Top 5 Things I Learned in Math 9

1. Exponent Laws

For me, exponent laws were big essentials that helped me out in math 9. They helped me remember when to add, subtract, multiply and divide the exponents in equations and gave me little tricks and tips that really came to my advantage while completing this unit. Exponent work was a little tricky for me so to learn these laws really made my learning experience a lot easier (Like how Ms. Burton says “work smarter not harder”.)
First, there is the Multiplication Law: If the question is a multiplication question and the bases are the same, you can add the exponents together and keep the base the way it was. Example: $5^6\cdot5^2$ = $5^8$
Then, there was the Division Law: If the question is a division question and the bases are the same, you can subtract the exponents and keep the base the way it was, similar to the multiplication law but instead dealing with subtraction. Example: $2^9\div2^4$ = $2^3$
After that, there was the Power of a Power Law: If the question looks like $(7^2)^2$ you can use this law. All you have to do is multiply the exponents and keep the base the way it was. Example: $(7^2)^2$ = $7^4$
And last but not least, there is the Exponent of Zero: If the question has an exponent of zero, you automatically know that the answer will equal to one. Example: $3^0$ = 1

I thought this was very useful when it came to this unit. Not only did this teach us how to find the missing side of a triangle but this also taught us about the cross multiplication technique which in my preference came in handy immensely. This was something that I believe is very good to comfortably know how to do for the years in math to come.
To find the missing side length (x), you have to create ratios by using the information in the given similar triangles above. This gives us the ratios 5/10, 10/20 and 15/x
Now this is where the cross multiplication comes into play. You will take one of completed ratios and place it beside the ratio that contains the variable. From there, you will multiply the information in a cross-like formation. Example: $\frac{10}{20}=\frac{15}{x}$ = $\frac{10x}{10}=\frac{300}{10}$ x=30

This was a huge part of math 9 so I feel that this was definitely very important for me. It is used a lot and will be used even more as math excels so this is why it is good to understand this concept and are able to execute it with ease. For me, sometimes I have a hard time remembering some of the steps in this concept so I feel that this is not only important but is also something that I can work and improve on. For me, practicing this makes all the difference in the world so that is why I feel so strongly about the importance of adding and subtracting polynomials.
When adding and subtracting polynomials without brackets in the question, all you need to remember to do is group your like terms together and simplify. Like terms are all the terms that contain the same variables and exponents. You cannot group unlike terms together or your equation will not work. Once you have grouped all your like terms together, you can start you add and subtract your like terms.
When adding and subtraction polynomials with brackets in the question, you do the exact same thing but you have to remember and essential step before you group and simplify. If there is a subtraction sign before a bracketed polynomial, you must remember to switch the term’s sign from negative to positive or vise versa. After completing that step, then you can move on to grouping the like terms and simplifying the equation.

This is one of the most used parts in math and it is a good idea to be able to comfortably understand how to properly do this for almost every single math unit. The tricks and tips that make dividing and multiplying fractions easier really seem to work with me so I feel that this was a very important unit for me.
When multiplying fractions, you need to “just do it” as Ms. Burton says. All you do is multiply across ans simplify if possible. Example: $\frac{3}{4}$ x $\frac{1}{2}$ = $latex \frac{3}{8}
When dividing fractions, all you need to do is flip the reciprocal and multiply the two fractions together like a multiplication question. Example: $\frac{5}{6}\div\frac{4}{8}$ = $\frac{5}{6}$ x $\frac{8}{4}$ = $\frac{40}{24}$

For me, this is the hardest thing that we learned. For the longest time I struggled with graphing, but now that I understand it more, I feel that it is really important. It is something that took me a while to fully understand but I feel more confident with it now and realize the impact it has in math 9.
When graphing, x is vertical and y is horizontal
Let’s say that step is represented by x and number is represented by y.
Here is the graph for the information above: