TEAS 7 Math | 1 Hour Tutoring with Formulas, Conversions, & More!

the te's 7 math tutoring replay will start in just a few seconds get access to live group tutoring on math science English and reading when you get the tas7 online course enjoy the replay hello everybody happy Thursday um my name is John I'm the founder of smart Edition along with my wife nurse Melissa and today is the first tutoring session that we are offering live in the course so we're excited to have everybody here today with us we'll be going over math we've got Ashley over here and uh I'll be moderating this session Ashley will be going through she's going to go over kind of some different math topics um different concepts and then we're going to do a bunch of practice questions so we'll do all that live here um so I'll go ahead and pass it over to Ashley to introduce herself let us know what we're going to go over today and then we'll get right into it all right thank you hi everybody I'm Ashley um in a moment I'm going to start sharing my screen so you can see a little slideshow I've made to go through a bunch of these practice problems um and there will be a few opportunities for you to take screenshots or grab your camera on your phone and take some pictures of some really important information that you'll need to know so have that handy I'm Ashley I've been a math teacher for over 10 years um I've taught in the classroom privately tutored students of really all ages and I just really love math so I hope that through our session today you can find some ease in the math that we are doing for the entrance exam so I have a few things we're going to cover today um these are basically three questions here that hopefully we will answer so what kind of math can I expect to find on my entrance exam we'll talk about that I'll give you some different examples and we'll do a bunch of prce practice problems we're also going to talk about what formulas and or conversions you'll need to know and have memorized so again another opportunity for you to take some pictures and have these resources available to you even after the session and then what will the problems look like well that's what we're going to spend a good chunk of this hour doing okay so we're going to be on for about an hour going through as many of these practice problems as we can get through so here's a great slide for you to take a picture or a screenshot of these are the type of math concepts you can expect to find on your entrance exam so we're going to do some examples of all of these you're going to need to know operations with fractions so we'll need to know how to add subtract multiply divide you will definitely see word problems so it's not just enough to know how to do the operation we'll also need to be able to apply it to lots of different types of problems we're going to do conversion problems which is something that we are going to spend a good amount of time on today I want you to see the conversions that you need to know have some strategies to memorize them and then also just see what types of problems will come up some will be pretty basic where you just have to do a simple conversion some will be word problems that are specific to your field okay we'll also talk about ratios and proportions percentages we'll solve some equations and then we'll talk about exponents and some Circle geometry problems okay so I'll give you just another second in case you did not get a chance to grab this with your screenshot or take a photo and then we are going to talk about some of those formulas and conversions you need to know so again as I'm going through this please give some feedback in the Q&A if you have questions about a concept that I'm talking about specifically and then feel free to chat amongst yourselves in the chat feature so so that we can all feel engaged okay so where we're going to start here is some formulas the slide is a little bit too big to get the whole thing in let's see if I can go out a little bit there you go so you should be able to just screenshot this whole page here so that you have this as a resource to look at so give you a moment again take a screenshot or a photo and then I'll just talk about what each of these formulas mean so that when we go and apply them later you have a little bit better of an idea so circles we need to know our circumference formula that's what C stands for so circumference is going to be Pi * diameter so sometimes we have to use pi and just leave it it's just representing a number that 3.14159 number that goes on and on forever right so sometimes we just use the symbol or sometimes you might round to 3.14 but your problem will tell you how to do that and then because we can use a four function calculator that allows us to do the math a little bit easier so again another thing you might want to have handy today is that calculator so that you can do some of these examples with me so we've got circumference here and then the next one here is area so area is going to equal Pi * the radius squared so one way it's just like kind of a silly pneumonic that I use to remember these form is Cherry Pie delicious okay circumference cherry pie delicious apple pies R2 okay so just a silly little pneumonic cherry pie delicious apple pies R2 can help you remember those formulas for circles and then I also just added here that the diameter equals 2 * the radius when you look at a picture of a circle okay the diameter goes through the center from one end to the other other whereas the radius just goes from the center outward so if you need to know the diameter you can multiply the radius by two and conversely you can also find the radius by just cutting the diameter in half so just a little something you can add there if you'd like talking a