 minutes it's only gonna be able to go 28 miles it would have to go over 70 miles an hour so I would make obviously that statement no okay it's only gonna go 28 miles or he's not gonna be able to do it in that sort of speed David travels from Birmingham to Glasgow he drives an average speed of 70 miles an hour for the first three hours and he then drives an extra or further 150 miles an average be 230 what cat has average speed from Birmingham to Glasgow so for the whole journey I take a similar approach as I did to the density question here but I'm gonna think about obviously using my formula now so I want to write down the formula which is speed equals distance over time and again we can put that into a formula triangle if we want I'm gonna do that so speed equals distance over time so speed distance time I'm gonna use a little formula triangle so let's see if we can tidy up what we've all got here in a little two-way table and again for each one we're gonna need a speed we're gonna need a distance I'm gonna need a time now we've got the first part of the journey the second part of the journey and we've got the total journey so let's split this all up and write in what we've got so far okay so at the moment we have he drives an average speed of 70 miles an hour for the first three hours so this first one here is three hours and he drives at a speed of 70 miles an hour the second part is his he drives 150 miles which is a distance he drives at an average speed of 30 miles an hour so it's gonna go just above there and we want to work out essentially the average speed for the whole journey which is this one just here now again we can't join together speeds it's gonna be somewhere there in between the 70 and the third thing so it's not like what we can do so this first distance here let's see if we can work that out so looking at our formula triangle distance is speed times time so we can do speed times time to work out that distance so 70 times 3 the speed of 70 times 3 since it will go 210 miles so again we can add these together to get a total distance at the end there because I'd be 360 miles in total he's got to do so we've got to do is get this total speed here sorry this total time and then we had a work out his speed so looking at this bottom one here which is the time for the second one so to get time you do distance divided by speed so distance divided by speed will be 150 divided by the speed of 30 which gives us a time there of 5 so that means in total it's gonna be driving for eight hours now we can work out his total speed because we've got his total distance in his total time I speed is distance over time so it's 360 divided by the total time of 8 there and 360 divided by 8 gives us an answer of 45 miles per hour so I'll just write that down 45 miles per hour again keeping it all nice and tidy in a table so it will make sense we've got some proportion here six taps take three hours to fill a tank with water how long would it take nine taps to fill the same tank and then we're gonna state any assumptions that we've made so six taps takes three hours it will take six times as long as long as that for one tap so one tap would take three times six which would be 18 hours it takes six times longer so one tap it takes 18 hours so from here if we know how many times we've got we can just divide this 18 hours by however many times if we have to tap so we can divide it by two which would give us nine hours we could do three taps divided by 3 would give us 6 hours but this particular question here said there's nine taps how long would it take nine taps so if we do our 18 hours divided by the nine taps because it's a total answer of two hours so these questions are all about working out first how long would it take one tap or whatever these questions are actually about normally so it says state any assumptions that you've made well I've assumed here that all these taps are running at the same rate okay that's my assumption all taps run at the same rate there we go it's obviously in that original statement six taps take three hours while one of those taps might be running a lot faster than the other and that would change our answer so we are assuming that all the taps are running at the same rate okay and looking at some ratio and proportion now so this says James has a full bag as a bagger full bag full of counters he takes a random a sample of 20 counters marks the mom puts them back into the bag and then he takes 30 counters at random come out to the 35 of them are marked estimate how many counters are in the bag so look at capture recapture here now if we just make a few statements because we're going to assume that the sample is proportional to the next one that he took as well or to the rest of the counters in the bag so initially he takes a sample of 20 counters out of we don't know that's what we're trying to work out so let's call that 20 over X on the next time he takes a sample of 30 and 5 of them are marked so we'll say that that's now 5 out of 30 so after the 35 were marked but previously was 20 that were marked out of something we don't know but we are going to assume that these are proportional so in order to work out how many that x value is we just have to think okay well how do we get from 5 to 20 and we do that if these fractions are equivalent by multiplying by 4 so in order to get that number on the bottom there we would multiply this by 4 and that would give us a hundred and 20 so our answer would be a hundred and 20 counters okay obviously we are making some assumptions here we are assuming that no additional counters were added to the bag in between the two samples not owing them were taken out as well obviously this little silly things like we're assuming that the marks haven't actually come off the counters or anything like that in this time frame ok so that is capture recapture there okay on to some direct and inverse proportion so there's two formulas that we can use here says a is inversely proportional to B so it's either gonna be a equals K lots of B or a equals K B or it's gonna be a equals K over B so these are the two that you have to remember now with inverse proportion it's this one here where K has been divided by B so we're gonna use that formula so just make sure you write them down straight away and then it gives us some values to put in so it says 15 for a so 15 equals K over and it says B is 4 so we can solve this