Basic Math SKills Self Test Number 3



this basic math skills self test number three is very similar to one and two same topics are going to be covered we've just changed the problems a little bit okay you have twenty different problems for you to try when you see a new problem and click on the stop sign and that will pause the video if you're watching this on YouTube try to work out the problem on a piece of scratch paper and then click on the go sign and you'll see the problem worked out number one you want to turn 0.72 five into a fraction and then simplify your answer click on the stop sign alright let's see how you did well seven twenty five that's going to be our numerator because we don't have to pay any attention to the decimal when we're figuring out what our numerator is but the decimal is very important when we figure out what the denominator is going to be here we have three numbers to the right of the decimal that means we're going to have three zeros in the denominator this is called if somebody were to say what this is they would say oh it's seven hundred and twenty-five thousandths and here is the fractional form 725 thousands all right we'll take a look at this and we say let's factor this we know that twenty-five will go into a thousand forty times so forty times twenty-five will give us a thousand and then we take a look at this and we say how many times will 25 go into seven hundred and twenty-five all right we know that 29 times 25 is going to be seven hundred twenty-five now we have a twenty-five in the numerator and we have a twenty-five in the denominator they cancel with each other they don't just go away they don't become zero they don't become two nothing they become the number one that's pretty important sometimes now we have twenty nine times one so that's just twenty-nine and forty times one is 40 and I don't see a way that we could factor this any further so what this means is if we did the top and bottom out if we divided 40 into twenty nine we would come up with zero point seven two five number two you're going to turn 7/16 into a decimal click on the stop sign okay let's see how you did it's just a long division problem so our seven goes in and 16 goes out we know that 16 will not go into seven so we'll just put a zero here and a decimal our answer is going to be smaller than 1 because 7/16 is smaller than one now 16 will go into 70 four times and 4 times 16 is going to be 40 plus 24 is going to be 64 what I just did was I know that 4 times 10 is 40 and 4 4 times 6 excuse me is 24 so then I just added 40 and 24 in my head and so we now could do the subtraction we wind up with a 6 60 will not to 6 16 will not go into 60 but we do know that it will go into 60 so it'll go 3 times and 3 times 10 is 30 3 times 6 is 18 that's 48 I do my subtraction and I wind up with 12 I know that 16 will not go into 12 but it will go into 120 and it will go 7 times 7 times 10 is 70 7 times 6 is 42 70 plus 42 is 112 that leaves me with 8 left over I know that 16 will not go into 8 but it will go into 80 exactly 5 times and this terminates because now is 0 so my answer is 0 point 4 3 7 5 ok let's see how we did the answer that we got for number 2 is zero point 4 3 7 5 and if we just shift the decimal 2 places that turns it into a percentage and a percentage means it's over 100 so we have the answer forty three point seven five over 100 if we did the long division on this we would get zero point four three seven five okay all units are in feet the rectangles are proportional what is the length of x click on the stop sign all right we have proportional rectangles we know that we've been told that so we need to find out the length of X we need to know what this length is right here and so a couple of ways we can do this we can compare the ratio the length of this side to that side with the length of this side to that side and it would look something like this we can put 4 over 6 equals X over 11 and then we cross-multiply and we'll get the same number so 4 times 11 is 44 and 6 times X is 44 now we have to solve for X so we have 6x and it doesn't matter if we say 6x equals 44 or for our X 6 equals 44 it's just more traditional to say 6x equals 44 so we know that we have 6x equals 44 whatever we do to this side we need to do to this side so let's divide both sides by 6 the reason we're dividing both sides by 6 is so we get X on one side by itself that 6 cancels with this 6 making it a 1 and making it a 1 1 times X is x over 1 and x over 1 is just X so now we have x equals 44 over 6 and then I would look at this and immediately say well I can cut 44 and a half to be 22 over three and forty four six and twenty two thirds are equivalent fractions that is if we did the top and bottom out on both of these we did the long division we would get the same answer and so now I look at this I know that 3 will go into 22 seven times and that will leave me with one left over and I'm doing in thirds so X is going to be seven and one-third feet or 20 2/3 feet okay number five uses the same drawing so now what you're gonna have to do is remember what you had for the answer for number four and that would be 7 and one-third feet or 20 2/3 feet the same amount what is the area of the larger proportional rectangle click on the stop sign all right you use the information in number 4 to help you figure out what the