little bit more about geometry we've got some area formulas here so triangle area equals 1/2 base time height rectangle area equals base time height and then for a square which is technically a rectangle so this formula would still work a special formula is just that the area is equal to the side squared because all of the sides of a square are the same and a little bit more geometry notice how a lot of these formulas are geometry that we need to know we've got our volume formulas over here on this side so cylinder cone okay so cylinder volume equals Pi * the radius squar time the height cone is 13 * pi * the radius squared time the height and then if we have a prism which is basically like think about a box okay you would just do a rectangular prism length time width time height or any prism maybe say you have the base as a triangle instead of a rectangle you would just do the area of the base so let me just make a little note of this that that capital b means area of the base and then you multiply that by the height and then lastly for Pyramid you're just going to do 1/3 times the area of the base times the height okay so a lot of information but I want to make sure you know what all of these letters stand for and the last formulas I have here for you are just our temperature conversions definitely need to know these okay if you know one then you can actually find both you just have to know where to plug in do I plug in my Celsius temperature or my Fahrenheit temperature but it can be helpful to have both of these memorized to save you a little bit of algebra when you're trying to solve for whichever temperature you're trying to find okay so we will see some of these examples later on I also have some conversions for you to have memorized again you really want to have these ready to go so when you see a conversion problem you are just able to plug it in use your calculator and not have to think too much about the specific math and allow yourself to really think about the word problem and what it's asking so have a quick little picture or screenshot of the volume and weight conversions and then I will arrow down so you can see the distance so shortly I will also show you a little trick to finding some of these metric conversions so metric units are when we're talking about um like centimeters or millimeters or kilometers like all of those units we actually can find some cool ways to convert without memorizing ing all of those conversions but some of them will be on here as a little bit of a repetition as well okay and then I have one more slide for you which will have some repeats but it is a little more content specific for your nursing exam these are the mass units or conversions that you really want to have memorized okay so micrograms I don't believe was on the last slide but that is an important one and then you have milligrams to grams and grams to kilograms and then also pounds to kilograms so those are conversions that you will want to know for mass and then we also have some for volume and so please feel free again to use that Q&A feature if you missed any of this okay I just want to make sure that you guys have these resources as we go through some of these examples so I mentioned just now when I was on that slide that there is kind of a cool trick that I want to show you if you are converting within the metric system so this is a pneumonic aonic is just a phrase and oftentimes the sillier the better it helps us remember it this just kind of a silly phrase to help us remember how to convert within the metric system in a little more quick and efficient of a way so the the pneumonic is King Henry died while drinking chocolate milk hence this silly little picture I have here for you okay so King Henry died while drinking chocolate milk well what does that have to do with the metric system each of these letters here of our pneumonic is a unit or a prefix of our metric system unit so kilo hect so this is DECA the W I use just to stand for a whole unit if I'm talking about grams or liters or meters that's where that would go and then I have Dei CTI and Millie so these are all our prefixes that go before our units and allow us to figure out how large of a unit we're talking about so let me show you how we can use this to convert pretty quickly so I have a bunch of examples here for you if this is something that is not really driving with you and you're like I already know how to convert I have them memorized I want to just try it on my own feel free to go ahead and pop some answers in the chat if you see my slide and you want to go ahead and just go for it that's totally fine but for those of you that feel like I'm a little bit confused when I have to do metric conversions or I struggle and it takes me a while this may be helpful so I'll do the first couple examples a little bit slower and then I'll show you how quickly this can really happen so for my first example I'm going to convert 3,200 millit to liters so my pneumonic up here a great strategy when you're taking a test is to if this is something that helps you write this pneumonic down write those letters down have it on your sheet ready to go because then I can reuse it over and over again so I need to go from milliliters to liters so I'm going from my m and then I'm going to end up my whole unit so this tells me to go one two three times to the left so when I say go three times to the left I'm talking about the decimal point so the decimal point in a whole number is always just hidden right at the end so if I'm going to swoop this one two three times to the left it's going to land right here so I got my little arrow there so I can rewrite this number as 3.2 and notice how I'm leaving off those trailing zeros I want to leave those off so I avoid confusion