ATI TEAS Version 7 Mathematics Numbers and Algebra (How to Get the Perfect Score)

what's going on all of my Healthcare brothers and sisters I hope that you're having a wonderful day the atit's version 7 mathematics portion has two parts the first part we're going to cover in this video and that is numbers and algebra let's get started so as always We Begin by looking at the objectives specifically what is it that I need to know to pass this exam well there's going to be a total of 18 questions out of the cumulative 34 questions for the mathematics portion and what you're going to need to know is converting among non-negative fractions decimals and percentages performing arithmetic operations with rational numbers comparing and ordering rational numbers solving equations with one variable solving real world problems applying estimation strategies and rounding rules to those word problems and then when it comes to solving little problems you're going to need to know how to use proportions ratios and rates of change as well as Expressions equations and inequalities so we're going to begin by looking at fractions specifically the relationship between the numerator and the denominator so fractions can be written in the form as A over B so typically on your exam you're going to see A over B right where A and B are both integers and B is not equal to zero you can never have a zero at the bottom of your fraction integers are set of whole numbers and they're opposites so the bottom integer is called the denominator and the top integer is called the numerator the line between them represents division so A over B really reads as a is divided by B so for example for the fraction three over four the numerator is 3 right that is that number on top that's our numerator and then our denominator is four that's the number on the bottom so how do we calculate percentage so a percentage is a number or ratio expressed as a fraction of one hundred it is often denoted by using the percent sign right that's that beautiful sign that looks like this that is our percent sign so for example we have 35 percent we know that 35 percent is equivalent to the decimal of 0.35 or the fraction 35 over 100. to calculate a percentage we're just multiplying that decimal by 100 or we're dividing the fraction by 100 to reduce it into its lower terms so as you can see if we were to divide this by 100 right 35 over 100 we're just going to move the decimal place over two times so we have the number 35 we know we have 35 percent this is where our decimal would be because we have a whole number and we're going to move it over two times one two and because we have a decimal in front of a number with nothing in front of that we add zero so 35 percent right is going to be equal to 0.35 which is also equal to 35 over 100 as we outlined in our example sometimes you're going to have to identify place values with decimals so every digit in a number has a place value associated with it the place value of a digit tells us that the digit is worth in relation to the other digits found within that number so for example we have 1234 here as an example there is a total of four digits with place values in the ones place place values in the tens place place place values in the hundredth place and place values in the thousand place so as you can see R1 Falls in a thousand our two falls in the hundred our three falls into the ten and our four falls into the one to find the place value of a digit you need to look at its position in that number the place value of the digit will be the base right so that's that 10 100 1000 so on and so forth to which that position corresponds the decimal part of a number can be read using place values as well so anything behind a decimal the place values of the digits to the right of the decimal is tenths hundredths and thousands right we have our decimal place here tens hundreds and thousands so for example we have the number zero I'm sorry .035 so this is where our digits fall so our zero falls in the tenths place our three falls in the hundreds place and our five falls in the thousands place all right so let's get started with the fun stuff right that's that kind of version of one thing to another starting with fractions to decimals and percentages so in order to convert a fraction to a decimal we have to divide the numerator remember that's our top number by the denominator which is our bottom number so for example we have three over four right we need to convert that uh to a decimal so how do we do that we divide three over four with a simple calculator you were going to have on your atits once you do that division you're going to find that it is 0.75 now we also need to convert fractions to a percentage right and as we talked about before we're simply going to multiply it by 100. so for example we have a decimal um we already figured out what our decimal was with three over fourths right we divided that it was 0.75 so 0.75 we have to convert that to a percentage and we do that by moving over per decimal so if we have 0.75 we're going to multiply that by 100 which means the decimal is going to move to the right not the left when you divide it's going to move to the left when you multiply it's going to move to the right so now we have 75 because our decimal falls behind our whole number so let's take a closer look at converting decimals to fractions and how we're going to do that is in order to convert a decimal to a fraction we have to divide the decimal by the place value of the decimal part and remove the decimal from the numerator so how do we do this so we have a fraction and let me I'm sorry we have a decimal that we need to convert that is 0.75 to a fraction we are going to divide 0.75 by a hundred that's the whole number because that 7 5 Falls that last number Falls in that hundredths place right so we're going to divide our 0.75 by 75 over 100 and that is going to be the answer to our fraction however we can