length of X was and now you need to use that information to find out what the area of the larger rectangle is area formula for areas Y rectangle is just length times width and so we're just now going to plug in those numbers so and that's what's nice about a formula is you just plug in the numbers and so we have I'm going to make it 20 2/3 that'll be easier times 11 and these are feet and this is feet and I'm just multiplying a fraction times a fraction you can just put that over 1 if I wanted so I have 22 times 11 and 22 times 11 is 242 and then 3 times 1 is 3 so it's 242 feet thirds there are 240 2/3 feets alright so now what I have is this is my answer but that's not a very useful answer so need to simplify that a little bit how many times will 3 go into 242 and so we come over here and we say top in 242 and 3-3 will not go into 2 but 3 will go into 24 exactly a times and so that gives us 24 we do the subtraction and we wind up with 2 3 will not go into 2 so we'll add a 0 we're at the end here so we'll put a decimal a 3 will not go into 2 but 3 will go into 20 and it'll go exactly 6 times and so that gives us 18 we do the subtraction and we get to again and so that tells us that we're going to be a loop here and so three will go into 20 exactly six times and we wind up with that being 18 and that's 2 and so we know that it's just going to be 80 point six six six six six six so we'll just put 80 point six six six put a line over that and we are dealing with feet squared because we're talking about area the correct answer is going to be 80 point six six six feet squared and this is also two-thirds so we could say that our correct answer is going to be 80 and two-thirds feet squared all right number six the square root of twenty two point three is between what two consecutive whole numbers now refreshing your memory or consecutive just means that they they come in order like seven and eight nine and ten fifteen and sixteen and so click on the stop sign all right let's see how you did square root of twenty two point three is between what two consecutive whole numbers well we're going to pick the square root of 16 and the square root of 25 it's hopeful that you can see that the square root of 22.3 falls somewhere between the square root of 16 and 25 now the square root of 16 that's just 4 and the square root of 25 that's just 5 4 & 5 are consecutive whole numbers so the square root of 22 point three is somewhere between 4 & 5 ok the triangles are proportional what is the angle measure of the unknown acute angle click on the stop sign all right what they're asking is what's this angle right here and so if we know that these are proportional then we know that this is 90 degrees and we know that this is 22 degrees and we also know that all triangles internal angles of all triangles sum to exactly 180 degrees so what that means is this angle right here that we'll call X because we don't know what it is and that's the traditional thing that we use when we don't know something we know that 90 i'm–it's degrees plus X degrees plus 22 degrees equals 180 degrees if I subtract 90 from each side I wind up with X plus 22 equals 90 because I've just subtracted 90 from each side so 180 minus 90 is 90 and now if I subtract 22 from each side I wind up with x equals 68 and we're talking about degrees so the correct answer is 68 degrees all right make a sketch of the coordinate plane then sketch a circle that has a radius of 1.5 and is centered at the ordered pair 3 comma 3 point 5 click on the stop sign okay I look at this and I think all right the Cartesian coordinate plane that I need to make is all going to be in the first first quadrant I won't be using the second quadrant third quadrant or fourth quadrant simply because everything is going to be taking place in the first my ordered pair the center is located at 3 2 3 & 3 point 5 so I'll sketch here 1 2 3 and point 5 would be somewhere about right there so the center of my circle is going to be here the radius of my circle is going to be 1 and 1/2 so I'm going to go down 1 and a half to about here that dot will fall on the circle and then I go over 1 and 1/2 this dot will fall on the circle and then I go up about that same amount and I'll go over about it so what this has done is give me a target so when I freehand sketch my circle I have some points that I can hit and there we go I now have a circle located at 3 comma 3 the ordered pair with a radius of 1.5 and it's all within the first quadrant ok number 9 it's pretty straightforward multiply a bunch of fractions click on the stop sign all right let's see how you did multiplying fractions is pretty easy you simply just multiply the numerators and then you multiply the denominators and then simplify so 7 times 3 is 21 times 1 is 21 so our numerator is 21 and our denominator 8 times 4 is 32 times 3 is 96 so we're gonna have 21 over 96 and now we need to simplify this I look at it and say hmm I know that 3 is a multiple here and threes a multiple here because 3 times 7 is 21 and 3 times 32 is 96 I now have a three in the numerator I have a three in the denominator and my final answer is going to be seven thirty seconds number ten it's just a division by a fraction click on the stop sign okay dividing by a fraction let's see how you did so we have nine divided by one half that's the same thing as 9 times 2 over 1 