Hello wonderful mathematics people. I'm Anna Cox from Kella Community College. Algebra topics. A quick review. First thing I want to emphasize is parentheses, exponents, multiplication, division, addition, subtraction. This is the order of operations. So the order of operations. The order says first we do parentheses and parentheses is really all grouping notation. Then we do exponents, multiplication and division. We need to remember to do same time from left to right addition and subtraction. Also same time from left to right properties, we're going to look at addition property. The addition property for associative says if we have A plus the ( B + C, that's really the same thing as the quantity A + B + C IE we can associate them in any order we want. We can Group B + C together first, or we can group A+B together. Multiplication. The same concept, but now we're multiplying, so a ( b * C or parentheses AB times C. Commutative property. Like a commutative college. It travels around. So a + b = B + a. We commute, we go back and forth. Or A * B equal B * a distributive property. If we have something multiplied by a parenthesis, that's really the same thing as saying the A is going to get multiplied by B and also the A is going to get multiplied by C This is also valid if it was subtraction in the middle. So AB minus AC constant, a number that never changes a variable, a letter that represents a number that may change coefficient, a number that is multiplied by a variable. So a constant something like 8710 -5 negative 30 variable ABXY coefficient 9X The coefficient would be the 910 Y. The coefficient would be the ten -7 Z, the coefficient would be that -7 Like terms, the variable portion of multiple terms is exactly the same. So if we have three X ^2 -, 7 X +4 minus ten X ^2 - 6 + 5 Y oops, 5X. Sorry, we're all in XS. Here's a three X squared, and here's a -10 X squared. The variable portions are the same. So then we combine our constants 3 - 10. So we'd get -7 X squared. We'd then look at the X portions -7 X and positive 5X would give us -2 X. They're like terms because it's just a single X on both of them, and the four and the -6 like terms because they didn't have any variable on them. So if we combine like terms in this example, we get negative seven X ^2 -, 2 X -2. Some other things we need to know about this R with two bars means all real numbers. This zero with a slash through it says the empty set, or it means the empty set. Sometimes that's thought of as no solution. It also sometimes is written as a set with nothing in it, hence the empty set. When we solve for a variable, we want to eliminate all fractions by multiplying by the common denominator. We want to move all terms with the variable that you're trying to solve for on one side and factor out if necessary, and then divide. So let's look at an example here. If we had 1 / A + 1 / b equal 1 / C, and let's say we want to solve for B, Our first step is going to be to multiply by the common denominator, which is going to be ABC. So if I multiply by the common denominator, we're going to get BC plus AC equaling AB. I'm trying to solve for B, so I want to get all the B terms to one side. So I'm going to subtract that BC over going to factor out the B. So we get a -, C left and then finally I'm going to divide so AC divided by a -, C would equal B I know that was quick, but hopefully that helps. Averages X1 plus X2 plus X3 plus... X to the n / n So if we have a bunch of things and we want to find the average 687123, we would take all those and we would add them together. And in this case, we would divide by 5 because there were 5 numbers, consecutive integers ** plus One X + 2. So say we wanted 456. How did you get from 4:00 to 5:00? You added one. How did you get 5 to six? You added one consecutive odd or even integers. A little trickier because now we're skipping the number in between. So if we wanted to get from 4:00 to 6:00, we had to add 26 to 8. We added two. Eight to 10 we added two. Now frequently people get a little confused if it's odd, but we still really have to add 2 to get to the next number. 5 to 7 add 27 to 9:00 add 29 to 11 add 2. The last thing I want to talk about in this clip is exponents. Exponents A to the m * A to the NA to the M plus NA to the m / A to the NA to the m -, n powers to powers we multiply them. So A to the M to the NA to the m * n negative exponent one over and anything to the zero power except for 0 to the zero, which is undefined, is always equal to one. Anything to 0 power is one. Thank you. Have a great day.