and 3,200 ml would equal 3.2 lers okay so let's try another one if I have 0.67 or 67 hundredths of a liter I want to convert to centiliter so I'm going to start here swoop one two times to the right this time so one two to the right right now my new number is 67 that decimal would be hidden at the end there right I don't necessarily have to write that so that would be 67 Cen okay so let's see how quickly this allows us to do a couple of these other conversions that we may not know right away so I have to go from decagrams to grams so I'm just going to swop Once to the left swop once to the left and my answer is 0.48 99 G notice how I added that zero to the front of the decimal point this here makes it clear that that decimal is visible right decimal is just a dot it can get lost at times we want to make sure that we have that zero for clarity now let's try to go from grams to milligrams okay so grams is a whole unit one two three times to the right let's swoop 1 2 3 three times to the right notice I have a couple empty spaces I just fill those with zeros and I get 5,300 mg okay how about from centimeters to kilometers I'm going to swoop one two three four five times to the left so let's see what that looks like 1 two 3 four five I should have given myself a little more space but let me just make sure I have the right amount of zeros here so it should be 1 2 3 four zeros after the decimal and then the 2 4 okay so I'll just give you a moment to try the last one on your own either using this strategy or if you already know the conversion to go from meters to millimeters go ahead and give it a shot 72 MERS would be how many millimeters Ashley there's a few questions are Le one question in the Q&A wanted to make sure that we go over a word problem um I'm pretty sure you have that queued up Y and sure the audience we're definitely going to do a couple of word problems yeah we've got a we've got a few word problems in here for sure and I know I have at least one specific to conversions so we will definitely do one of those okay and another Q&A this is this is um one probably just good to go over she's asking what is whole numbers so just a base Baseline definition of whole numbers cool so a whole number is essentially a number that doesn't have a decimal or a fraction at the end of it so you can think about it as numbers that we count with right 1 2 3 4 five 6 7even goes on until Infinity right you can go as high as you want for whole numbers but we're not going to have anything after the decimal place and we're not going to have any fraction attached to it so when you think of a whole number that is what we're talking about so I hope that makes it a a little more clear thank you cool and then just for this final example if you used this strategy you would have swooped three times to the right 1 two 3 if you know your conversion then you would just have multiplied by 1,000 which we will definitely do some examples where we're just using our straight up conversions as well but it would be 72,000 mm okay so again for some of you this may be a thing that you just you take it and you want to apply it and you want to use it and for some of you you may leave it you may say this isn't really for me I have my own strategies and that's great but now hopefully everybody has a strategy they can use when we get to our conversion problems so we're going to jump into a mixed review of the content that you will see we'll go through one or two examples of each of the different topics we mentioned in the first slide starting with operations with fractions so I've got a couple examples here the first one we need to add so let me just I think I zoomed out before let me zoom in a little bit more so that you can see 38 plus 56 is the problem we need to solve so when we are adding or subtracting okay fractions we add or subtract we need to have what we call a common denominator okay so the first thing here is to realize we do not have a common denominator and I know that because the bottom of my fractions both of those numbers are different so the denominator has to be the same in order to add my fractions so two strategies you can use to find a common denominator you can just multiply your denominators so I could just do 8 * 6 and if your multiplication tables are a little rusty that's why you have a four function calculator go ahead and plug it in your calculator and you would get 48 so we could use 48 as our denominator like rewrite these as something over 48 plus something over 48 okay we want to get those equivalent fractions so then I can add them together so I'll show you how to do this and then really quickly I'll show you another strategy that would be a little bit quicker for this example but for this way that I'm showing you it works every time you can always just multiply those denominators to get your common denominator so we're finding equivalent fractions I went from 8 to 48 by multiplying by six so I do it on the bottom I also have to do it on the top so 3 * 6 would give me 18 now if I'm doing 6 * 8 to get 48 I have to do 5 * 8 which would be 40 and then I can add these two together because I have a common denominator and get get 58 over 48 okay 58 over 48 now all of my answers are either regular fractions okay where the top is less than the bottom or they've been converted to mixed numbers which means I pull out whatever whole unit or whole number I have and then simplify my fraction so we have got to simplify this into a mixed number so 48 goes into 58 one time I can pull out one group of 48 and 58 minus 48 would tell me I have 10 left over so this is my mixed number but it's not simplified notice how 10 and 48 are both even that means that we can divide each of those by two and get my final simplified version of 1 and 