 ## Basic Math Self-Test #2

okay this basic math skills self task number two is very similar to number one same topics will be covered and we'll use the same format so just changed a few things and let's see how you do okay this self test has 20 different problems for you to try when you see a new problem click on the stop sign to pause the video try to work the problem out on a piece of scratch paper or something then click on the go sign to start the video and you'll see the problem worked out number one turn zero point seven to zero into a fraction then simplify your answer click on the stop sign okay let's see how you did well when you're turning a decimal into a fraction whatever this number is without any regard to the decimal that's your numerator so our numerator is 7 to 0 just like if I had one point two as my decimal my numerator would be 12 and my denominator would be 10 because I'm dealing with tenths all right so I will take a look at this my nomination it because I have three places to the right of the decimal so we'll come down here and we'll put three zeros and we'll stick a 1 in front of that so that's the fraction that this decimal represents however we need to simplify this so how do you simplify something well you can factor it and then you can cross out the similar factors that are the same factors that are in the numerator in the denominator we'll take a look at this and we'll say first of all 72 times 10 is 720 and 100 times 10 is 1,000 I have a 10 in the numerator and I have a 10 in the denominator so I can cancel them they just become 1 this just becomes 1 and so I now have 72 over 100 and that's an equivalent fraction to 720 over 1,000 okay factor this a little bit more 72 is the same thing as 2 times 36 and 100 is the same thing as 2 times 50 so this is an equivalent fraction to this I have a 2 in the numerator I have a 2 in the denominator becomes 1 becomes 1 so now I have 36 over 50 36 over 50 can be further factored and we're going to factor 36 as 6 times 6 and then we're going to factor 6 times 6 is 2 times 3 so we'll go 2 times 3 2 times 3 times 2 times 3 because this is 6 and this is 6 6 times 6 is 36 that's completely factoring my numerator my denominator I can say is 2 times 25 and 25 can be factored as 5 times 5 and that's as far as I can factor it so now I have a 2 in the numerator and a 2 in the denominator and then I have a 3 a 2 and a 3 so I can cancel this one and I can cancel this one and we have 3 times 2 is 6 times 3 is 18 we have 18 and 5 times 5 is 25 so that's 25 18 over 25 is the simplified fraction of 0.7 to 0 if we were to do the long division problem of 25 into 18 we would come up with this same de Mille right here all right let's move on to the next one number 2 turn 7/8 into a decimal click on the stop sign 7/8 into a decimal let's see how you did it's just the top in bottom out kind of thing so we'll put the top 7 in and we'll put the 8 on the outside remember 7/8 that's the same thing it's just 7/8 and so this is the one vision form 8 will not go into seven so I'll put a zero here I don't know how to decimal which means that my answer is going to be smaller than one well 7/8 is smaller than one all right I could add a zero here now and eighty will go into seventy eight times because 8 times 8 is 64 so we have a 64 here it's kind of the value of knowing your multiplication tables and then we do the subtraction so we wind up 70 minus 64 is 6 and 8 will not go into 6 but it will go into 60 7 times 7 times 8 is 56 again a good thing to know your multiplication tables we do the subtraction and I wind up with 60-56 is 4 and 8 will not go into 4 but it will go into 40 exactly 5 times and that's a 40 and that terminates and we're finished so our answer is zero point eight seven five and I put the zero here in front so that that Q's anybody who's looking at this to know that it's followed by a decimal anytime you see a number starting off with a zero you know that there's going to be some decimal that follows that and so we'd have 0 1 1 and that would be the decimal 11 hundreds if we were to turn that into a fraction okay number three turn the decimal answer that you got for number two into a percentage remember it was 0.875 so we have 0.875 you shift the decimal two places and that gives you the percentage so the answer here is eighty seven point five percent because percent means per 100 so what this means is we have eighty-seven point five out of a hundred and if we were to do the long division process on this we would come up with this answer here this is the percent if we're