for K we can times both sides by 4 to isolate K there and we get 60 equals okay okay equals 60 and now what we can do is we can put that 60 back into the original formula here give us our formula so a equals 60 over B and that is a formula for a in terms of B and sometimes you might just be asked just to write a formula for a in terms of B and there it is but this question says find the value of a 1 B equals 12 so what I've got to do is stick B into the B equals 12 into my formula down here so if we do that I'm going to do it to the side we get a equals 60 over 12 and 60 divided by 12 equals 5 so our final answer there is 5 so every time you just think which formula we're gonna use plug your pieces in find your value of K and then reuse that in your formula for whatever values you need okay so this question says directly proportional to so we're going to use any other formula this time it's a equals K B but you've got to read the question carefully because this one says directly proportional to the square root of B so we need to put a square root in with my B so using the same formula but just putting my square roots you remember it could say squared or cubes or cube root it or anything but that's my formula I'm gonna use then it says when a is 18 B equals 16 so if we put those values in a is 18 so 18 equals K and I put a times sign in here the square root of 16 and you can do that in your head hopefully the square root of 16 is 4 so I'm just gonna put K times 4 now again we can actually find the value of K here we can divide both sides by 4 I divide both sides by 4 we get a decimal here cuz there's 18 over 4 so 18 over 4 equals K now if you simplify that down that's how that divide top and bottom by 2 we get 9 over 2 which we can either leave us that or we can turn into 4.5 I might just leave it as 9 over 2 for the moment see where we ended up with this but we've got our value of K so if we put that back into our formula now so just putting that back up here for our value of K we get a equals 9 over 2 root B there we go and there is our formula for a in terms of B a is 9 over 2 or 4.5 times root B and then it says find the value of B when N equals 2 so if we put those into our formula there a equals 2 so to eat Falls 9 over to Ruby okay alright so we need to rearrange this so I need to divide both sides by 9 over 2 or divide both sides by 4.5 if we've got a calculator that's fine if we don't know we can just do 2 divided by 9 over 2 remember infraction rules that would be 2 over 1 and you would times it by the flipped version 2 over 9 and that would give us 4 over 9 so 4 over 9 equals root B and if you've got a calculator you can just type that straight in so 4 over 9 equals root B in order to find out what beers we just need to square both sides and when you square both sides there 4 squared is 16 9 squared is 81 there we go and we get 16 over 81 so our final answer there is a fraction there we go just following those normal fraction rules there that would've been absolutely fine with the calculator but just a different way to approach this of it it's non calculator okay so we've got one of these questions with lots of ratios going on it says in the back of shapes feature either circles or squares and then they're white or black and gives us some ratios about them and wants us to work out what fraction of all the shapes are white now if I start to break this information down a bit it says fraction so I'm gonna just start to turn these into fractions now it says we've got circles and squares and that's in the ratio 3 to 5 so in total that's 8 so we've got 3/8 circles and five-eighths that are squares and then it gives us some information so it says the ratio of black circles to white circles is 5 to 7 so we have a look at this we've got black and white and that is 5 out of 12 5 plus 7 and 7 are 12 for the white ones okay then it goes onto the squares so we've got 1 2 3 and again that's black 2 white 1 2 3 so it's 1/4 and 3/4 now for treat this just like a probability tree because it has some a fee for the total fraction so if I think well what's the probability of picking a white is there white a white shape so if we have a look at the circles we can go through the 3/8 and down the white shapes there too 712 so just like on a probability tree we would do 3/8 and multiply it by 7 twelfths and that's going to have with a fraction of circles that are why I can do the same with the squares so five eighths multiplied by that one they're three quarters so five eighths x three quarters and that's going to take me time with a fraction of squares that are white now if it weren't these out times in fractions it's nice and easy so times in the top let's just move this to the side a little bit so times in the top there we would get 21 over 96 times a nice on the right we would get 15 over 8 times 4 which is 32 and there's our two fractions not just like with probability here we just need to add these two together which means we need a common denominator so not very nice but you might have spotted here that this fraction simplifies and if we divide the top and bottom by 3 21 divided by 3 is 7 and 96 divided by 3 is 32 so actually we can now add these two fractions together we've got 7 over 32 here and 15 over 32 here and if we just add those together to finish that off now there's a common denominator 7 over 32 and 15 over 32 gives us a final answer of 22 over 32 and again you could even simplify your answer there if you want it doesn't say 2 but if we have both of them because they both divide by 2 we get 11 over 16 so completely up to you there we've got two different answers 22 over 32 or 11 over 16 would be a fine answer there but obviously in that scenario it's quite nice because once simplified to make a common denominator if not you just have to apply your normal fraction rules there to get you coming to the later on some equivalent ratios here so in ratios are equivalent if we think about this logical idea here 1 to 2 is also equivalent to 2 over 4 now I can apply a little trick here because if I strew there we can also make the same and the one over to the left over the right is equal to 2 over 4 and we know that's correct isn't it 1/2 is equal to 2/4 and I apply that same trick to this question here even though we're involving some algebra now we've got 3x plus 5 that's not a 3 we've got 3x plus 5 in the first one so 3x plus 5 over the second one there X