5 24s so the fourth answer here would be our solution so there are a few steps to this find a common denominator turn that improper fraction into a mixed number and then have to simplify it something else that would have been helpful is rather than using 48 as my common denominator I could have just looked for a multiple of eight and six because there actually is one that is lower than 48 we call that our least common multiple LCM and 8 and six share a multiple of 24 so 24 could have been the denominator we chose because 8 * 3 is 24 so 3 * 3 would be 9 6 * 4 is 24 so 5 * 4 would give me 20 right so just converting those into equivalent fractions and now when I add I get 29 over 24 and similarly I still have to turn it into a mixed number so 24 goes into 29 once with five left over that would have allowed me to jump straight to this solution without having to simplify so both are great strategies but sometimes if we can use that least common multiple it saves us a little bit of work okay so just remember main thing I want you to know when we are talking about adding and subtracting fractions is that you need to have a common denominator right so this was also a good review of that mixed numbered improper fraction and vice versa as well as simplifying so lots of different things going on here for our next example we're going to try division with fractions and actually this one is division of mixed numbers so again I'm trying to show you a few different topics within this content at the same time because this is likely what you will see so how am I going to divide these mixed numbers for me personally what I like to do is I like to turn them into improper fractions so all that means is I'm going to have a fraction with a numerator over a denominator just happens to be the numerator is bigger than the denominator sometimes you call that a topheavy fraction but that's fine because then we can actually divide it so here's my strategy to go from mixed numbers to improper fractions I'm just going to write this a little bit bigger so you can see what I'm doing yeah I think that's help I think that's helpful as some of the the question stem part is a little small they're a little small okay super helpful okay cool perfect so what I want to do here is I want to take the denominator and multiply it by my whole number so 12 * 1 is 12 then I'm going to add the numerator back onto that 12 and get 17 this is the same thing as 17 over 12 okay so all I'm doing is converting that mixed number into an improper fraction if I do the same thing for 1 and2 2 * 1 is two plus that one on top gives me three this is the same thing as three over two okay so now how do I deal with this division so how I have always done it has been using again another little kind of silly pneumonic that just is one of those ways that just helps me remember exactly what I'm doing KCF what that reminds me of is KFC right Fried Chicken KCF that is just something that is always stuck in my mind of how do I divide fractions well let's see what that stands for the K stands for keep so I'm going to keep 17 over2 as it is the C stands for change I'm going to change my division to multiplication and then my f stands for flip I'm going to take this fraction and flip it so 2 over three so KCF means Keep Change Flip okay so that is how we can multiply fractions okay I'm taking Division and turning it into multiplication because the strategy for multiplying fractions is pretty simple okay from here all I have to do is multiply across the top 17 * 2 which is 34 and across the bottom 12 * 3 which is 36 and then notice how that is not one of my answers that is because I didn't simplify 34 and 36 are both even that's a really great thing to look for when we are doing our fractions is if they're both even that means I can divide both of them by two and that means that they can be simplified so 34 / 2 is 7 36 / 2 is 18 so my final answer would be 17 over 18 so as we go through some of these other topics um I'd love to have some engagement where you guys are dropping your answers in the chat if you're not already so as we go to some other multiple choice or little short response questions feel free to be putting those in the chat so you guys can interact with each other as we go as well so I promised you some more conversions these are ones that may not necessarily be metric only metric conversions we may be converting within the English number system or from metric to the English number the system like we'll have to figure out what some of these units are but if you took pictures or screenshots of those conversion tables those will likely come in handy here if you don't have all of these memorized so I'm gonna actually give you a moment before I jump into this and I just want to see how many of these you can do I'll give you about 30 seconds and see a good little self assessment for yourself which of these conversions do you already know okay we need to go from inches to feet millimeters to centimeters gallons to pints and then pounds to ounces and then I also at the bottom here have a conversion for military time so I give you about 30 seconds feel free to drop it in the chat so we can see if we're getting the same answer and you can give a little self assessment of which one of these you know and which one of these do you kind of need to spend a little more time on and memorize so for this first one when I'm going from inches 2T I need to know the conversion that 12 in equals 1T okay so that's the key here to solving this problem and what that means is that when I'm going from inches to feet I'm essentially just having to divide by 12 so if I take 27 divided by 12 okay this might be a great one to just plug into your calculator because it's not going to work out perfectly