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 Author Topic breadofknowledge Posted - 13 April 2011 2:6 To avoid being accussed for plagirism this is copied and pasted... from a linkThis page is designed to help you better understand, work with, and solve equations. Click any of the links below to go to that section and begin understanding equations. Addition and/or subtraction in equations Multiplication and/or division in equations Combinations of the basic operations in equations Quiz on Basic Equations -------------------------------------------------------------------------------- Equations are something that you will constantly be using throughout your math career. Learning and understanding the basics is an integral part of "getting off on the right foot" when dealing with math. This section will help you better understand, work with, and solve equations when they have addition and/or subtraction in them. Changing the order of the addends (numbers you're adding) doesn't change their sum (what they equal when added together). Example: a + (b + c) = (a + b) + cAny number plus 0 (zero) equals itself. Example: a + 0 = aIf two sides of an equation are equal, you can add or subtract the same amount to both sides, and they will still be equal. Example: a = b a + c = b + c a - c = b - c When solving equations, remember that addition and subtraction are inverse operations - they undo each other (i.e., 10 + 9 - 9 = 10). To solve equations using addition and subtraction, first decide which operation has been applied, then use the inverse operation to undo this (remember to add or subtract from both sides of the equation). 1. Solve: x + 79 = 194 Solution: x + 79 = 194 x + 79 - 79 = 194 - 79 x = 115 You need to get the variable by itself (isolate the variable). To undo adding 79, subtract 79 from both sides. 2. Solve: x - 56 = 604 Solution: x - 56 = 604 x - 56 + 56 = 604 + 56 x = 660 You need to isolate the variable. To undo subtracting 56, add 56 to both sides. Back to Top -------------------------------------------------------------------------------- This section will help you understand, work with, and solve equations of a slightly more complex nature - equations involving the use of multiplication and/or division. Order of operations: The operations inside parentheses () and brackets [] are done first. Then any operations involving exponents (which you will learn about later). Then do all multiplying and dividing from left to right. Finally, do all addition and subtraction from left to right. Multiplication can be written three different ways: 9 * x 9x 9(x) A fraction bar is also a division symbol. Changing the order of multipliers (numbers you're multiplying together) doesn't change their product (total when the numbers are multiplied together). Example: ab = ba Zero times any number is zero and 1 times any number is the number. Examples: x(0) = 0 (0)x = 0 x(1)= x 1 * x = x If two sides of an equation are equal, you can multiply or divide each side by the same quantity (number or equation) and it will still be equal. Examples: a = b, c <> 0 ac = bc (a / c) = (b / c) When solving equations, remember that multiplication and division are inverse operations, therefore they undo each other (i.e., (4 * 8)/8 = 4). To solve equations using multiplication or division, first decide which operation has been applied, then use the inverse operation to undo this (remember to multiply or divide on both sides of the equation). 1. Solve: 6x = 36 Solution: 6x = 36 (6x) / 6 = 36 / 6 x = 6 You need to get the variable by itself (isolate the variable). To undo multiplying by 6, divide by 6 on both sides. 2. Solve: x / 5 = 10 Solution: x / 5 = 10 5(x / 5) = 10(5) x = 50 You need to isolate the variable. To undo dividing by 5, multiply both sides by 5 Back to top -------------------------------------------------------------------------------- This section will help you understand, work with, and solve complex equations that involve different combinations of multiplication, division, addition, and subtraction. Order of operations: The operations inside parentheses () and brackets [] are done first. Then any operations involving exponents (which you will learn about later). Then do all multiplying and dividing from left to right. Finally, do all addition and subtraction from left to right. Multiplication can be written three different ways: 7 * x 7x 7(x) A fraction bar is also a division symbol. Also, be sure to refer to the above sections if you have forgotten or need to review any of the other material covered. When solving complex equations, like the ones used in the examples below, be sure to remember that multiplication and division are inverse operations along with addition and subtraction. Therefore, they undo each other (i.e., (5 * 2)/2 = 5 or 10 + 4 - 4 = 10). To solve these equations, first decide which operation has been applied and then use the inverse operation to undo this (remember to apply the operation to both sides of the equation). 1. Solve: 7x - 7 = 42 Solution: 7x - 7 = 42 7x - 7 + 7 = 42 + 7 7x = 49 (7x) / 7 = 49 / 7 x = 7 The variable needs to be isolated. To undo subtracting 7, add 7 to both sides. Adding 7 hasn't isolated the variable, so we need to continue. To undo multiplying by 7, divide both sides by 7. 