and so we could make that a fraction now we're just multiplying two fractions so 9 times 2 is 18 and 1 times 1 is 1 and any number over itself is just that number so the correct answer is 18 refreshing your memory I'll take a quick peek here at why it is that we flip over the dividing fraction if I have 1/2 divided by 1/2 you know that 1/2 will go into 1/2 exactly one time so the answer to this is going to be 1 but if I have 1/2 divided by 1/2 and I flip over the dividing fraction and then multiply I should still get 1 so I have 1/2 times 2 over 1 having just flipped over the dividing fraction and now I multiply 1 times 2 is 2 and 2 times 1 is 2 and any number over itself is 1 alright number 11 what is the area of the figure shown click on the stop sign give it a whirl okay the figure shown is called the trapezoid the formula for finding the area of a trapezoid is base one plus base two all of that multiplied times the height and all of that divided by two that's the formula this is a base the bases of your just your parallel lines and this is another base so it doesn't matter which one you call base water base two you simply just add these together and so four and a half plus six and a half is 11 now I have 11 times 3.2 and all of that divided by 2 11 times 3.2 is thirty five point two and all of that divided by two and this is my final answer is going to be in feet squared so I could be I would be good form to go ahead and keep the measurements the units connected to this so now I have thirty five point two divided by two and that's going to be equal to seventeen point six and my answer is going to be feet squared so my correct answer is seventeen point six feet squared all right number 12 make a sketch of the depiction below and then reflect it across the x-axis click on the stop sign okay let's see how you did well this is our x-axis and we're reflecting it across the x-axis so you should have made something that looks like that and if you did that you're getting it right number thirteen sketch the drawing below and reflect the figure across the y-axis click on the stop sign okay this is our y-axis and we're going to reflect it across it so I'm going to attempt to freehand something that shows the reflection so looks something like that and so if you do something that looks like that you're getting it right all right what is the area and perimeter of a right triangle that has two legs that are four feet and five feet and a hypotenuse that is six point four feet click on the stop sign okay it's my strong suggestion that you always make a sketch so let's see it wants to know we have a right triangle and it tells us that one of the legs is going to be four feet and one of the legs is going to be five feet and our hypotenuse is going to be six point four feet now so let's feet that's feet and that's feet then it says what's the let's tackle the first a easy one first that'll be the perimeter what's the perimeter well the perimeter of anything is just you total up all the sides so it's the edge so four plus five plus six point four is going to be fifteen point four and perimeter is just length is going to be feet so that's our perimeter now it says find the area well in order to find the area that we need to know the formula and the area formula for a triangle is base times the height all of that divided by two and it's a formula so we just plug in the numbers so it's four times 5/2 four times five four times 5/2 is going to be 20 divided by two and how many times will to go into 20 they'll go exactly ten times and we're talking about ten feet squared so the correct answers are ten feet squared and 15 point four feet for the perimeter sketch a triangle and label three of its main parts click on the stop sign okay well we'll sketch the triangle see how you did all right this is a leg this is a leg this is the hypotenuse this is the area this is a right angle this is an acute angle this is an acute angle those are some of the main parts of a triangle okay here we're going to be adding and subtracting positive and negative integers click on the stop sign all right we're going to start off I only just draw a number line here we're going to start off at negative 11 and then we're going to add negative 10 which means that we're going to go to negative 21 and then we're going to add 32 which means that we're going to go in this direction on the number line that'll take us from 21 to adding 32 will take us back to 11 so we are at 11 on the number line and now we're going to take away a negative amount taking away a negative amount is a positive thing so one of the ways that I remember that is I will use this minus sign right here to turn this into a plus sign and if I use it it goes away so it's no longer there and so now I'm at whatever my answer was plus 9 and 11 plus 9 is going to move me in this direction and that's going to make it the final answer being 20 perhaps another way that might help you remember how to deal with taking away a negative thing I do that another way that I do that is taking away a negative thing is a positive thing all right what are the measurements below click on the stop sign well let's see the distance from here to here is one inch it's divided into 16 equal marks and those 16 equal marks are called sixteenths and by the way the sixteenths the marks that are between here are