dealing with hundreds so that's why it's called a per one hundred eighty-seven point five percent number for all units are in feet the rectangles are proportional what is the length of x click on the stop sign okay let's see how you did they're proportional which means that whatever we multiply this length by to get this length we would multiply this link to get the same answer over here they're proportional so if we compare three to seven then we have to compare x – 12 if we compare three to X then we have to compare seven to twelve if we compare X to 3 then we have to compare 12 to seven doesn't matter how you do it you just need to keep things straight so we're going to compare three to seven so all right three to seven and I compared three to seven so I'm going to compare X to 12 and that's going to equal x over 12 now what happens is if I cross multiply 3 times 12 that equals 36 and if they are truly proportional seven times X will also equal 36 so now I come down here and I say 7 X I want to find out how much X is because that's what we were originally told to do we're going to find out how much is X all right seven X does equal 36 how do I solve for X well works like this I come in and I divide both sides of my equation by 7 that keeps everything in balance and so I now have a 7 in the numerator it's a factor and I have a 7 in the denominators a factor so they cancel they become 1 and that I have 36 over 7 so what I really have now is x equals 36 over 7 and then I have to do the long division problem on that so let's clear a space here so thinking ok now I'm gonna do the long division that I have and need to do for top it and bottom out so I have 36 and I want to know how many times will 7 go into it well 7 times 5 is 35 so we'll put a 5 here and that's 35 and that leaves me with 1 left over and so I could put a decimal error I can turn that into a fraction let's get rid of that decimal all right so that leaves me with 1 left over and I'm dealing with sevens there that's 5 and 1/7 and that's exactly what it is in feet or we could continue on and find out what it is in decimals and so let's move this 5 and 1/7 over here I have 5 and 1 7 feet and clean up this a little bit so we can continue to work all right and take care of that add in a couple more things no I have seven how many times will 7 go into 36 so to go 5 that's 35 that leaves me with one left over seven will not go into one so I'm now down smaller than one so I come down and I can add a zero here seven will go into 10 one time and that'll leave seven do my subtraction that will leave me with three seven will not go into three but it will go into 30 and it will go into thirty four times and so that's 28 there we go now I do my subtraction that leaves me with two seven will not go into two but it will go into 20 two times and so that's 14 and that leaves me with six left over and you know this could go on and on and on so we're going to chop this off truncated after three decimal places so X is exactly 5 and 1/7 feet or it's approximately five point 1 4 2 it's not exact because I could continue doing a long division here and I get a whole bunch more numbers out over here all right moving on to number 5 all units are feet what is the area of the larger proportional rectangle okay this is the same drawing from earlier click on the stop sign and try to work it out now let's see what you got well remember we had five point 1 4 – I believe it was let's go back yep five point 1 4 2 and the area for a rectangle is just length times width so we'll stick in our x and y values here and that would just simply be 5 point 1 4 2 times 12 and 5 point 1 4 2 times 12 we'll set that puppy up over here I go five point one four two and that's feet times 12 feet so just line everything up this way not giving any consideration to my decimal I'll deal with that later 2 times 2 is 4 2 times 4 is 8 2 times 1 is 2 and 2 times 5 is 10 now I come in and add a 0 and now I'm going to go 1 times 2 is 2 1 times 4 is 4 1 times 1 is 1 and 1 times 5 is 5 add it all up I have 4 I have 0 I have 6 7 carry the 1 see this was 10 so I put a 0 carry the 1 7 this is 1 and that is 6 now I count the number of decimals that I have up here 1 2 3 1 2 3 and I have 61.7 0 4 feet squared all right if I were to approximate this let's say I wasn't worried about the decimal here it's just 5 times 12 5 times 12 is 60 I'm going to have an answer that's going to be a little bit more than 60 and here I have it getting answers a little bit more than 60 so I can feel pretty confident that my answer is correct and