GED Math Preparation [2019] Study Guide

associative property the associative property states that when adding or multiplying a series of numbers it does not matter how the terms are ordered remember that simplifying within the parentheses is the first step using the order of operations so you can remember the associative property the rule for the associative property because the numbers are grouped or associated with one another let's look at a couple of examples a plus B plus C is equal to a plus B plus C so again we're going to do what's in the parentheses first let's try this with 2 plus 3 plus 4 equals 2 plus 3 plus 4 so again we're going to follow our order of operations or PEMDAS we're going to start by adding 2 plus 3 5 plus 4 is equal to 2 plus and again following order of operations 3 plus 4 which is 7 5 plus 4 is 9 and that does equal 2 plus 7 which is also 9 so you can see it doesn't matter which terms we add first since we're doing addition it doesn't matter what we do first let's see what happens when we do the multiplication side so again I'm going to use 2 times 3 times 4 is equal to 2 times 3 times 4 according to PEMDAS we have to start inside our parentheses so that's 2 times 3 times 4 is 12 is equal to again starting in our parenthesis 2 times 3 is 6 times 4 2 times 12 is 24 and that does equal 6 times 4 which is also 24 like the commutative property the associative property is only true for addition and multiplication let's look what happens when we try to use it on subtraction and division so if we try to use the associative property it would look like a minus B minus C but again it's not going to be equal to a minus B minus B so I'm going to use numbers like 8 minus 4 minus 2 does not equal a minus 4 minus 2 again using order of operations 8 minus 4 is 4 minus 2 does not equal 8 minus 4 minus 2 is 2 4 minus 2 is 2 and that does not equal 8 minus 2 which is 6 as you can see the associative property does not work on subtraction let's use it on division now so with division it would look like a divided by B divided by C again will not equal a divided by B divided by C I'm going to use the same numbers we used for subtraction so 8 divided by 4 divided by 2 does not equal 8 divided by 4 divided by 2 let's simplify order of operations 8 divided by 4 must be done first 2 divided by 2 does not equal again parenthesis first 8 divided by 4 divided by 2 is 2 2 divided by 2 is 1 and that does not equal eight divided by two which is four and that's the associative property factors factors are numbers that are multiplied together to obtain a product for instance in 2 times 3 equals 6 2 & 3 are the factors common factor a number that divides exactly into two or more other numbers for example the factors of 12 are 1 times 12 2 times 6 and 3 times 4 so the factors of 12 are 1 2 3 4 6 and 12 the factors of 15 are 1 times 15 and 3 times 5 so the factors of 15 are 1 3 5 and 15 the common factors are 1 & 3 those are the factors they have in common prime number prime numbers have 2 distinct which means different factors 1 and itself the very first prime number is 2 because the only numbers the only factors of 2 are 1 & 2 1 times 2 is 2 some people think that one would be the first I'm number but one only has one factor 1 1 times 1 is 1 so 1 is commonly thought of as neither prime nor composite a composite number being a number that has more than two factors so 2 would be the first prime number then 3 because 3 has only two factors one times three is three four would be composite since one times four is four and also two times two is four five would be prime it's only factors are 1 & 5 6 would be composite one times six is six and two times three is six seven would be prime since it's only factors are one and seven eight would be composite one times eight is eight two times four is eight nine would also be composite 1 times 9 is 9 3 times three is nine ten would also be composite 1 times 10 is 10 2 times 5 is 10 11 would be prime 1 times 11 is 11 and so on and so forth there are an infinite number of primes a prime factor is a factor that's prime so in our example above in 12 and 15 the prime factor of 12 would be 3 2 & 3 and the prime factors of 15 would be 3 & 5 you can also do prime factorization the prime factorization of a number for instance the prime factorization of 12 would be 2 times 2 times 3 that's where you write the product of a number only using primes and the prime fact fifteen would be three times five unlike just writing the factors of a number with prime factorization you use only prime numbers as factors to multiply to get the result of the product you are seeking rates and unit rates ratios are considered rates when they compare two different units like miles per hour or cost per ounce a unit rate is one in which the numerator of the fraction is compared to a denominator of one unit that way you can tell for instance like how much just one ounce of something costs and you'll see unit rates a lot at the grocery store under or next to the price of an item it'll tell you how much that item costs for every one ounce or for every one thing in the package so let's look at a problem dealing with rates and unit rates Dave is driving 240 miles to his aunt and uncle's house if he gets there in four hours how many and here's the key right here in the question how many miles per hour did he drive on average in that question they're telling you how to set