simplify that fraction into its lowest form so with 75 over 100 we have to figure out what number can we divide the numerator and the denominator by in order to get the simplest forms well in this particular case 25 the number 25 is easily dividable with 75 as well as 100. so when you divide 75 by 25 you get three and when you divide um 100 by 25 you get four giving us the answer of three fourths another example of converting a decimal to a fraction can be in this particular example we have 0.584 well we have an additional number right so we can't divide it by a hundred this time we have to divide it by a thousandth right because that last number Falls within that thousandths place so in this particular case our 0.584 is going to become 584 over 1000. and the last conversion we're going to look at is converting percentages to decimals as well as fractions so we start by converting our percentage to a decimal and we talked about this before if we divide we're going to move the decimal place to the left if we multiply we're going to move the decimal place to the right so as we can see here in our example we have to convert 75 percent to a decimal how do we do that we divide we put 75 over a hundred right we're going to divide that so we know that we have a whole number of 75 any whole number is going to have the decimal place after the whole number and again we're dividing we're going to move it two times to the left one two our decimal place goes in front of our 75 but now we no longer have any placeholder before that decimal so we have to add a zero right so that gives us 0.75 and then lastly we convert our percentage to our fraction we kind of already did that in our previous example right so now we need to convert 75 percent to a fraction so how do we do that we place 75 over 100 because as we know our percentages are typically a hundred percent right 75 percent usually Falls within that 100. so again we can simplify this and we did this before and how do we do that well we go ahead and we look for that common number that we can multiply or sorry divide both our numerator and our denominator by in order to get a simpler term a simpler fraction and we know that that number was 25 right so if we divide 75 by 25 that gives us 3 and if we divide 100 by 25 that gives us 4. so our simplified fraction of 75 over 100 is three-fourths so we're going to start moving on to order of operations the order of operations is a set of rules that determine the order for which operations occur that's addition subtraction multiplication division Etc the order of operations is often abbreviated as PEMDAS so the P stands for parentheses first the E stands for exponents that's our powers and our square roots our MD is multiplication and division so anytime we have multiplication and division in one of these order of operations questions we move from left to right okay we don't do multiplication first or division first it's whatever falls on the left and then we just move our way down to the right same thing with addition and subtraction we start from the left and move our way over to the right so for example and it's a little hard to tell so I'm going to write it out we have 3 squared Plus 2 squared which operation should we perform first is it the addition or the exponents well as you can see based on what we have here in our PEMDAS example we're going to do the exponents first right that is the very first thing that we're going to do so 3 squared is equal to 9 it's basically 3 times 3. and 2 squared is equal to 4 right now all we have left is addition and that part's super easy 9 plus 4 is equal to 13 and it gives us our answer of 13. so we had a pretty simple problem before now we're going to get a little bit more complicated right so this is multiple step problems so we're going to begin by looking at our example and our example is 24 divided by 12 plus 17 minus 11. so how do we do this do we have any parentheses no right so we don't need to worry about parentheses do we have any exponents now that I can see here right so that is also a no so now we have multiplication and division and remember we talked about that before we're going to move from left to right when we're looking at multiplication and division in this particular case it's a little bit easier because we only have one form of the multiplication and division in that's division so we start with that 24 divided by 12 is equal to 2 right 12 times 2 is equal to 24 that can also help you get there as well so now we have a problem that is 2 plus 17 minus 11. so we move on to our addition portion right so again addition and subtraction we move from left to right so in this particular case we have 2 plus 17 that's equal to 19 right and then we have 19 minus 11. and that is equal to 8. so the correct answer for this multiple step problem is going to be eight and lastly we're going to take a closer look at operations with parentheses so we have our expression here we have parentheses 15 minus 12. plus 18 divided by parentheses 21 minus 11. so again we just moved down our PEMDAS right so do we have parentheses yes absolutely we do we're going to move from left to right so 15 minus 12 is equal to 3 and 21 minus 11 is equal to 10. so now we have eight of three plus eighteen divided by 10 is equal to what so now we're going to take a look at this do we have any exponents again moving down the line no no exponents right no powers no square roots do we have any multiplication or division yes absolutely we do so what do we do we have 18 divided by 10. that is going to give us 1.8 and we just keep moving our equation down so now we have 3 plus 1.8 what does 3 plus 1.8 give us it gives us 4.8 so the correct answer for this operations with parentheses is going to be 4.8 let's take a closer look at defining rational numbers as well as irrational numbers we're going to start with those rational numbers so rational numbers are numbers that can be expressed as a fraction a