that I've handled the decimals okay number 6 the square root of 18 is between what two consecutive whole numbers click on the stop sign all right works like this see how you did first of all consecutive just means that they come together on the number line like 9 and 10 so we have 9 and 10 or 13 and 14 those are consecutive numbers and they're whole numbers so the square root of 18 hmm the square root of 18 comes between a couple of whole numbers but what two whole numbers if we take a look at this we go the square root of 16 and the square root of 25 square root of 16 is 4 square root of 25 is 5 so the square root of 18 comes between the square root of 16 and 25 and so it falls on the number line somewhere between 4 and 5 number 7 triangles are proportional what is the angle measure of the unknown acute angle that one right there click on the stop sign ok let's see how you did well if they if these triangles are definitely proportional and this right here means that it's 90 degrees then that means that this is 90 degrees if this is 28 degrees then that means this is 28 degrees so this is 28 degrees and this is 90 degrees and every single triangle in the known universe and Beyond when you total up the internal angles are always totalling to 180 degrees so what we know is 90 plus 28 plus some unknown and we'll just call that X because that's what we use for a num we know that these three right here when added together will equal 180 so let's say we got 90 degrees plus 28 degrees plus some unknown degree we know that that equals 180 degrees well to find out how much X degrees is we'll first let's see we can just subtract 90 from each side it's a pretty easy thing to do so if we subtract 90 from here then that just goes away and this becomes 90 because I've kept the balance so now I have 28 degrees plus the unknown degree equals 90 if I subtract 28 from each side I keep the balance in check there and so that means x equals what's that 60 to 62 degrees so x equals 62 degrees and if I wanted to see well is this right well I can come back up here and I can plug that in and see what I get and get rid of all that and so if I stick 62 degrees here in my equation my original equation then will it equal 180 90 plus 28 plus 62 does equal 180 so the unknown angle was 62 degrees number I make a sketch of the coordinate plane the Cartesian coordinate system then sketch a circle that has a radius of 1 and is centered at the ordered pair 3 negative 3 click on the stop sign okay we're going to make a sketch let's see how you did here all right it's 3 negative 3 4 first of all I'm just going to draw my x-axis and then I'm going to draw my y-axis and so put it over here because this ordered pair right here this the center is going to be in the fourth quadrant it's not going to be in the first it's not going to be in the second and it's not going to be in the third it's going to be in the fourth all right so now I just freehand sketch in 1 2 3 1 three it's not perfect but it's pretty stinking close this is my x axis this is my y axis and so I go X is my first number in the ordered pair you know 1 2 3 and then I'm going to go negative 3 1 2 3 so there's the center of my circle and it says it has a radius of 1 so I'll go up 1 in this direction and that point will fall on the circumference of my circle and I go this way in 1 and that point will follow there's some circumference of my circle and I go about the same distance over here that point will fall in the circumference of my circle and I'll go down a radius of 1 here and that point will fall on the circumference rule now I plotted some points so it's a easier for me to come in and kind of freehand sketch a circle with a radius of one located at 3 negative 3 it's in the fourth quadrant number 9 multiply these fractions click on the stop sign okay let's see how you did multiplying fractions is exceedingly easy you simply just multiply all the numerators multiply all the denominators and then simplify it's necessary so 1 times 3 is 3 and 3 times 4 is 12 so our numerator is 12 and then I come in and I say 2 times 4 is 8 and 3 times 8 is 24 I have 24 so my fraction is this but I haven't simplified it yet maybe you can recognize that yet can be simplified to 1/2 but let's take a look at how you do that so we have 12 over 24 and 12 over 24 well you can just factor that and 12 is the same thing as 3 times 4 and 4 is the same thing as 2 times 2 so factoring this is just 2 times 2 times 3 because 2 times 2 is 4 and this is 3 that's 12 and then we could come down here I could say 24 that's the same thing