up the problem they're telling you to put miles over hours so we're going to start with that miles per hour and now we can substitute the information in from the problem so they told us how many miles he's going 240 miles and they told us how many hours four hours so we can put that into our rate 240 miles for his four hours so right now this would be considered a rate since we have two different units or miles an hour hours but to determine our unit rate or to figure out his average we would need to divide or simplify our rate to find our unit rate so if we want to have a denominator of one then we're going to have to divide 4 by 4 to get our 1 and if we divide our denominator by 4 then we must so divide our numerator by 4 240 divided by 4 is 60 so again this is miles per hour so what this unit rate tells us is that on average he was going 60 miles for every one hour so your answer could be written as 60 miles per hour is how fast Dave was going on average converting improper fractions to mixed numbers to convert an improper fraction to a mixed number first we're going to divide our numerator by our denominator 22 divided by 5 is 4 with a remainder of 2 4 is our whole number while 2 is the numerator of our fraction and the denominator stays the same so 22 fifths as a mixed number is 4 and 2/5 let's look at one more again to change an improper fraction to a mixed number we're going to start by dividing our numerator by our denominator 18 divided by 4 is 4 4 times 4 is 16 so we have a remainder of 2 4 goes into 18 4 times with a remainder of 2 out of 4 since our denominator stays the same the same this mixed number is special because we can simplify this fraction 2/4 and when you can simplify you always want to do that so 4 on 2/4 simplified would be 4 and 1/2 since the GCF of 2 and 4 is 2 we divide both numerator and denominator by 2 2 by 2 is 1 and 4 divided by 2 is 2 so 18 fourths as a mixed number is 4 and 1/2 adding and subtracting fractions to add and subtract fractions first make sure that the denominators are the same if they aren't like in five ninths minus 1/6 then we need to find the least common denominator the least common multiple of nine and six can be found by listing the multiples 9 18 27 etcetera 6 12 18 our least common multiple is 18 so we're going to change both of our fractions five ninths to something over 18 and one-sixth to something over 18 9 times 2 is 18 so since we multiplied our denominator times 2 we must also multiply our numerator times 2 5 times 2 is 10 6 times 3 is 18 so we must also multiply our numerator times 3 and we get 3 18 so that means that 5 9 minus 1 6 is equal to 10 18 minus 3 18 now we just subtract our numerators and put that difference over our denominator of 18 10 minus 3 is 7 then if you can simplify the result you should but in this case 7/18 cannot be simplified so that's our answer let's look an addition problem again we've got to see if our denominators are the same and if they aren't then we need to change them so that they are so we're going to find the least common denominator for three and five which means we're finding the least common multiple for three and five so I'll list the multiples 3 6 9 12 15 and my multiples 4 5 5 10 15 so my least common multiple is 15 which means I'm going to change both my denominators to something over 15 2/3 equals something over 15 and 4/5 equals something over 15 so to get from 3 to 15 we have to multiply times 5 so we need to do the same to our numerator 2 times 5 is 10 5 to 15 we have to multiply 5 times 3 so we do the same to our numerator 4 times 3 is 12 which means that 2/3 plus 4/5 is the same as 10 15 plus 12 15 and again we add the numerators and put that result over our denominator 10 plus 12 is 22 and this is an improper fraction since our numerator is larger than our denominator so we'd want to change it to a mixed number to change this improper fraction to a mixed number we're going to divide our numerator by our denominator 22 divided by 15 is 1 since 15 goes into 22 one time with 7 left over out of and the denominator stay the same so 1 + 7 15 is our result multiplying and dividing fractions to multiply two fractions simply multiply the numerators and multiply the denominators 3 times 2 is 6 and 4 times 5 is 20 then we can simplify 6 and 20 are both divisible by 2 so divide your numerator by 2 and the denominator by 2 you 6 divided by 2 is 3 and 20 divided by 2 is 10 so 3/4 times 2/5 is 3/10 now there is somewhat of a trick or a shortcut when multiplying fractions so I'll show you that 3/4 times 2/5 when you're multiplying fractions before you multiply look and see if you can cross cancel when you're cross canceling you're looking at a numerator and a denominator so 3 and 5 if we look at 3 & 5 there's nothing we could divide both of those by however you could by 2 and 4 both by 2 so 4 divided by 2 is 2 and 2 divided by 2 is 1 then you multiply like normal 3 times 1 is 3 and 2 times 5 is 10 so cross canceling saves you the step of simplifying but you get the same result make sure that you don't ever try and cross cancel numerators with each other it's only those diagonal numbers that you can cross cancel to cross cancel a numerator with a denominator now let's look at division we're going to divide two thirds by three fourths and you know it's funny about dividing fractions is that you don't we don't divide fractions instead we copy the first fraction we