over B remember we talked about that before A and B are both integers and that denominator cannot be equal to zero that is they can be written as a ratio of two integers if that makes sense so we have an integer on top integer on the bottom the bottom number cannot be equal to zero so some examples of this can be negative one-half this can also be written as negative 25 over 50 right if we were to simplify it in its simplest terms that's what it would equal we can also look at three-fourths right that can also be written as 75 over 100. we've done a ton of math problems so far with that example we also have 0.125 remember that last number 5 Falls within the thousandths place so we have to divide it by a thousand so that can be Rewritten as 125 over one thousand we have negative 0.75 again that 5 Falls within the hundredths place right so we divide it by a hundred so that can be Rewritten as negative 75 over 100 and then lastly we have negative 15 which here it's listed as an example that can be written as negative 15 over 100 but that's absolutely false just ignore that but we can see that negative 15 is a whole number making it a rational number so now we're going to take a closer look at irrational numbers so irrational numbers can't really be expressed as fractions they'll never truly be equal to what they're expressing this means that they cannot be written as a ratio of two integers right so for an example Pi Pi you're going to see all the time and while it is written here as a fraction it's not completely equal to that fraction right because Pi is such a long number there's just no way to make it into a fraction you also have the square root of 16. the square root of 16 is one of those weird numbers because there really isn't such a whole number that's going to be equal to the square root of 16. so while we do have an approximation of it being equal to 25 over 41 it's not exactly equal to that and then lastly we have e this is approximately equal to 27 over 28. you see this all the time on your scientific calculators when you're doing those calculations however e is not really equal to that 27 over 28 it's just an approximation so that's how you get irrational numbers versus rational ones so how do we put these rational numbers into order so rational numbers can be ordered by least to greatest or greatest to least in order to put rational numbers in order from least to greatest we line them up in order from left to right the numbers are larger as you go from left to right right so your negative numbers are least they're going to be on your left and your positive numbers are going to be greater they're going to be on your right so we have an example here of negative 15 negative 0.75 0 0.125 one half and three-fourths that is how we go from least to greatest what I would suggest is when you're taking the test that you convert these numbers into fractions or into decimals probably in this situation would be better to do it in decimal points that way you're able to see um specifically that one half and that three-fourth being greater than 0.125 and how that goes down the line so again go back and review that if you're still having a little bit of trouble and we'll do some practice questions um in order to put our rational numbers from greatest to least we're going to line them up from right to left right so the numbers are going to be larger as you go from right to left so in this case you've got three over four one half 0.125 0. negative 0.75 and negative 15. so all we did is literally reverse it our greater numbers are going to be on the left and our more negative numbers are that's going to be our lower numbers are going to be on the right when you're ordering negative numbers remember again like I said that smaller number um is going to be wherever that least is and then those more positive numbers there's going to be the larger ones are going to be wherever the greatest is there's also a case of absolute value of negative numbers always being less than the absolute value of positive numbers and we'll talk about that a little bit later so now let's look at comparing our rational numbers so sometimes we're going to have to look at rational numbers and compare them by their relative size that is which number is larger or smaller than the other so for example if we compare numbers negative 15 and negative 1 because negative 15 is less than negative number but we just talked about that the more negative the number the less it is we can write it as follows negative 15 is less than negative one you can also find the answer by using a number line or plotting your values sometimes that'll be available to you therefore the value that is farthest right away from the center is going to be the Lesser number right so as we go all the way to the left that's usually where your negatives are the farther left you go the lesser the number it is the closer rights you go right the closer back to midline it's going to be greater because as we know when we're looking at a graph as we move to the right the numbers get more positive and as we move toward the left the numbers get more negative some of the symbols that you're going to see that you're gonna have to be very familiar with are the examples that I have listed here so we have the sign for greater than the easiest way to remember this is that remember Pac-Man Pac-Man is going to eat the biggest numbers right so whatever number is bigger it's going to eat so we have greater than and then we have greater than or equal to that's that little Dash that falls behind the greater than right we have equal to we're very familiar with equal to we use it all the time with our math equations we have less than or equal to right we talked about that before less than or equal to again it's going to be eating the bigger number so if your number on your left is greater or I'm sorry is less than the number on your right then your little Pac-Man is going to be facing the