as 2 2 times 2 times 2 times 3 because 2 times 2 is 4 2 4 times 2 is 8 and 8 times 3 is 24 so there's my denominator all right I can cancel this with this it becomes 1 this is where you'll see it's kind of important that it becomes 1 and I can cancel this with this and it becomes 1 and I can cancel this 3 with this 3 and this becomes 1 and that becomes 1 so 1 times 1 times 1 is 1 and 1 times 1 times 2 times 1 is 2 because you see if these just went away if they became nothing if they became 0 I wouldn't have a 1 in my numerator and I now need in one of my numerator so this is why they don't go away and become nothing when you cancel them they become 1 so that's how you would simplify this to be 1/2 all right number 10 click on the stop sign ok we're going to divide 7 by 3/4 well I've told you other times that all you have to do is flip this puppy over and then multiply and so the 4 goes into the numerators position and the 3 here would go in the denominators position and students often say oh you flip over the second fraction will you notice that we really don't have a fraction here unless we were to say oh yeah that's over 1 but you don't flip over the second fraction you flip over the dividing fraction that's what you flip over so this becomes 7 times 4/3 and how do you multiply fractions you simply multiply the numerators multiply the denominators 7 times 4 that's 28 and 1 times 3 that's 3 and so we need to simplify this if we can simplify this any and let's take a look at this nope I don't see how I can simplify it but what we do have is an improper fraction and I need to turn that into what's called a mixed number and their words how many times will 3 go into 28 well 303 times 9 is 27 so it'll go 9 times that'll leave me with 1 left over and then I'm doing in 3rd so it's 9 and 1/3 is the improper number and this is the excuse me is the mixed number and this is the improper fraction okay they're the same amount these equal the same thing if you wanted to check hey how am I doing here is is this right just do this 3 times 9 is 27 plus 1 is 28 and you're dealing in thirds that's 28 thirds okay number 11 click on the stop sign okay let's see how you did well first of all this is a trapezoid and trapezoids have the formula for finding their area as a equals b1 the base one plus base two all of that in parentheses times the height all divided by 2 now it doesn't matter which one of these you call base 1 and base 2 the bases are just the parallel lines if I have these lines here that are parallel and so it doesn't matter which one I call base 1 or base 2 because all's I'm really doing is just adding these numbers and if I add 4.5 to 6 I get the same answer that if I had 6 to 4 point 5 so all right six plus four point five is ten point five and I want to multiply that times the height which is feet at another direction that's times four feet and all of that divided by two okay 10 times 4 is 40 plus 1/2 is 2 so I'm at 42 feet squared divide that by 2 and that's going to give me 21 feet squared that's my answer number 5 click on the stop sign ok let's see how you did well make a sketch of the depiction below and then reflect there's a keyword reflected across the y-axis that's another key thing there this is my y-axis and I want to reflect it so I would come in and make a sketch that looks something about like that and since I'm reflecting it the circle would be over here because it's as if there was a mirror right here number 13 click on the stop sign okay let's see how you did sketch the drawing below and copy the figure across the x-axis alright now we have the x axis and we're going to make a copy which means it's going to look just like this but it's going to be down here and so let me kind of freehand this puppy like this it goes like that this goes like that this goes like that that and that that's about as good as sketch as I can make so that's a copy across the x-axis number 14 click on the stop sign all right this is a kind of a two-part problem you got to find the area and you got to find the perimeter start with the perimeter because that won't be kind of easy all right Larry we have a triangle and I would encourage you to always make a sketch see what your triangle looks like this is 3 feets as one of the legs is 3 one of the legs is 4 and the hypotenuse it's 5 then it says what's the perimeter Wow the perimeter is just the total distance around that's it you just add up all the numbers 3 plus 4 that's 7 plus 5 and be 12 so we're talking about 12 and it says their feet it's 12 feet equals the perimeter you got that