change division into multiplication and we flip our last fraction so we copy the first two thirds we change division into multiplication and we flip the last fraction over so it's now four thirds and now we multiply like normal 2 times 4 is 8 and 3 times 3 is 9 and that can't be simplified so eight ninths is our answer when dividing fractions just remember CCF copy the first fraction exactly as it is change division to multiplication and flip the last fraction decimals decimals use place value to represent an amount to read a decimal like we have here first read the number to the left as a whole number followed by and then read the number to the right of the decimal followed by the last place value so this number would be read as 641 and five thousand one hundred twenty nine ten thousandths this number could also be represented as a mixed number 641 and five thousand one hundred twenty nine ten thousandths let's look at another decimal five and eight thousand one hundred thirty nine ten thousandths we could write this number as an improper fraction by taking the five plus this would be eight tenths since it's in the tenths place plus one hundredths plus three thousandths plus nine ten thousandths which would give us 58 thousand one hundred thirty nine ten thousandths so we've seen a decimal in decimal form we've seen it represented as a mixed number and also as an improper fraction you adding and subtracting decimals when adding and subtracting decimals first line up the decimal we have four and twenty three hundredths plus nine and seventy-five thousandths same with subtraction five and six hundred twenty nine thousandths minus 45 hundredths then if you have any empty spaces you can fill in with zeros adding zeros to the back of your number to the back of a decimal doesn't change the value of your number so these numbers are still what they were they're still equal and then we just add or subtract like we usually would zero plus five is five 3 plus 7 is 10 so write your zero carry or one one plus two is three plus zero is three bring that decimal down 4 plus 9 is 13 so our answer for our sum is 13 and three hundred five thousands now for subtraction we're going to do the same thing except now we're subtracting 9 minus 0 is 9 2 minus 5 we can't take 5 from 2 so we need to borrow from our 6 just like we usually would and add a 1 on to our – which makes 12 12 minus 5 is 7 then 5 minus 4 is 1 we bring our decimal down and 5 minus 0 is 5 so our result or our difference is 5 and 179,000 dividing decimals to divide decimals first move the decimal point in the divisor so that it's a whole number then move the decimal point in the dividend the same number of places and finally move the decimal point up so that you know where it goes in your answer this means that now we're doing we're dividing 25 into 789 and 5/10 now we just divide as we would with whole numbers until we get our no remainder or you know it's a repeating decimal so 25 goes into 78 3 times 25 times 3 is 75 we subtract and we get 3 bring down the 9 and 25 goes into 39 one time 25 times 1 is 25 we subtract 9 minus 5 is 4 3 minus 2 is 1 then we bring down our 5 25 goes into 145 5 times 25 times 5 is 125 then we subtract 5 minus 5 is 0 4 minus 2 is 2 and then we have to add on a 0 so that we can continue since our remainder isn't 0 we still have 20 here we need to add on a 0 to bring down because we can add as many zeros after our decimal places we like without changing the number 25 goes into 208 times 25 times a is 200 so that when we subtract we get a remainder of zero now that we've reached a remainder of zero we're finished dividing and our result is 31 and 58 hundredths supplying decimals when multiplying decimals instead of lining up the decimal point we line up the last digits on the right so if we were multiplying 4 and 23 hundredths times nine and seventy-five thousandths we want to line up our last digits so 3 is the last digit in 4 and 23 hundredths and 5 is the last digit and 9 and seventy-five thousandths here's my 7 my 0 my decimal and 9 now we multiply just like we multiply whole numbers so starting with 5 5 times 3 is 15 carry the 1 5 times 2 is 10 plus 1 is 11 carry the 1 5 times 4 is 20 plus 1 is 21 and then I'll get rid of these for our next number now that we're multiplying times the 7 we need a zero placeholder 7 times 3 is 21 right your 1 carry your 2 7 times 2 is 14 plus 2 is 16 right your 6 carrier 1 7 times 4 is 28 plus 1 is 29 get rid of those then we need 2 zeros for placeholders and when we multiply times 0 0 times 3 0 0 times 2 is 0 and 0 times 4 is 0 we just get a line of zeros so moving on to our last digit now we need 3 zero placeholders before we multiply times 9 9 times 3 is 27 right the 7 carry the 2 9 times – is 18 plus 2 is 20 right the zero carry the – 9 times 4 is 36 plus 2 is 38 then just like we would with any other whole numbers we're going to add our results together 5 plus all these zeros gives us 5 1 plus 1 is 2 1 plus 6 is 7 2 plus 9 is 11 plus 7 is 18 right our 8 carry our 1 1 plus 2 is 3 and then we have 8 + r3 to determine where the decimal point goes when you've multiplied your decimals together we're going to take how many places how many numbers there were behind our decimal and our first number and how many numbers there were behind our decimal in our second number and add those together so since we had two numbers behind the decimal here and three numbers