but we will have a decimal as our answer 27 / 12 gives me 2.25 or 2 and A4 feet so inches to feet we're just going to divide by 12 if we were going in the opposite direction so this is from inches to feet if I was going in the opposite direction rather than divide I'd have to multiply so I like to use my conversion over here to help me fig remember am I dividing or multiplying because 12 ided 12 is 1 but in the opposite direction 1 time 12 would have to get me back to 12 so sometimes we can get um a little bit lost in our thoughts or step in our head do I need to divide or multiply and this is a strategy that can help keep that clear if that's something that feels like it can be a little tricky for you for the next one we're going to take 67 millimet and turn it into cenm so if you know how many millimeters are in a centimeter you're good to go right you can just figure out do I need to divide or multiply but I want to just again show you guys for this other strategy how quickly we can use are pneumonic King Henry died while drinking chocolate milk and just go from millimeters to centimeters soup once to the left and that means this would be 6.7 CM so if you had used the conversion all you had to do is divide by 10 okay this next one going from gallons to pints if you know how many pints are in a gallon you can do this in one One Step okay this wasn't something that was on our conversion sheet we have a couple other steps we could do to figure it out but if you know that already you can do it in one step the sheets that I gave you are not like an exhaustive list of all of the conversions you'll need to know but it actually did have enough information for you to figure it out so I want to show you if you only memorize the ones that we gave you in this presentation to figure out how do I go from gallons to pints what you would have to do is know a couple things you'd have to know well there are four quarts in one gallon and then there are two points in every one qut okay so I could go from gallons to quartz just by multiplying by four so 8 * 4 would give me 32 well that's in quarts now if I want to go from quarts to pints I'm going to have to multiply that by two to get my answer of 64 okay so using some of these that maybe you already knew or saw from our conversion table you could convert using multiple different conversions from one just to go from one unit to the other or maybe you already knew that there are eight pints in a gallon and you could just multiply by eight cool all right and we have one more conversion here before we do a time conversion I'm going to take 12 and 1 12 lb and turn it into ounces the key here is to know that one pound is equal to 16 oz so if I'm going from pounds to ounces notice how it's getting larger I'm multiplying by 16 so I'm just going to take 12 1/2 and plug in my calculator multiplying that by 16 okay so 12.5 * 16 would give me 200 o cool and just another example of a conversion that you may not see on a chart to memorize but you do need to know is how do I go from our 12-hour clock time into military time into that 24hour time so if I have 9:27 p.m. the key here is to notice that PM means after noon right it's afternoon in our time we go up to 12 and then we start back over at 1 so the key here is to know that when I see PM if we're after 12: p.m. starting at 1 2 3 we always have to add 12 back to it so 9 + 12 gives me my hour of 21 and then the minutes 27 just get plopped on there I drop that colon so in military time that would just be 2127 cool so we got some conversions and I do have here one example of a word problem that you may see a doctor writes a prescription for 0.5 L of liquid medicine to a patient how how many milliliters will the medicine bottle be filled with okay so if I have this given to me and I need to find how many milliliters okay essentially what I'm doing is converting from liters to milliliters so the question is 0.5 L equals how many milliliters so if that strategy of using lumanic has been helpful for you go ahead and try it if you know your converion again go ahead and try it by multiplying or dividing to get your new unit of milliliters and feel free to drop the answer in the chat let's see how we do with a question like this so I'll just give you about 15 seconds or so I think this is one of those questions that you either know it or you don't and that's okay because I'll go over it so for this here I'm going to just show you the conversion to go from liters to milliliters I just have to multiply by 1,000 so 1 12 * 1,00 would give me 500 millit so if you put that as your answer nice job you got it cool so we do have quite a few more topics I want to try to get through in the next 20 to 25 minutes so I'm going to zip on to the next topic here we're going to talk a little bit about ratios and proportions um before we look at this example specifically ratios and proportions are essentially something that we want to think about as fractions so you'll notice when I'm doing this problem I'm going to use fractions to help me solve it there are other ways to do it but when we're trying to solve some of these more complicated ratio and fra uh sorry ratio proportion problems fractions can be really helpful so ratios just as a quick little note can be written in a few ways so say I have a ratio of a to B okay if I were to literally write that out A to B it would look like this I could write that as a colon b or I could write that as a fraction of A over B it's very important to note that the order in which you write a ratio and where you put those numbers is very important these are not the same these are not the same as B to A or B over a right A over B and B over a are definitely not the same thing if you think about a fraction 2 over 3 versus 3 over2 