2. Solve: 5(x + 2) = 25 Solution: 5(x + 2) = 25 [5(x + 2]/5 = 25/5 x + 2 = 5 x + 2 -2 = 5 -2 x = 3 The variable needs to be isolated. To undo multiplying by 5, divide by 5 on both sides. Dividing by 5 hasn't isolated the variable, so we need to continue. To undo adding 2, subtract 2, from both sides This page is designed to help you better understand, work with, and draw graphs. Scroll down or use the links below to begin understanding graphing. The coordinate plane and points Graphs of lines Quiz on Basic Graphing -------------------------------------------------------------------------------- In the coordinate plane, or the rectangular coordinate system, the vertical y-axis and the horizontal x-axis intersect at a point called the origin. This section will help you better understand the coordinate plane and how to graph points on the plane. The origin's coordinates are (0,0). Points are named by an ordered pair. Example: (4,2)The first number in an ordered pair is the x-coordinate, and the second number listed is the y-coordinate. Example: When graphing, the coordinate plane will be labeled with "tick marks" denoting the scale. Beginning at the origin, count along the x-axis scale until you find the tick mark labeled with the x-axis coordinate of your point, and then count along the y-axis scale until you find the tick mark labeled with the y-axis coordinate of your point. That is the location of your point! However basic this seems, it is a necessary skill for graphing lines and other equations. Back to Top -------------------------------------------------------------------------------- This section will help you to understand how to better graph linear equations. Linear equations can be graphed when in the form y = mx + b m equals the slope of the line. b equals the point where the line crosses the y-axis. This is called the y-intercept. When graphing linear equations, "plugging in points" is a suggested method of solving the equations and putting them in a graphical format. To plug in points, select an x-coordinate (be reasonable in the number you select for the x-coordinate) and put the x-axis coordinate in the equation in place of x. Then solve the equation. This will give you a y-value. Put your chosen x-value and the y-value you solved for together, and you will have an ordered pair (a point) that you can graph. Repeat this process about 4 or 5 times and then connect the points you have graphed. The line you see will be the graph of a linear equation. 1. Graph: y = 2x + 1 Solution: y = 2(0) + 1 y = 1 (0,1) An x-coordinate of 0 was selected. The equation was solved for y. The resulting ordered pair is (0,1). x / y --------- 0 / 1 1 / 3 2 / 5 -1 /-1 The process described above repeated 4 times. The results are shown to the left in table form.This page is designed to help you better understand how to deal with fractions and their uses in Pre-Algebra. Click any of the links below to go to that section and start understanding fractions. Lowest Common Multiple Greatest Common Factor Multiplication of fractions Division of fractions Common Denominators Quiz on Fractions -------------------------------------------------------------------------------- The LCM is something that you will use throughout math. It is especially useful when multiplying and dividing fractions. This section will help you better understand the LCM and its uses. When finding an LCM, use only multipliers that are whole numbers. Examples: 4, 8, 43, 104Be sure to be aware of all the numbers you are finding an LCM for. When finding LCMs, be aware of all the numbers you are finding common multiples of and remember that you can only use whole numbers for multipliers. Also, always be aware of zero, which is not an LCM. Problem: Find the LCM of 4 and 5. Solution: Make a table similar to this: Multiples of 4 Common Multiples Multiples of 5 48121620... 20... 510152025... 20 is a multiple of both numbers. It is also the first one (lowest of all multiples), thereby being the lowest common multiple. Back to Top -------------------------------------------------------------------------------- The GCF is something that you will use throughout your "math experience." It is especially useful when dealing with fractions. This section will help you better understand how to find and deal with GCFs. When finding a GCF, use only whole numbers. Examples: 2, 9, 27, 201Be aware of all the numbers you are finding a GCF for. When finding GCFs, be aware of all the numbers you are finding common factors of and remember that you can only use whole numbers for factors. When finding a GCF, unlike the LCM, you must list all the factors because you're finding a greatest factor, not a lowest multiple. Problem: Find the GCF of 8 and 12. Solution: Make a table similar to this: Factors of 8 Common Factors Factors of 12 1248 124 1234612 4 is a factor of both numbers. It is the largest of the factors listed, therefore it is the greatest common factor. Back to Top -------------------------------------------------------------------------------- The multiplication of fractions is one of the more important things you'll learn in math. In fact, it is so important that you need to know how to do it in order to divide fractions, add fractions, and many other things. This section will help you better understand the important skill of fraction multiplication. Do not cross-multiply fractions. Like the multiplication of whole numbers and decimals, you can multiply more than two fractions together in one problem. Example: 1 3 4 12 3 - * - * - = -- = - 2 2 5 20 5When multiplying fractions, multiply the numerator(s) by the numerator(s) and the denominator(s) by the denominator(s). Also, after finding the product of the fractions, be sure to reduce the product to its simplest form (that is one instance of GCF use). 