>>12187700Sorry for getting back late anon, I had no internet access last night. I'm going to cover the following topics:
>fractions and base 10>parabolas and distributive property>exponentials>sine, cosine, tangent>differentiation and integrationSo first up is fractions. I will explain what they mean and how to compute them. A fraction can be thought of as either division, or as a ratio. 2/4 as division breaks 2 into 4 parts, which means each part is size 1/2. Ratios give the same result, because the existence of 2:4 means for every one unit (2), there are 2 units (2*2=4), the base rate is 1:2. A fraction is equivalent to its other forms because the numerator and denominator are just scaled by the same factor. 1/2 is half the size numerator, broken into half the parts, compared to 2/4, so the end result is the same piece size. Now, here is how you can compute any fraction into a decimal. For example, we can use something complex, like 1/237. We can do something sly here, let's first find out how many times 237 goes into 1000. It goes in 4 times, because 250*4=1000, and each 237 is 13 less than 250, so after 237 goes in 4 times, there is 13*4 =52 pieces left over. This means 1000/237 = 4*237/237+ (52/237), which is just 4 + 52/237. This turns the improper fraction 1000/237 into a proper fraction, as well. However, we wanted 1/237, not 1000/237, our answer is 1000 times too big! So what do we do? Simply divide our answer by 1000, (4+52/237)/1000. Because we have two separate pieces, we can divide each by 1000 individually as 4/1000 and 52/237*1000, or sum them and divide after. It is easier in this case to sum then divide at the end, as you will see. The process we did for 1/237 can be done for 52/237, except instead of needing to multiply the numerator by 1000, we only need to multiply by 10 to make 520, the first multiple that's greater than 237. 520/237 = 2+46/237, all divided by 10 leaves us so far at 4+((2+46/237)/10)/1000.