other direction right it's going to be facing other way eating the bigger number and then we have less than which here it's not listed right it should just be this and again there's no line underneath it it's just less than it's eating the bigger numbers so if the number on the left is less than the number on the right then the little Pac-Man is going to be eating the bigger number giving us a less than symbol all right so we're going to start looking at solving equations with one variables in order to do that we have to be able to identify the terms of an algebraic equation so an algebraic equation consists of terms such as a number variables or products of that of those numbers terms can be separated by addition as well as subtraction signs so we have a constant which is defined as the number itself it's not attached to a variable there's no X or Y attached to it we have a variable which is a letter that represents an unknown quantity we usually use X or Y and then we have a coefficient that is the number being multiplied by the variable so let's take a look at our example here we have negative 15x minus 18 is equal to 30. well our consonants as we know those are those numbers that are not attached to variables is going to be 18 and 30 right negative 18 is not attached uh to a variable as well as 30 is not attached to a variable and we say negative 18 because we just pull over that minus sign because it's going to make the number negative our variable right is going to be negative 15x we know that because this is the only number that has that X attached to it and then lastly we have our coefficient that is the number that's being multiplied by the variable we already know that negative 15x is our variable so the coefficient the number that's being multiplied by the variable is that negative 15. if we were to take the X away right we're only left with negative 15. that is what's being multiplied by our variable so let's talk about inverse arithmetic operations so the inverse of an arithmetic operation is an operation that undoes the original operation sort of your example the inverse of addition is subtraction right and the inverse of multiplication is division the inverse operations of addition and subtraction are opposite of each other and that's the same to be true for multiplication as well as division this has to be true in order for an operation to undo each other so for example if you had something that said you need to multiply this so let's say you had 1 plus X is equal to 3 and you're trying to figure out what x is equal to right as we know over here our 1 is a positive number right it doesn't have a negative in front of it in order for us to isolate X we need to get rid of that one over here on the left hand side of the equation how do we do that we inverse the arithmetic operation we're going to uh subtract 1 from each side right so if we have 1 minus 1 that is going to automatically cancel it out then we are left with X is equal to we have 3 minus 1 2. so as we know X is going to be equal to 2. that is what we are talking about with inverse arithmetic operations is we are either going to have to do the opposite of addition and subtraction multiplication or division so let's take a look at another example we're going to implement a sequence of steps in order to solve an equation so to solve this equation you need to find the value of the variable in this case the variable is X we have no coefficient right there's nothing before the X so we're looking at a simple equation here so we have X plus 18 is equal to 30. so I'm going to go ahead and just write that down here so that way it's just a little bit bigger perfect so now we need to isolate X in order for us to identify what x is equal to we have to remove that positive 18 from the left side of our equation how do we do that we just talked about it we're going to use inverse arithmetic right we're going to minus 18 from each side of the equal sign so when we minus 18 positive 18 minus 18 is equal to 0 right that gives us our X isolated on the left hand side so then now we have 30 minus 18. 30 minus 18 is equal to 12. so we know that our X is equal to 12. what I will tell you is always plug in your X to your original equation to see if it makes sense 18 plus 12 is equal to 30. absolutely makes sense we can say for sure that the X the variable in our equation is equal to 12. so again we're going to take a look at another example and we're going to be solving proportional relationships right that's equations and inequalities with one variable so a proportional relationship is a relationship between two quantities in which the ratio of one quantity to another is constant or when one fraction is equivalent to the other so let's just take a closer look at our equation here let's leave out all the verbiage and we'll just figure this out together so we have 6 x is equal to 19 right well again we need to use our inverse arithmetic that we discussed before because we need to isolate X now before it's really easy right because we had addition as well as subtraction but in this particular case we have multiplication right we have 6 is multiplied by X so in order to isolate x what we need to do is we need to divide it by six and we're going to divide both sides of the equal sign by 6. so 6 divided by 6 is equal to 1 right so that helps us isolate our X on the left hand side now we're left with 19 over 6. that's pretty much our answer unless I wanted you to divide it down to a decimal point we can say that 19 over 6 is equal to 3.17 but when you're taking your exam most likely they're just looking for this fraction in order to identify that you're able to use that inverse arithmetic now we're going to start looking at real world problems right word problems everybody hates them I get it but we're going to work through them and hopefully we can figure them out together the first step to solving these word problems is to read the problem carefully