right you doing it right good for you now we got to calculate the area of this thing and the area of all triangles is exactly equal into this formula right here it's 1/2 the base times the height it doesn't matter really what you call the base and it doesn't matter really which call the height you just have to multiply this number by that length times this length and they're going to be in feet so I know that it's going to be an area I think so it's going to be feet squared so I have 1/2 times 3 feet times 4 feet and so that's going to be 3 times 4 is 12 that's 12 feet and so I have 12 feet squared because I'm multiplying feet times feet and that's all divided by 2 if I multiply times 1/2 that's the same thing as dividing by 2 and so I wind up then having 6 feet squared that's my area number 215 click on the stop sign okay sketch a circle and label four main parts we need four parts of this well every circle has a center and every circle has a circumference and every circle has a radius every circle has a diameter and every circle has an area it's a two-dimensional object okay and that's what Center 1 2 3 4 5 that's 5 so if you got four of those you're doing it right number 16 click on the stop sign okay we're adding and we're adding and subtracting positive and negative integers so I'm going to make a number line here to kind of sketch this out to talk you through to see how you did well I'm going to start with 10 on my number line so it will just make a spot here and we'll call that 10 and then it says I'm going to add negative 10 which means I'm going to go in this way so I go this way and I wind up at 0 and I'm at zero and Isis ad 30 so I'm going to add 30 so there's 10 20 30 and I'm at 30 and then it says to subtract negative 7 take away a negative number that's the same thing as adding 7 more so I'm going to come over here to and my final answer is going to be 37 now taking away a negative thing is a positive thing even in your life taking away a negative thing as a positive thing the way I remember this and I've done it since I was a boy is that if I need this negative this line right here to come over here and turn this into a positive I've used it so it's no longer here and so what that means is now I'm adding 7 take it away negative 7 is the same thing as adding 7 that answer is 37 ok number 17 click on the stop sign all right let's see how you did well first of all these are sixteenths there are 16 little marks between the 0 and the 1 and they're the same 16 little marks between the 1 and the 2 you don't have to learn them all over again they're the same little marks it's that way between the 2 and the 3 there are 16 little marks if there's 16 1 sometimes you'll find a rule it has 8 on there or something like that or even more so we can look at this and say that's 1 16 to 16 3/16 4 16 5/16 so a is 5/16 and that cannot be simplified any more inches to little marks there so if I meant 5/16 here that's 616 7/16 816 9/16 1016 so that's 10 16 and I can perhaps recognize that 10 sixteenths and 5/8 are the same thing so that's 5/8 inches and so here I am at 10:16 11 12 13 14 15 16:16 say that's exactly one inch 16 16 17 18 19 you could call C 1916 but if you told somebody that he said hey cut me a piece of wood there in 1916 they'd think you were stupid so here we are at 1 and 1/16 two sixteenths 3/16 1916 is the same amount of stuff as one and three sixteenths and they're inches so two little Mark's that means inches all right so we continue to count we're at 16 16s here we would be at 32 sixteenths here so we could say 33 34 35 36 37 we're at 37 16 and again if you told somebody to cut you a piece of wood at thirty seven sixteenths they'd think you were nuts but we are at two and 1/16 to 16 3/16 four sixteenths five sixteenths so we are at two and five sixteenths inches if you got them right you're doing well okay number 18 how many minutes are in 7/8 of an hour click on the stop sign okay well let's see there are 60 minutes in an hour and we want to find out what that is how much is 7/8 so it's going to be less than 7/8 is less than 1 there's going to be less than 60 minutes so we're going to multiply the fractions here 7/8 times 60 over 1 and 60 times 7 equals 420 and 1 times 8 equals 8 all right we could do the top in bottom out on this but that might be a lot of work so let's go ahead and try that oh we do 420 and acres on the outside we're doing the long division here eight will not go into four but eight will go into 42 five times and that's 40 and we do our subtraction and we bring down the 2 and 0 and so let's