SOLUTION: Find the common ratio of 3/4, 1/2, 1/3, 2/9, ...........

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Question 1205045: Find the common ratio of 3/4, 1/2, 1/3, 2/9, ...........
Found 3 solutions by ikleyn, MathLover1, math_tutor2020:
Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
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Divide the next number by the previous number.

Do it as many times as possible and compare the quotients in order for to make sure that they are all equal.

Happy calculations (!)

        Making calculations is the students' honorable duty and a privilege !


Same as plotting graphs and making tables.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find the common ratio of 3%2F4, 1%2F2, 1%2F3,+2%2F9, ...........
divide second term by first term
%281%2F2%29%2F%283%2F4%29=4%2F%282%2A3%29=2%2F3
divide third term by second term
%281%2F3%29%2F%281%2F2%29=2%2F3
divide fourth term by third term
%282%2F9%29%2F%281%2F3%29=%282%2A3%29%2F%289%2A1%29=2%2F3
all results are same, and the common ratio is 2%2F3



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

1/2 = 2/4
The first two terms are 3/4 and 2/4
Divide the numerators only (2nd term over 1st) and we get r = 2/3 as the common ratio.
We can ignore the denominators because they cancel out when dividing. This applies only when we have the LCD.

Or you could look at the 2nd and 3rd terms
1/2 = 3/6
1/3 = 2/6
The 2nd and 3rd terms, when finding the LCD, are 3/6 and 2/6 in that order. Follow the same idea as the previous paragraph to get r = 2/3

I'll let you check the other pairings.