behind the decimal here then our result will have five numbers behind the decimal two plus three is five one two three four five so this is the result of multiplying my two decimals together one of the most basic concepts in algebra is the single variable equation this a single variable equation consists of a variable usually X and some other numbers and all you have to do to solve it is isolate X on one side of the equation by performing the same operations to both sides of the equation so let's look at some examples here this first one we have X plus 13 equals 25 minus 19 so to isolate X we need to get this 13 to the other side of the equation to do that we need to subtract 13 from both sides of the equation so this will cancel and what we're left with is x equals 25 – 19 – 13 and so now what we have to do is solve this part over here and we've got the value of x so it's do these one at a time x equals 25 minus 19 is 6 so x equals 6 minus 13 and 6 minus 13 equals negative 7 so in this equation x equals negative 7 in the second example we have 10 minus X plus 38 equals 54 minus 17 now in this equation we have a negative x so the first thing we want to do is get X to be positive so to do that we can add X to both sides of the equation and that will give us 10 plus 38 equals 54 minus 17 plus X okay the next step is going to be to move these numbers over to this side so that X is over there by itself so we need to subtract 54 from both sides and add 17 so what we have now is x equals 10 plus 38 minus 54 plus 17 and so once again we'll just do these one at a time 10 plus 38 is 48 48 minus 54 is negative 6 and negative 6 plus 17 is 11 so in this equation x equals 11 computation with percentages in problems involving percentages it is usually easiest to convert to a fraction or a decimal let's look at two examples first we're going to calculate forty percent of sixty two of in math means to multiply so we're doing 40 percent times 62 so now we need to convert 40 percent either to a fraction or to a decimal I'm going to convert it to a decimal and to do that all I have to do is take my decimal and move it two places to the left so forty percent as a decimal is four tenths or 40 hundredths times sixty to four tenths times 62 is 24 and eight tenths so 40 percent of 62 is twenty four and eight tenths you can use mental math to find percentages and on this one what we could do is find 10 percent of 60 two first and then multiply that times four since 10 percent times 4 would be our 40 percent of 62 so to find 10 percent of sixty two we would just move the decimal one place to the left so that would be six and two tenths and then we want to do that four times so we just multiply that times four so six and two tenths times four which would again give us 24 and eight tenths and this you could do a little easier in your head let's look at one more often times percentages are used to calculate the tip when you go out to eat at a restaurant so here we're going to calculate a 20% tip on a $28 and 75 cent me so we want to know what is 20% of $28.75 since that's how much we need to lead them 20% of how much our total bill was so again of is multiplication and we want to convert our percent to a decimal so move it two places to the left so we're really doing two tenths times $28.75 and two tenths times $28.75 is five dollars and seventy five cents so we would need to leave them a $5 and seventy five cent tip what would our total bill be our total bill would be how much our food costs plus how much we're leaving in a tip so $28.75 plus five dollars and seventy five cents five plus five is ten write your zero carrier 1 7 plus 7 is 14 plus 1 is 15 carrier one bring down our decimal 8 plus 1 is 9 plus 5 is 14 write your 4 carrier 1 2 plus 1 is 3 so our total bill would be $34.50 with the tip included an equation consists of two mathematical expressions separated by an equal sign and so for instance we might have an equation that says one plus one equals two and this is true because this value is the same as that value now the beauty of equations is that you can perform any operations the same way on both sides of the equation and the equation remains true so for instance we can add 5 to both sides of this equation and the equation is still true we can multiply both sides of the equation by 7 and the equation is still true we can divide both sides of the equation by 13 and this equation is still true and so anything you perform on both sides of the equation equally do not invalidate the equation similar to equations we have what's called an inequality so we might have the inequality one is less than 2 and so this consists of a mathematical expression on one side and the mathematical expression on the other side and a sign that indicates which side is greater or lesser so that's what we have here this is read as 1 is less than 2 and similar to equations we can perform the same operations on both sides of the inequality sign and it can remain true so again we can add 5 to both sides and it's still true 6 is still less than 7 we can multiply both sides by 7 and it's still true this side is now 42 and this one is equal to 49 so it's still true and we could divide it by 13 and it's still true the one thing that we can't do with inequalities without changing them that we can with equations is multiplying or dividing by a negative number so if we wanted to multiply both sides of this inequality