Question

The numerator of a fraction is randomly selected from the set {1,3,5,7,9}, and the denominator is randomly selected from the set {1,3,5,7,9}. What is the probability that the decimal representation of the resulting fraction is not a terminating decimal? Express your answer as a common fraction.

Answer 1

help plz

Answer 2

The total number of fractions that can be created is 5 times 5 (since there are 5 numbers to pick from on the top and 5 on the bottom). Thats 25 total combinations.

The only way you will get a non-terminating decimal is when the denominator is a 3, 7, or a 9, and the numerator isnt equal to the denominator, or a multiple of it. So lets try and count how many ways that can happen:
\[\frac13,\frac53,\frac 73\]thats 3 ways for a denominator of 3.
\[\frac17,\frac37,\frac57,\frac97 \]thats 4 ways with a denominator of 7.
\[\frac19,\frac39,\frac59,\frac79\]thats 4 ways with a denominator of 9.
so thats 19 total ways to end up with a non-terminating decimal.

Therefore the probability of getting a non-terminating decimal is:
\[\frac{19}{25}\]

Answer 3

11/25

Answer 4

Why is your answer different?

Answer 5

whoops! i guess it shows im tired lol i added 3 7 and 9

Answer 6

hes right, i added the wrong things. i was supposed to add 3+4+4 = 11

Answer 7

thx for helping guys