and identify the information that is being given as well as the information that is needed right there's always something that we need out of the information that is provided the next step is to identify the problem type and the equation that needs to be solved once the equation is identified then you can solve the equation the last step is to check your work by substituting the answer back to the original problem so here's an example of a word problem we have a plumber who charges 25 for a service call plus fifty dollars per hour for service write an equation to find the cost of a plumber's service if he works for eight hours so the first step is to read the problem and identify the given information right the given information is that the plumber charges 25 to the service call that's a one-time charge right and fifty dollars per hour for the service the needed information that you need is the Plumber's service for the hours that they work right that's that h the next step is to identify the problem type and the equation that needs to be solved and then of course our last step is going to be checking our work by substituting the answer back to the original problem so when we're taking a look at this we know that we have to figure out the costs we're just going to use the letter c for this particular plumber we know that this plumber is going to charge us 25 dollars right that's a one-time charge for them to come out and they charge fifty dollars per hour for them to come out to your house so right away we have automatically already put in our equation right we already know what it's going to be the total cost for this plumber to come out is going to be that 25 one-time fee and then fifty dollars for every hour that they're there if the plumber let's say the plumber comes out and they work two hours right they're at your property for two hours all you're doing at that point is plugging in the amount of hours so as We Know we'll have C is equal to 25 that one-time Cost Plus 50. times the two hours so if we times 50 by 2 we get a hundred right and then we just have 25 left for the total cost so we know that if this plumber was to come out to our house fix whatever the problem was they're going to charge us a total of 125 dollars if they spent two hours doing the work you can do this by absolutely substituting your answer and for the cost and then performing it backwards otherwise we already know the answer for this word problem so let's take a look at solving word problems using percentages so percentages are a way of expressing the number as a fraction of 100 we talked about that before percentage numbers increase or decrease in word problems so in order to solve these particular problems that involves percentages increasing or decreasing you need to identify the following information one what is the original amount two is the percentage increasing or decreasing and three what is the new amount right that's what the problem is looking for once you have this information you can set up and solve your equation so for example we have an example here if a store is offering a 20 discount on an item that was originally costing the person a hundred dollars the new price of the item would be eighty percent of the original price right it's going to be eighty dollars because as we know we are decreasing that's what that word discount means right we're decreasing 20 percent so if we divide or a hundred dollars times point two then we get eighty percent right we get uh or we get eighty dollars um you can also divide it by point eight if you were looking for the total cost as well we know that it's the item is still going to cost us eighty percent because we're only getting a 20 discount so either way you will get the same answer it's just how you choose to find it so here is a long confusing one right we're going to be looking at a percentage increase so we're really going to break this down so the population of a town increased by 12 percent from 2010 to 2011. the population in town in 2010 was 20 000 people the question is asking what was the population of the town in 2011. so as we know the original amount of the population in 2010 was 20 000 people right there was a percentage increase in one year of 12 percent what ultimately isn't the new amount that's what we're looking for so to find the new amount we had to set up the equation right so we're going to have we're looking for the new amount hmm new amount is equal to 20 000 because we know that was the original population plus that 12 because we know that there was a 12 percent increase so how do we figure this out right there's a variable here that we don't know what is that new number so what we're going to do is we're going to multiply 12 percent by the original population so if we multiply 12 percent right times that twenty thousand it is going to give us two thousand four hundred that is how much the population increased right so we know that based on 12 we can use our decimal we can move it over twice to the left that gives us 0.12 we're going to multiply that by 20 000 people who are originally there to get what was that increase of the new population in 2011. however we're not done right because what the question is asking was what was the population of the town in 2011 that population of that town in 2011 wasn't 2 400 people there's still that original 20 000 people were there so now we're just going to take that 20 000 and we're going to add what we got from the percentage increase to the original population so twenty thousand plus two thousand four hundred people which was the increases equal to 22 400 people so based on this particular question it's asking what was the population of the town in 2011 it increased by 2400 people the original population was 20 000 giving us a new grand total of 22 400 people in the population of 2011. so now we're going to move on to measurements so metric measurements are going to be huge when you enter