by negative one that would make it untrue because in the most simple of examples if we have an equation that says one is less than two and we multiply both sides by negative one that becomes negative one is less than negative true negative two which is not true so what you have to do if you multiply or divide both sides of an inequality by a negative number what you have to do is reverse the inequality sign and so this is now a valid inequality once again because we switch this sign after multiplying by negative one to show in real simple terms what that looks like if you have one is less than two and then you want to make it negative you can say negative one now is greater than negative two and that is the true expression of the inequality and so you can have greater than or less than and you can also have a greater than or equal to which is something of a combination of equations and inequalities so we would write greater than or equal to as a greater than sign with a line under it similarly less than or equal to would be less than with the line under it and so this is kind of a more formal definition of equations and inequalities and what you can do with them linear equations Muriel has ten coins in her pocket all of them are quarters and dimes and their total value is one dollar and sixty cents how many of each type of coin does she have we can solve this by using a system of equations we're told that she has ten coins in our pocket and that they're all quarters and dimes so if we use D for the number of Dimes and Q for the number of quarters then one of our equations could be her number of Dimes plus her number of quarters is ten total coins next we're told that the total value is a dollar sixty well dimes are worth ten cents so ten times however many dimes she has plus quarters are worth 25 cents so 25 times however many quarters she has will give us a total of 160 we've eliminated the decimals so we just move the decimal over two times to the right for all of our numbers so instead of ten cents we have ten set of twenty-five cents we have 25 and instead of a dollar 60 we have 160 but you could leave the decimals in there if you wanted to now solve this system we've got three options we could graph both of these and see where they intersect we could use substitution or elimination and it's your choice for this particular problem I'm going to use substitution so I'm going to solve for D in my first equation so I can substitute in my second equation so D is equal to and I have to subtract Q from both sides so negative Q plus 10 to solve for D subtract Q from both sides and you get negative Q plus so in my second equation I'm going to use negative Q plus 10 to substitute for D so we have 10 times the quantity instead of D negative Q plus 10 plus 25 Q is equal to 160 now we can solve for Q to do that first we need to distribute 10 times negative Q is negative 10 Q 10 times 10 is 100 so plus 100 plus 25 Q equals 160 notice all for Q we need to combine like terms negative 10 cubed plus 25 Q is 15 Q plus 100 is equal to 160 subtract 100 from both sides we get that 15 Q is equal to 60 now we divide both sides by 15 15 divided by 15 is 1 and 1 times Q is just Q we get that Q is 4 which means she has 4 quarters so how many dimes does she have well we know that her number of dimes is equal to negative Q so negative 4 plus 10 so her number of dimes is negative 4 plus 10 6 so we can say Mary L has 4 quarters and six dimes in her pocket you word problems and addition solving word problems is made easier if you know what certain words mean for instance here we have a list of words that all indicate addition so if when you're reading a word problem you see more than increased by sum total or in all then chances are you're going to be adding something together let's look at an example two more than a number is 15 what is the number the first thing I'm going to do is translate these words into a mathematical sentence so two I'm going to write the work that the number to more than I know tells me to add when it says a number well that's something I don't know what number is it and so but something I don't know then I can put a variable there like an X or a wire really anything you want to use is in math means equals and then equals 15 so the only kind of trick here is that more than tells you to reverse the order it's not just addition it means instead of doing two plus x I'm really doing X plus two equals 15 so now you can probably just look at this and see what number you would have to add to 2 to get 15 and that number would be 13 which means X is 13 if you don't know by looking at it what the answer is then you can solve it algebra like algebraically here by subtracting 2 from both sides but again you would get that your number is 13 word problems and division here we have a list of some words that indicate division so if you're trying to solve a word problem and you come across the word quotient per out of or ratio you'll know that you need to divide something let's look at an example if the quotient there's one of our keywords of a number and 10 is 3/5 what is the number so again we saw that keyword quotient which tells us we're going to be dividing something we're going to be dividing two numbers and those numbers were dividing our a number and 10 and they must be divided in that order so when we write our division problem we could write it as X divided by 10 or we