plus 4 is equal to the first one 2 X plus 4 over X plus 2 and there we go now we've actually got an equation that we can solve so this is more of an algebra question but it's a trick with the algebra there sorry with the ratio so what we can do them we've got two fractions either side we can cross multiply so I'm going to times the X plus 4 up to this side and times the X plus 2 up to the top of this one so we get a double bracket we get 3 lots 3x plus 5 x that right denominator X plus 2 and that is equal to 2x plus 4 what's on the top of there multiplied by that left denominator which is X plus 4 so all we need to do now is expand base these brackets out and then do this in quite quick steps of the first one we get 3x squared plus 11x plus 10 and on the right one here we get 2x squared plus 12x plus 16 so we've got quadratics and we just need to make it equal 0 I'm gonna do this in quite a quick step I'm going to move if we think here on the left hand side to the other side so I'm going to minus 2x squared minus 12x and minus 16 and that's now going to equal 0 so 3x squared minus 2x squared leaves us with x squared 11 X take away 12 X leaves us with 1 X so minus 1 X + 10 takeaway 16 is minus 6 and that have equals 0 and then we can solve it so all I did was minus 2 x squared minus 12x minus 16 from both sides so that equals 0 now we can solve it so looking at this now I just need to factorize it so the factors of 1 & 6 are the 1 and 6 or 2 & 3 and it's gonna be 3 in the middle there so it'd be X plus 2 and X minus 3 and that would give us minus 1 in the middle and that's what equals 0 so we've got two solutions here which is why it says find the possible values of X got this solution here you've got X could equal minus 2 and you got the one to the right of that as well you got X could equal 3 so there's your two solutions x equals 2 and x equals 3 finish that off last question here we've got a speed sign graph very similar to a velocity time graph as well similar process and what we do separte sighs find an estimate for the distance traveled in the first 10 seconds I know that them are formulas speed is distance over time so actually working out distance is speed times time which just means all we have to do is work out the area underneath the graph so normally it would say to split this into equal widths okay I haven't actually had to get to this one we're going to split it into five equal widths so along the bottom along the time it goes up to ten so each or I'm gonna draw in I'm gonna split it to so every two seconds I'm gonna split the shape up and draw it in here we go and I'm gonna connect those up together here to make the shape so I've got a triangle there a trapezium another trapezium another trapezium and a final trapezium there this is gonna be quite awkward for me to do on here but I'm gonna give it my best shot so the height of this triangle I'm gonna write them all in because the base of all these shapes is two but I just need to work out the area of all these shapes so the height of the triangle there as best as I can see looks like 27 the heights is 27 the heights the next trapezium that's okay nice 44 I just need to be super accurate with these the height of the next one is 50 the height of this next one here is what looks like 44 again to me and this final height at the end here is 20 so what I need to do is work out the area of the mall so I'm gonna label these up on two three four and five and work out the area of all these shapes so shape number ones a triangle so base times height two times 27 and hobbit is 27 so to sum look at the unit is meters per second so the shape one is representing 27 meters shape two we've got the air of a trapezium here don't forget Arabic Arabic peas in formula which is apt to get the parallel sides or a plus B divided by two and then times it by the height which in this case is the two did the distance between them now it's really nice when you've got a distance of two between them because actually dividing by two and times but you cancel each other out so I can you just have to add up those two parallel sides so for number two 2744 is gonna give us 60 71 71 meters again plug it into this formula if it doesn't have a width of two number three is gonna give us 94 44 plus 50 so 94 meters number 450 plus notice the year to summer force the same again 94 meters again and then number five is 44 plus 20 so 64 meters so all we need to do is add them all up so I'm gonna do on the calculator so adding all of those up we've got 27 plus 71 plus 94 + 94 plus 64 and that gives us a total distance there of 350 meters all right there we go just adding them all up let's put that down the bottom there 350 okay so one more thing that we can have a look at on here in its Part B it says work out the an estimate for the acceleration at two seconds now this is a bit awkward to do on the same graph but what I'm gonna do is I'm just gonna get rid of some of the drawings here around the two second mark you know in order to get an estimation for the acceleration we've got to draw a tangent at this point here and that can be awkward but obviously just gone up from to there to find out where that is so you just gotta get your ruler really carefully and make sure that it just touches at that point and then skims off that's very hard for me to on the screen here but that's it drawing a tangent there and all you need to do is draw a little triangle underneath or above and work out the rise over the run off the change in Y over change in X okay so if I just draw this in and a little tip of it non calculator is to try and get that change in X to be 1 I'm just gonna have a look to see if I can actually do that so if I go from here I'll go across 1 2 3 4 5 squares that's a change in X of 1 and I get that distance there which for me actually perfectly goes to 10 so it so gonna be different on the page because it's quite hard to do it on here but that gives me a 1 and a 10 and obviously to work out the gradient you do the change in Y over the change in X and the mine comes out as changing Y is 10 and the change in X is 1 and it's sloping upward so it is positive and that gives me a gradient of ten so in terms of an acceleration here my acceleration would be ten meters per second squared actually four units for acceleration there so ten meters per second squared is my acceleration right and that's the end of ratio and proportion [Music] [Music]