1. Problem: 3 6 - * - 4 7 Solution: 3-->6-->18 - * - = -- 4-->7-->28 Multiply the numerator by the numerator and the denominator by the denominator. 18/2 9 ---- = -- 28/2 14 Find the GCF of the numerator and denominator and then divide both the numerator and denominator by that number. The resulting fraction is the answer. Back to top -------------------------------------------------------------------------------- Division of fractions isn't a skill that gets around quite as well as multiplication, but it is very useful! This section will help you understand how to divide fractions. Cross multiplication is involved in the division of fractions. Flip the second fraction of the two being multiplied at the time upside down to do the problem correctly. As indicated above, there can be more than two fractions in a division problem involving fractions, but you can only divide 1 fraction by 1 fraction, so you have to do a problem like that in more than one part. Example: 1 3 2 4 2 20 5 - / - / - = - / - = -- = - 2 4 5 6 5 12 3 When dividing a fraction by a fraction (remember, a whole number can be written as a fraction (i.e., 4 = 4/1)), flip (take the reciprocal of) the second fraction and then multiply. Be sure to reduce the quotient (simplify the answer). 1. Problem: 6 2 - / - 1 3 Solution: 6 3 - / - 1 2 6-->3-->18 - * - = -- 1-->2-->2 Take the reciprocal of (flip) the second fraction. Mutliply the numerators. Multiply the denominators. 18/2 9 ---- = - 2/2 1 Find the GCF of the numerator and the denominator and divide each by that number. Because (9/1) is the same as the whole number 9, the answer is 9. Back to Top -------------------------------------------------------------------------------- To be able to add or subtract fractions from fractions, you need to have the denominators be the same, or common. (This is one of many instances where the ability to multiply fractions correctly will come in handy.) This section is designed to help you better understand the process involved in finding a common denominator in order to be able to add and/or subtract a fraction from another number. To add or subtract a fraction from another number (whole or fractional), the denominator needs to be the same. Example: 1 3 4 3 - + - cannot be done, but - + - can. 2 8 8 8When a fraction has a numerator and denominator that are the same number, the fraction is equal to 1. Example: 2 - = 1 2Multiplying by 1 does not change a number, even though the form might change. Example: 4 4 2 8 - = - * - = -- 5 5 2 10 When finding a common denominator so you can add or subtract fractions, you find the LCM of all denominators of the fractions you are dealing with. Once you've found this number, make the denominators equal this number. To do this, you multiply the denominator and numerator (the denominator is one factor of the LCM) by the corresponding factor of the LCM. 1. Problem: 4 2 - + - 3 5 Solution: 15 The LCM of 3 and 5 is 15. 4 2 --- + --- 3*5 5*3 Since the denominators have to equal the LCM, you have to multiply 3 by 5 and 5 by 3. Now both denominators are the same. 4*5 2*3 --- + --- 15 15 Because you don't want to change the problem in any way, each part of the problem has to be multiplied by 1 (not one-third or one-fifth as you did in the second step). To do that, you have to multiply the numerator by the same number as you multiplied the denominator by. 20 6 -- + -- 15 15 Now that you've got the denominators the same, you can add the fractions together. 26 -- 15 You cannot reduce this fraction, so this is the final answer! Back to Top -----------------------------------------ok so this is me again XD in order to successfully study... you need to take some time to right your own problems mix shit up I have been studying for like 23 hours back to back to make this happen for you guys.... so bare with me /so here is a go figure thing to do ok for example...x/5 =10 so wtf is that right lol well I am going to show you inverse operation.... so x/5=10 5( x/5) = 10(5) x =50 Que : wtf did i just do? well i used inverse operations....which means to get the sum I have to reverse or inverse the operation and operation as in multiply or devide simple right? so i took x and made it vanish! MAGIC not really ... we want to solve for x .... not solve x/5..... this is a common thing for people to mix up so dont reply and say duh and if you already know this then why reply? there are some who need help and are far behind rome was built from the dirt first so is math...again x/5= 10 since this is devision... / means devide...since this is devision we multiply the 5 to both sides and get the numbers with out the varible...and solve the problem :) for multiplying you do the oposite take this example ... 6x=36 (6x) / 6 = 36/6 for x = 6 so... this is explained as simple as i could...so dont get mad at meeeeeee :( so i took the the i did not even use GCF with this because it is algerbra language its way more different than pre-algerbra..so all i did was simply used the oposite operation and switched over the varible and solve the equation... any questions? i just taught you how to solve and find out how to devide and multiply equations solving for XXX SO EMAIL ME @ jesuschosetoloveyou@yahoo.comand reply I know some easy steps and how to get you your GED!!!! for math so far....

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