healthcare because we use it for everything the metric system is a system of measurement that is used by many countries around the world except for the United States the most common units of measurement in the metric system are length we use meters weight or mass we use grams capacity or volume we we use liters and when it comes to any kind of temperature we use celsius it's important to note that area is measured by square units and a volume is measured by cubic units we're going to dive much further into detail about the metric system in our other video but it is something that they just touch base on with this particular portion of the exam next we're going to move on to estimation and rounding of numbers one way to increase your speed and accuracy on the atit's math portion is to practice estimation and rounding of numbers this will help like help you quickly see the answer that should be in your head without having to do all of these calculations so for example if you're asked to round the number 45.687 I'm sorry 0.678 to the nearest whole number then you're going to be looking at the number that falls within the ones place right so we have 45 .687 the number we are looking at is 6 right this is what Falls within that ones place you will need to round up the number to the tenths place which is this one right here in order to get your whole number so what I will tell you is that anytime a number is greater than 5 or equal to five you're going to automatically round up if it's less than 5 meaning it's zero to four then you're going to keep the number the same so in this particular situation we have 45.678 we know that the number six is greater than the number five so we're going to round up so this particular equation is asking us to round to the nearest whole number rnr's whole number is going to be 46 however if for some reason say we had 45.45 again rounding to the nearest whole number we can see down here that 4 is less than 5 right it's not equal to or greater than 5. so we would just say that the nearest whole number to this equation is actually 45 because we're not going to round up because we don't need to since the tenths place is less than 5. so let's talk about proportions a proportion is a ratio in fraction form that equals another ratio in fraction form so when we're writing and solving proportions we really need to use the following steps we need to read the word problem carefully and identify all the information that is being given we need to draw a picture or a diagram to help us visualize what the problem is asking we need to to determine what quantity the equation is looking for this is that unknown quantity right those are those variables that we're trying to figure out we need to identify two equivalent ratios in the problem we need to write a proportion using the equivalent ratio and we need to cross multiply to solve the proportion and as always we need to check our answers so here is an example of a word problem that uses proportions so let's say that you have a ratio of docs to cats in a shelter that is 12 to 25. if there are a hundred animals in the shelter here we go 100 animals in the shelter how many of them are dogs in order for us to solve this problem we need to figure out what the unknown quantity is for the numbers of dogs that are in the shelter the ratio is going to look like 12 to 25 that's what we did and then 100 times x we're trying to figure out I'm sorry X not 10. just kidding times and I'll just put in parentheses so you can tell the difference times x right we're trying to figure out the number of dogs that are in that shelter so how we write this in regards to proportions is we write 12. over 25 is equal to X over a hundred because as we know the ratio to dogs to cats is 12 to 25 right we have 12 dogs and 25 cats so a 12 and then we have our X we're trying to figure out how many dogs and we have 25 cats to 100 total animals so how do we solve this so we do this by cross multiplication right so let me get a different color here we are going to cross and multiply these and cross multiply these in order for us to get our variable and our answer that we're looking for so 12 so what it's going to look like is 12. 100 is equal to 25 X right so now we need to do a little multiplication so we have 12 times 100 is equal to 1 200 right and then 25 times x is equal to 25x so we talked about this before we need to isolate X in order to get our answer so how do we do this we divide right we divide 25 divide 25. and that is going to give us I'm just going to write it up here because I'm running out of space X is equal to 48. so as we know there are a total of 48 dogs in the shelter and if we were to plug in that 48 to our equation it's going to give us the correct answer now let's take a closer look at direct proportions and constant personality so our portion is a direct portion of two equivalent ratios in the form of Y is equal to KX the constant of portionality that's K is the number that represents the relationship between the two variables so for example you're going to have direct proportional equations such as Y is equal to 3x or Y is equal to 10x or Y is equal to x divided by 6. you can also have not Direction not directly portional equations such as Y is equal to 5x plus 10. Y is equal to x minus 15 or Y is just equal to 5. that is how we tell the difference between direct proportional and non-direct proportional right when non-direct proportional we don't have we have another Co um another constant right at the end so Y is equal to 5x plus 10. Y is equal to negative 15. Y is just equal to 5 right whereas in our direct proportional we have a coefficient and a variable 3x 10x x divided by 6. so we're moving on to solving word problems using ratios and rate of change so one is a ratio a ratio is a comparison of two numbers by division so for example 4 to 5 or 4 divided by five right so really what is a rate unit rate and rate of change how do we figure that