There are many things that I have learned about grade 9 math so far, even though I have done many of these types of questions in grade 8 you still have a little bit of different ways to do math and different rules. For example, say there was a question that was written like this is grade 8; (10 + 5)÷(7-2). Although in grade nine math you would write it as a fraction so it would look like (10+5) on top of (7-2) in a fraction looking question. I find this actually really good personally it makes the question easier for me because 1: I makes it look way less complicated and that I wouldn’t mind doing it instead of seeing a super long question and thinking that is going to suck. 2: It breaks it up more clearly for me in some questions. For example, if you have a crazy long question that look really complicated and takes you a while to do and maybe you forget to put in or miss that little division symbol and then you mess up the whole question and then it was just a waste of your time. So, that little rule makes it a lot easier for me personally.
Another example I would like to show is about exponents, in the exponent questions I did last year you would have to do all the actual work, an example for what I am talking about is if 2 to the power of 8 was being multiplied by 2 by the power of 4. Then if it was grade 8 math I would have to multiply all of it and do all the work and have to lay the question out and make it look like this this: 2x2x2x2x2x2x2x2 = 256 and then multiply that question by 2x2x2x2 = 16, and then take those two answer and multiply them together which would be 4096. So, thankfully I have learned a way to not do all that and not have to do all that work. Instead all I would have to do is take both exponents from each base and add them together, and the opposite way with division, you would just subtract the exponents. So, to re-right the question in an easier and more officiant way. Take 2 to the power of 8 and since the bases are the same same you would just add the exponents together, which would look like this : (8 + 4) which you turn into the final and easy answer of 2 to the power of 12.
One more example of what I have learned about grade 9 math is that when you are dealing with exponents and negative numbers, brackets really help when it comes to deciding whether the answer in the end will be a negative or a positive. Picture you come across a question that looks a little like this -a² . In the beginning I would think that it would be positive because -a x -a would equal a positive, but since exponents are lazy they don’t see the negative symbol so it would just always be negative without the brackets but if the question looks like this: (-a²) then it would force the exponent to see the negative symbol and count it in which would make it a positive number. When I found out this rule it helped me out quite a bit with my homework because it wasn’t always guessing whether it was going to be negative or positive because I didn’t know why I kept getting the symbol in front of the number wrong, but now I know which helps I guess.
Those are three good examples of what I learned about grade 9 math and how it helped me in different ways to make math easier for myself and I would think everyone else thinks these rules and tips make math questions easier too.
polynomials:
What is a polynomial? – A polynomial is a name for more than two algebraic terms, especially several terms that have different of the same power. The vocabulary in polynomials are degree, constant, coefficient, leading coefficient, binomial, trinominal and monomaniacal.
A degree of polynomials is the highest exponent in the equation that is above zero. Constants are the number that do not have a variable in the equation. A coefficient is a number before the variable in an equation. For example, in the equation (10x³ – 5y² + 8) the coefficient would be the 5 and the leading coefficient would be the 10, the constant would be the 8 and the degree would be the exponent number 3 that is connected to the x. Also a binomial is the expression for two different terms. A trinomial is a expression used for when three terms are being used, and a monomial is when only one term is being shown/used.
When adding or subtracting polynomials they must have the same variable. For instance, in the equation (3xy² + 4x – 8y³ + 6xy¹ – 5x²) the only way to simplify this question is to add all the x’s together, all the y’s together and all the xy’s together separately as well as the exponent attached to those variables. So, first would add all the xy’s together like this (3xy² + 6xy¹ = 9xy³), then you would do the x’s like this (4x + (-5x²) = -1x³), and then lastly there is only one y so you do nothing with that. And at the end it would be (9xy³ – 5x² – 8y³).
Now when it comes to multiplying and dividing polynomials it is way different. So, when you multiply you first multiply the coefficients, then you either include the other variable into the term and the add all the exponents into the term as well and the same thing for dividing except you cancel out the variable that are the same to each other, so you would be eliminating some of the exponents. To better show muktiplication in polynomials i will show you an equation. (2x(5xy²)) So, first you would times 2 by 5 which would equal 10, then you would take the x from the two and add it to the x beside the 5 which would make it x², and then since there is no y attached to the 2 you just leave it alone on the one attached to the 5. And at the end of it all the equation would turn from a binomial to a monomial and it would look like this (10x²y²).Now for dividing an example is (10x²y³ ÷ 5xy²). So, just like multiplying you would start of with the coefficient but instead you will be doing the opposite which would be (10÷5=2), then you would cancel out all the x’s (x² – x = x¹), then lastly the y’s (y³ – y² = y¹). So, the end result would be (2xy).
Some of the same things used in this section of math that is the same as units that we were using before are the exponents, in polynomials when multiplying, dividing, subtracting and adding exponents and variable is the same in the other unit and the polynomials unit.