changing the order of that changes your value so one thing I just want to note here is that your order and where you put those numbers is very important so let's zoom in here and try a little word problem using ratios and proportions if a recipe calls for three parts flour to two parts sugar how much sugar does a baker need if she uses 12 cups of flour okay so pretty relevant if you like to bake especially these days around the holidays you may need to do a problem like this and you might not think about it too much when you're in your kitchen but I just want to break down how we could do this regardless of what the numbers were and what we're talking about flour and sugar or be anything else right so if I have three parts flour to two parts sugar that's essentially a ratio of 3 to2 I'm going to write that as a fraction so I'm just going to write three and I'm going to write flour okay over two and I'm writing sugar I'm just using those to remember what am I putting on the top and what am I putting on the bottom flowers on the top sugars on the bottom so when we're doing a ratio or a proportion it needs to maintain the same value so if I'm using 12 cups of flour this ratio will be equal to 12 cups of flour right flour is on the top to how many cups of sugar I'm just going to label that X okay this is what I'm trying to find how much sugar do I need for 12 cups of flour so two ways to solve this think about them as equivalent fractions 3 to 2 = 12 to what well 3 * 4 is 12 and 2 * 4 would give me my answer of eight okay so if you're pretty good at equivalent fractions or just see patterns and numbers you might have seen that pretty quickly but if you want another strategy to solve a question like this we could cross multiply so 3 * X and 2 * 12 so cross multiplication comes up a lot when we're talking about these proportion problems and essentially we just go across the equal sign and do 3 * x = 2 * 12 and now I just have a pretty easy algebraic equation to solve divide by 3 and I'll get x equal 8 so your answer either way would be eight cups of flow okay so this is a fairly basic question but this strategy and that's really what I want to hone in here is strategies you can use this strategy will work for any numbers no matter how complicated they get okay so let's try a percentage problem 32 what is 32 out of 160 as a percent Okay so we've got four multiple choice options here and to give you a moment just to see if you have a strategy that you could use to to try to turn this into a percentage and then I will offer one up for you in 15 seconds so what I would do here is for me I'm a mathematical person in so I'm going to offer a way to do this a little bit more mathematically and then we can talk about how we can just think about numbers as well because that may not work for everybody so if I'm going to do this 32 out of 160 that automatically makes me think of 32 over 160 32 out of 160 so essentially all I have to do is simplify this fraction which will give me a decimal and then I can turn it into a percent really easily so if I have a decimal going to a percent is easy peasy so when we have a fraction that fraction bar essentially is just division so this is the same thing as just doing 32 / 160 go ahead and plug that in your calculator and you will get 0.2 so 0.2 is my decimal version now I want to figure out well what is that as a percent well percent means out of 100 okay percent you might notice that c n t at the end Cent 100 cents in a dollar or 100 years in a century what we have to do here is just multiply by 100 to get 20 perent okay so really important skill for your entrance exams and some of the word problems you will see is being able to convert back and forth between fractions decimals and percentages so this is one way that you could do a question like this you also could use your multiple choice options to help you here and say well 32 out of 160 what does that seem pretty close to so I know that like 30 out of 150 30 * 5 would be 150 so it probably goes into 32 probably goes into 160 about five times just estimating and trying to think about these numbers so what goes into 100 five times well that would be 20 and that would check out here but that would also allow me right off the bat to get rid of 12 because that seems like it's quite low and it's definitely not 50% because that would have to be half of 160 which would be 80 so right off the bat with just kind of thinking about what I know about numbers I could get rid of two of these options as pretty unreasonable and then just have have to figure out if it's 20% or 22% so that is another strategy as we're looking at multiple choice questions to allow you to focus in on the answers that make sense and get rid of the ones that don't all right let's try some algebra solving equations with one variable I'm going to give you one that's a little bit more simple and then we're going to do an example that's a bit more complicated so we're going to solve for the unknown value or for the X so I'm going to write this a little bit bigger again because it's just a little bit small in the way it's written X over -2 - 3 = 5 so I'm trying to solve for x I have to get rid of anything else that's on the left side of this equal sign so I have x / -2 and then minus 3 so notice how these are one fraction these are attached here but it would be really easy for me to get rid of this minus three just by adding so that's what I'm going to do first using an inverse operation the opposite of subtraction is addition I'm going to add three to both sides and I'm left with x / -2 = 8 now again using inverse operations to get that variable that X by itself x / -2 well what's the inverse of division that would be multiplication so I basically just have to multiply by -2 to