out well a rate is a ratio that is used to compare two different units so for example 60 miles per hour is also written as 60 miles right per an hour the unit rate is the rate in which the second number and the ratio is one unit you can find the unit rate by dividing the numerator that top number by the denominator right so again we have this same example so 60 miles per two hours or 30 miles per hour that's our unit rate and then we have rate of change and this is the speed at which something is happening it can also be known as the unit rate right so we talked about that a little bit before so for example the rate of change in population the rate of change in temperature the rate of change and distance so now we're going to look at using ratios and rated change to solve problems so when we're solving problems it's often helpful to think about the relationship between different quantities in terms of ratios and rates of change so for example what we used before if you know that the rate or the ratio of dogs to cats and a shelter is 12 to 25 and you also know that there is a hundred animals in the shelter then you can use these relationships to solve for the number of dogs in a shelter you can also use rate of change to solve problems so for example if you know that the average rate of change in a population over a period of time is 0.02 percent you can use this information to predict what the population of a city is going to be in the future these problems are easily solved with a representation of a graph to plot out your points these points usually form a slope within the lines and lastly we have Expressions equations and inequalities so what are expressions equations and inequalities well an expression is a mathematical phrase that contains numbers variables and operators so for example we have 10 minus 2y we have X right we have four parentheses x minus 16. those are expressions then we have equations right and that's usually denoted by having an equal sign so for example 10 minus y is equal to 10. X is equal to 10. 3x minus 10 is equal to 4X plus 8. this is an equation because all of these have an equal sign in the equation and then lastly we have an inequality that's the expression that contains those inequality signs that we talked about before that's that less than uh greater than less than or equal to or greater than or equal to those types of signs have a difficulty understanding specifically what inequalities are I highly recommend you go back and re-review that um so that way you can tell the difference between which way the Pac-Man is eating the greater number previously we looked at solving a lot of equations but we haven't really looked at solving inequalities so we're going to take a closer look at that to finish out this portion of our review inequalities are mathematical phrases that contains those inequality signs we talked about before they can be used to represent situations where one value is greater than or less than another value so for example the inequality X is greater than y right remember our Pac-Man is eating the greater number that is how it's going to read X is greater than y inequalities can be used to solve problems by representing relationships between two different quantities in a problem so for example we have X plus 2 is greater than 12. so just like with our other problems we need to isolate right our variable that X and how do we do that the same thing that inverse arithmetic we're going to minus 2 from each side so that is going to leave us with x is greater than 10 right if we were to plug that in that's going to make sense there's also times when you're going to have to use where you're going to have to reverse the direction of the inequality when we're multiplying or dividing negative numbers okay so with addition we're not moving that inequality sign however if we are multiplying or dividing right negative numbers then we're going to have to move our inequality size so let's take a look at this example so in this example we have negative 2y is less than negative eight so in order for us to isolate y right we're trying to figure out what that variable is what is y equal to we are going to have to divide negative 2 from each side and do you see why that is our negative 2 is being multiplied by y so the inverse arithmetic of multiplication is going to be division so by us dividing that now we have y right we have y isolated and on the other side uh negative 8 divided by negative 4 is equal to four however because we divided that negative number multiplying negative numbers whatever the case may be we have to reverse our signs so before our sign was less than right so now our sign needs to be greater than it is a rule that you're going to be you're going to have to become very familiar with when you're taking your atits because they are going to trip you up a lot of these inverse arithmetic questions as well as these questions with inequalities when it comes to multiplication and division I hope that this information was helpful in understanding the specific portions of the mathematics atit's version 7. as always if you have any questions make sure you leave them down below I love answering your questions head over to www.nursechung.com where there is a ton of additional resources available over there for you and as always I will see you in the next video bye

Channel: Nurse Cheung

Views: 121,786

Keywords: ati teas, teas test, ati teas 7, teas 7, ati teas test, teas exam, teas math, ati teas review, teas 7 math, teas math review, ati teas 7 math, teas test study guide, how to pass the teas test, ati teas secrets study guide, ati teas 7 study guide, teas test 2022, ati teas science practice test, ati teas math, ati teas 2022, teas practice test, ati teas, ati teas math 2022, teas 7 math practice test, ati teas 7 practice test, teas test version 7, ati teas study guide 2022

Id: 0Y3ck_utb4A

Length: 50min 17sec (3017 seconds)

Published: Thu Sep 29 2022