Try these problems on a sheet of paper so you can (VISUALLY) see my new math trick and see how it works.

Problem 1.

Lets say you have any given ratio like 3/4, and then you multiply it by a ratio that has the same number in the numerator and the denominator (like 2/2 ) and you will get an answer (which is 3/4 * 2/2 = 6/8) Then you combine the numerators from 3/4 and the answer (6/8) and you will get the number 36. Then you combine the denominators from 3/4 and the answer (6/8) and you will get 48.

Then the numbers 36 and 48 will make a new ratio(36 will be the numerator and 48 will be the denominator). This new ratio will reduce down back to 3/4, which is the original ratio.

Problem 2.

Lets say you have the given ratio 1/4, and then you multiply it by a ratio that has the same number in the numerator and the denominator (like 3/3) and you will get an answer (1/4 * 3/3 = 3/12). Then you combine the numerators from 1/4 and the answer (3/12) and you will get the number 13. Then you combine the denominators from 1/4 and the answer (3/12) and you will get 412. Then the numbers 13 and 412 will make a new ratio(13 will be the numerator and 412 will be the denominator). Now since there is one DIGIT more in the number 412 than in the number 13 (we take the number 412 and count its digits which = 3 digits, then we take the number 13 and count its digits which = 2 digits, then subtract 2 digits FROM 3 digits to get 1 digit), we will have to take the denominator from the original ratio (1/4) and the answer(3/12) , (which both denominators appear in the number 412, which is the denominator of our new ratio). You take the denominator from 3/12 and since 412 is ONE DIGIT larger than 13, the number 1 in the denominator of 3/12 will be taken out (because ONE DIGIT will tell you that you need to take off the number 1 in the number 12 because you ALWAYS take ONE DIGIT off the left digit in the number 12 (which is 1)), and you add the number 1 to the denominator of the original ratio(1/4), which 4 + 1 = 5. So the number 1 in the number 12 is cancelled and you are left with number 2. Then you take 5(which came from the step we did from above) and the 2 and you combine them to make 52. 52 will be the NEW denominator and 13 will be the numerator(remember 13 from a while back from the previous steps) and you make a new ratio off of those. So 13/52 will be the new ratio. Now this ratio will always reduce back down to 1/4(which is the original ratio)

I know these might be hard to visualize but try this trick with any given ratio and it will work.