get that to cancel out but if I do it on one side of the equation I always have to do it on the other to maintain balance that's essentially what an equation is it's just something that we keep balanced so I do it on one side I have to do it on the other and this would simplify to x equal -16 so that was just a little two-step equation to get you warmed up for or one that looks a little more complex so this is an equation that we are going to try to solve together kind of a lot going on here so let's break it down we have two times in parentheses notice these parentheses they're important 4x + 1 - 5 = 3 and then minus and I have another set of parentheses over here 4X minus 3 so before I start to move things over trying to get the variables by itself I want to simplify wherever I can and in this case that means trying to distribute or multiply out to drop those parentheses so I'm going to distribute on the left side this two and then on the right side I actually have to distribute this negative sign which is the same thing as multiplying by a negative one so that's going to be my first step is to distribute and then I can start to simplify a little bit more so 2 * 4X 2 * 4 is 8 so that's 8 x 2 * a positive 1 would be a positive2 the minus5 stays along for the ride equals 3 and then let's see what happens when we distribute this minus sign -1 * 4X is -4 x -1 * -3 notice I'm multip multiplying a negative * a negative or Distributing that negative side in there is going to force me to change that to a positive three now that I've distributed I can combine like terms so I'm looking at the left side of my equation first if I have variables I can put together Swit together on the left side I will but I only have constants so I'm going to add these these 8X can't combine with anything but I can do + 2 - 5 which would give me a -3 and then on the right side again I can only combine my constants here 3 + 3 is 6 and then I have minus 4X so sometimes we start solving these equations and we get stuck at this point because we're like What do we do we have a variable on both sides of the equation well your goal is to get them on the same side because then I can get it by itself so same way as we were using inverse operations in the last example to move things over I'm going to do that as well so -4x I want to move that over so what I'm going to do is add the 4X to get it to cancel out and I'm going to add it to the left side as well to maintain balance so 8 x + 4x gives me 12 x - 3 = 6 now I have a pretty simple equation to solve at this point I can add three to both sides and get 12x = 9 and then lastly I will divide each side by 12 and if you plug this in your calculator you're going to get a decimal but notice how all of my answers are either fractions or whole numbers so what that means is I really just have to simplify my fraction so I have 9 over 12 I'm just going to rewrite that up here I got x = 9 over2 how do I simplify that well what do 9 and 12 what factor do they share they both can be divided by three so I'm going to divide by three to get 3 over 4 as my final answer okay so we started out with a pretty complex equation once we distributed combine like terms and then moved the variables over to the same side it got pretty simple and then we just had to deal with the fraction so this is the type of equation that you can expect to see and have to demonstrate your knowledge of solving on your exam that does look a little complex asle but you did a good job um solving that how are you looking on time we've got about 10 minutes or so left I don't know how many questions you have I think we're good I'm just going to bounce through a few exponents practice how we use that since we can't use our calculator for some of those and then I've got two Circle problems so I think we'll be good to finish right up around seven all right cool sounds good cool awesome and thank you guys so much for sticking around with me I know I'm doing a lot of talking but I hope that the explanations are clear and you're able to follow along and feel more comfortable with some of these topics so like I just said we're going to do some exponent stuff and then we're going to do a couple Circle problems and we're going to wrap it up so let's just talk about exponents real quick essentially an exponent is just some number as the base raised to the exponent which just tells me I'm multiplying whatever that base number is times itself a certain number of times so 5 squared just means 5 * 5 5 * itself twice so 5 * 5 would give me 25 okay so pretty straightforward what happens when I have to do two to the 3 power so 2 to the 3 power or 2 cubed means I have to take two and multiply it by itself three times 2 * 2 * 2 please please please do not make the mistake of just doing two * three and getting six because that's not our solution here when we are using an exponent we have to do 2 * 2 to get four and then multiply that number by two to get our solution of eight so 2 to the 3 power would be eight sometimes we also have to deal with negative so notice again I'm really pointing out parentheses because this can change a a math problem just by adding parentheses so these parentheses are important let's try to do -3 to the 3 power I'd have to do -3 * -3 * -3 so what do I do here well if I do -3 * -3 I get a positive 9 and then I have postive 9 * -3 a positive * a negative is a negative 9 * 3 gives me 27 so that would be my solution this would be a different answer than if I just had -3 to the 3 without those parentheses so definitely important for us to notice parentheses when we are solving problems and not Overlook them so another example of that and when we might need to see these exponents in an application is when we're asked to evaluate an expression