see 8 will go into 2002 times yeah 2 times and so that's 16 and that leaves us with 4 left over and 8 will not go into 4 or at the end here so we got to add a decimal 48 will go into 40 exactly 5 times so there are 52 and a half minutes in 7/8 of an hour hmm does that make sense this is a little bit less than 1 this is a little bit less than an hour number 19 click on the stop sign okay Thomas charges \$10 per hour for his handyman services if he works 8 to 12 hours per day for the week Monday through Friday what is the range of his gross pay I have several things here let's take a look at this the guy's making \$10 an hour some days he works eight hours no days he works 12 hours or somewhere in between the two he works only Monday through Friday that's five days and what is the range range means what's the least amount of money that he's going to make to the most amount that he's going to make and gross pay gross just means the total amount of money that was going to make instead of sometimes you get what's called net pay and net pay is after they've taken out some withholding and some things like that so how much money would he make if somebody was paying him in cash all right let's see on Monday let's just take a look at this Monday he works either 8 or 12 hours so he works a minimum of 8 and he works a maximum of 12 hours and they're 5 days in a week so let's just multiply that times 5 to get what's the minimum number of hours that he would work for a week and that would be 40 and if he were to work 12 hours a day day then that means he worked 60 hours so he's going to work somewhere between 40 and 60 hours for the week okay but he's making \$10 an hour so making \$10 an hour here and he doesn't get any overtime with his handyman service he just gets a straight \$10 an hour so 40 times 10 that's 460 times 10 that's 600 so he's making somewhere between 400 and 600 so the range is 400 to 600 or that's about a \$200 range that he makes so that's 400 to 600 least to most or the difference is \$200 okay number 20 let's take a look click on the stop sign all right let's see how you did well first thing you need to do is that which is in the parentheses and that which in the parentheses is pretty straightforward it's just 3 times 7 is 21 1 and 6 times 4 that's 24 so we have a fraction here I'm going to multiply that times a decimal I could turn this into a decimal and then multiply it or I could turn this into a fraction let's see excuse me I'm going to turn this decimal here into a fraction and that would be times 37 over 10 because you see whatever the number here is that's my numerator and however many places I have in the decimal here that tells me what I'm dealing with how many zeros I have so I only have one decimal place of one zero and so that's 10 so I'm at 37 tenths now okay looks to me like I can simplify this one so 21 is the same thing as 3 times 7 and 24 is the same thing as 3 times 8 all right I can cancel 3 with the 3 and so now I have 7/8 times 37 over 10 and that equals 8 times 10 is 80 and 7 times 37 see I have 37 times 7 so 9 7 is 49 carry my for twenty-one twenty five twenty five to fifty nine is my numerator 259 all right there's my improper fraction that is the correct answer however you might need to you might have been instructed to turn that into a mixed number or simplify that as much as possible so let's get some room to work here you can always go get you know a piece of scratch paper all right let's see how do I turn 259 and 80 so that would be 259 my number N and I'm going to divide that by 80 all right 80 will certainly not go into two and 80s will certainly not go into 25 but 80 will go into 259 three times because three times 80 is 240 over 240 and that leaves me with 19 left over at the end so I'll add a decimal here so 3 times 80 is almost 259 that's going to be 3 and some decimal points and 80 will not go into 19 but it will go into 190 and so let's see 2 is 160 and that leaves me with 30 left over 80 will not go into 30 but it will go into 300 so 80 times 3 is 240 leaves me with doing some subtraction here 60 and 80 will not go into 60 but it will go into 600 and it will go 7 times 7 times 87 times 8 that's 56 56 and I have a 0 and that leaves me with 40 and 80 will not go into 40 but it will go into 400 and let's see 5 times 80 is 400 so five times 80 is 400 and so we do the subtraction we line it with zero so our answer is three point two three seven five that's the end you're now ready to try other basic math self tests you may contact me at alan morris at yahoo.com As found on YouTube