exactly the same 16th March that are between 1 & 2 and between any two numbers on the number line so or on the ruler so what we can do here is just count them we have 1 2 3 4 5 6 we have 6 sixteenths well 6/16 can be simplified and 6/16 equals the equivalent fraction of 3/8 perhaps what you might notice is that the distance from here to here is 1/8 that's two eighths that's 3/8 all right B is 1/16 two sixteenths three sixteenths it's three sixteenths can't simplifies three sixteenths anymore so it's three sixteenths of an inch that's what those two little marks mean and now we'll take a look at the next one here we have this is one inch and one inch is the same thing as 16 16 so we have 17 16 eight sixteen nine sixteenths one inch is the same thing as 16 16 so here we have seventeen sixteen eighteen sixteen nineteen sixteen twenty sixteen so we could say that this is 2016 that's not the best form and so perhaps you notice that you are at one and one two three four sixteenths so we're at one and four sixteenths however one in four sixteenths inches can be simplified and we can simplify that to one and 1/4 because 4/16 simplifies to 1/4 and these are inches now here we have D we are at 2 and we have 1/16 two sixteenths 3/16 four sixteenths 5/16 6 16 7/16 8 16 s we are at 2 and 8/16 2 and 8 16 simplifies to 2 and 1/2 and we're dealing in inches so if you got those right you know how to read a ruler all right how many minutes are in one eighth of an hour click on the stop sign okay let's see how you did well there are 60 minutes in an hour and we're going to multiply that times 1 over 8 and we can put 60 over 1 just to make it a fraction now we're multiplying 60 minutes in an hour so we have 60 divided by 8 that's now just a long division problem we come down here 60 goes in it goes out 8 will not go into 6 but 8 will go into 60 it'll go 7 times 7 times 8 is 56 we do the subtraction that gives us 4 8 will not go into 4 but it will go into 40 we reach the end here so we place the decimal and 8 will go into 40 exactly 5 times and we terminate so the question was how many minutes are in 1/8 of an hour 7 point 5 minutes okay number 19 paula charges $10 per hour for her handyman services if she worked six to 11 hours per day for four days what is the range of her gross pay click on the stop sign okay let's see how you did refreshing your memory gross pay just means the total amount that she got and range means what's the low number to the high number so let's see let's just kind of chart this out let's get it organized she makes $10 an hour for handyman service if she works 6 to 11 hours a day so let's say on day 1 she works either 6 or 11 hours and on day 2 she does the same thing 6 to 11 hours day 3 she does the same thing and day 4 she does the same thing well so 6 times 4 number of days that she worked will be the minimum number of hours that she worked at that week and that's 24 hours and if we want to know what's the maximum number of hours that she could've worked we can just multiply 44 times 4 the number of days that she worked and we'd get 44 so she either worked 24 hours or 44 hours or somewhere in between the range of the hours that she worked was 24 to 44 but she makes 10 bucks an hour so we'll multiply those times 10 and so we have 240 dollars or we have four hundred and forty dollars so Paula either makes 240 dollars or she makes four hundred and forty dollars or somewhere in between the range is 240 to 440 number 20 we're going to have to multiply a little bit here and divide so click on the stop side and give it a whirl all right let's see how you did first thing we need to do is that which is in the parenthesis so we multiply 5 times 7 that's just 35 and 6 times 9 that's 54 and we're going to divide that by 2.7 a couple of options here we can turn this into a fraction we could turn this into a decimal I think I'm going to multiply this times 27 tenths we can turn this into 27 tenths 27 over 10 and then to multiply our tubing to divide by a fraction I just flip it over so now this is going to be times 10 over 27 and this one's pretty easy I 35 times 10 is 350 and my denominator is going to be 54 times 27 that's going to be 14 58 1458 and I simply now can simplify this or I could do the long division process top and bottom out and if you do the long division process on this you should come up with the answer of zero point two four zero zero and goes on after that so correct the two decimal places our answer is zero point two four that's the end you're now ready to try other basic math skills self tests you may contact me at Allen Morissette yahoo.com

27 thoughts on “Basic Math SKills Self Test Number 3”

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  5. #1- How do you know that 29×25=725 so fast when simplifying fractions? Is there a method? I would have had to play around with numbers to get a total close to 725. I noticed you know them in other examples too. Thank you

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  8. 9 ÷ 1/2 = 4.5??????!!! it's hilarious that somebody told you to stop lying. .. maybe she mean9x1/2.. anyway thank you sir, this video helps me alot .. If you dont mind. If u have any other page i would like to follow you on twitter, Facebook, etc. I know I'll need your help in the future.THANK YOU SO MUCH!

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