like this one so when we're asked to evaluate expressions like this we're simplifying and trying to find the value of this expression but we have to do it in an in a spefic specific order that is called order of operations or that is also sometimes referred to as pemos you may have heard that maybe that reminds you of grade school learning pemos please excuse my dear Aunt Sally is one thing that I'm sure plenty of us have heard in our lifetime so what this stands for is the order of which we're doing operations parentheses then exponents then we do multiplication and division we just work from left to right and then addition addition and subtraction again we just worked from left to right so I'm going to start simplifying and practice some of the stuff with exponents so I'm doing my parentheses first so I have to deal with this so the first thing I have to do within those parentheses is the 4 squared so 4 squared is 16 and then I'm going to subtract 10 16 - 10 would just be six so all of this stuff in the parentheses just simplifies to six so I'm going to write everything else as I saw it before okay so 3 squ + 5 * 6 - 8 now if I simplify done with my parentheses I move on to my exponent now it's outside of those parentheses so that's the next thing I can do 3^ 2 is 3 * 3 which is 9 + 5 * 6 - 8 parentheses exponents are done let's see if we have any multiplication or division well this represents multiplication so 5 * 6 is 30 and I'm just working my way down sometimes this is called the pizza method we're getting smaller and smaller skinnier and skinnier until eventually we get our final answer now I'm going to do addition and subtraction working left to right then 9 + 30 comes first and finally I get 39 minus 8 to give me a answer of 31 okay so so one way that you may see exponents is within your order of operations types of questions when they ask you to evaluate an expression okay and we've got one more question um I want to talk a little bit about circles and then we'll do one example and we'll be good to go so when we are talking about circles we need to know some terminology so this specific specific question which is from one of our courses just asked you to identify a diameter of the circle so if I'm looking at this full circle the diameter would be a line that goes through the center from one end to the other so the only line that goes through the center through that center of the circle from one end to the other is here so the diameter would be either be written as b d or you could write it as DB the order doesn't particularly matter okay what if I asked you to find a radius well there's actually quite a few here here's one radius c o another radius could be o or o d all of those could be examples of radi of this circle and then the one here that we didn't talk about AE this is really just called a chord it just goes from one point of the circle to another without going through the center so that's called the chord so just a little bit of vocab that you want to know when we are talking about circles so when we see a problem like this we know what we're doing so the circumference of a circle is 45 in find the area of the circle in square in round to the nearest tenth use 3.14 for pi so I need to know those Circle formulas in order to solve this problem so we talked about a little bit before we need to know circumference is equal to Pi * diameter and area is equal to Pi times the radius squared so again that silly little pneumonic that might be helpful cherry pie delicious apple pies are two okay so let's just plug in what we know to try to get our way over to finding the area circumference is equal to 45 so I'm plugging that in for C they're telling me to use 3.14 for pi and I need to find my diameter because that's the only thing in our circumference formula we don't have yet so I'm just going to divide by 3.14 again we're just going to let our calculator do this for us and I'm just going to round to a couple decimal places I get about 14.33 as my diameter so how does that help me find my area well if you remember diameter is just 2 * the radius or in other words the radius is half of the diameter so cut that in half if I just take 14.33 divide it by two this is about 7165 okay you probably at this point point could probably just write it as seven and be okay okay because if I look at my answers none of them are really too close together so rounding should be okay at this point so I'm just going to say my radius is seven so let's plug that in 3.14 * 7^ SAR okay so again there's another an example of when you might see an exponent 7^ SAR is 49 so I have to simplify 3.14 * 49 and when I do that I get about4 as my answer so remember that I rounded a little bit right my answer here was seven which was less than what the actual radius would be and I rounded here too because when we're using decimals sometimes we get in our calculator a long decimal so this is where once we get an answer we need to now just choose the one that is the best fit for what we got so the closest by far here is 162.5 so depending on how you round your answer you may have a different strategy than me as you're working through different problems you you may get closer to 162.5 or a little bit farther away but either way just using that question of like what's the most reasonable answer we can get this as our answer but still know that 162.5 is the solution okay so that's the last one I have for you guys today

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Keywords: teas 7 math, teas 7 math tutoring, ati teas 7 math, ati teas 7, teas 7, teas 7 exam, teas 7 test, ati teas 7 math review, teas 7 math review, teas math review, teas math, ati teas math

Id: y8Ow3cceUFQ

Length: 59min 35sec (3575 seconds)

Published: Mon Nov 20 2023