could write it as X divided by 10 but it must be in that order if we reverse it to do 10 divided by X then that is not what is written here in this problem that would be if the quotient of 10 and a number so order is very important since it was written if the quotient of a number and 10 then we must have that number first divided by 10 and you'll see here that I put X and I put an X because we don't know that number it just said a number so when we don't know a number we use a variable in place of that let's finish the sentence if the quotient of a number and 10 is 3/5 is is equals 3/5 now since I chose to write it this way X divided by 10 equals 3/5 it looks like a proportion and that's because it is 1 all the proportion is is a ratio equal to a ratio and that's what I have here so to solve this proportion we're going to cross multiply x times 5 is 5x and that's equal to 3 times 10 which is 30 and now we need to solve for X this is 5 times X and the opposite of multiplying is dividing so we divide both sides by 5 5 divided by 5 is 1 1 times X is X and that equals 30 divided by 5 which is 6 so the quotient of 6 and 10 is 3/5 and that's true 6/10 does simplify to be 3/5 word problems and multiplication when you come across a word problem that has any of these words product times twice or of chances are you're going to have to multiply now this is not a comprehensive list of all of the words that would tell you to multiply but this is a few of them let's look at an example if Mary Ann opens a bank account with $450 and earns 12% in interest each month what will her total balance be at the end of the first month so what they're asking us to find is our total balance since I don't know the total balance then I'm going to have to use a variable for that so let's say t-then is going to be our total balance and in order to find my total balance I'm going to have to take what she's starting out with her $450 and the amount that she earns in interest in that month so my total balance will be found by taking the starting value and adding the interest to find my total balance and so to find my total balance I'm going to have to know the starting value so we'll use an S for starting value which is $450 and I also have to know my interest so we'll use I for interest and interest is going to be found by doing 12% of the amount of money she has in her account so we're going to do 12% of $450 okay so to find my total balance I'm going to have to take my starting value and add my interest to that and my starting value is $450 so my total balance is going to be $450 plus my interest and my interest we said was 12% of $450 and there's one of those words that means multiplication so in order to find my interest I'm going to have to do 12% times 450 but first we're going to change our percent to a decimal so we move our decimal two places to the left so we get 12 hundredths times 450 as our interest and 12 hundredths times 450 is 54 so our amount of interest that we earned in that month was $54 therefore our total amount is 450 plus $54 and then we just add those two amounts together therefore our total amount is 504 dollars and that's how much money we have after one month word problems and subtraction when you read a word problem and you see words like difference less than decreased by or fewer than you know you're going to need to subtract let's look at an example six less than a number is eight what is the number since they're asking us what the number is that means we don't know it and if we don't know a number then we use a variable for it so right here where we see a number I'm going to put a variable I'm going to use X this phrase less than tells us that we need to subtract so we have 6 we're subtracting we've got a number is is an equal sign 8 but less than is a tricky phrase it does mean to subtract but again you have to reverse the order of the things you're subtracting like if I said I have five dollars less than Jimmy has that means that Jimmy has more money than I do so I have to do Jimmy Jimmy's money minus five dollars in order to find out how much money I had so 6 less than X is going to be X minus 6 is equal to 8 so what number would I subtract 6 from to get 8 that number is 14 so that means X is 14 now if you didn't know that the number was 14 then you could solve this algebraically by adding 6 to both sides so you'd have again x equals 14 because 8 plus 6 is 14 you

  1. Hello Everyone 🙂 Thanks for watching! I hope this helps with your GED test review. Don't forget about:
    GED Math Practice Test:
    More GED study guide videos:

  2. I'll be taking my Ged Math test this Friday. God I'm so nervous. It's the last test I need to get the diploma. I'll come back with an update if I pass or failed and list on what's on it.

  3. 25:32 "these numbers are equal" well, technically they are not. the precision values are different so its not really fair to compare them.

  4. This video helped me a lot in understanding fundamentals & getting through the GED math exams. Thanks a lot for making such videos.!!

  5. Cross cancelling does not save you a step. You still make two seperate calculations either way. Simplify or cross cancel how is that removing a step? I always thought that was just more confusion to add on to an already complicated process. I had crap teachers and 30+ kids in my class during the 80s and 90s.

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