ok so I got 25:150 and I reduced that to 5:30
Now I know since 5 is the lowest I can go with that number it will be 1:over something
But I'm confused as to what to do with 30 because the lowest term it can go to is 2 but the answer in the book is 1:6 instead of 1:2 why is that I need to know
The greatest common factor of 25 and 150 is
25.
25 will be the "key" that unlocks the solution to this problem.
(25/
25)=
1
(150/
25)=
6
therefore,
(25/150) is equivalent to (
1/
6)
Or 25:150 is equivalent to 1:6
Whenever you are looking for common factors you should draw a factor tree, one for each number you are factorizing. This is just an example. Idk if you have seen this yet but it helped me and eventually if you avoid using a calculator you will just know automatically what the factorizations are for most 2 digit numbers.
150__________________________
25____________________________________________________________________ _|_\__________________________|_\____________________________________________________________________
25__6________________________5_5___________________________________________________________________
|_\ _|_\_____________________________________________________________________________________________
5_5_3_2____________________________________________________________________________________________
All of the bottom row numbers have themselves and 1 as common factors so we call them prime numbers.
5,5,3,2 is the prime factorization of 150 because all the numbers are primes and 5x5x3x2=150.
5,5 is the prime factorization of 25 because all the numbers are prime and 5x5=25.
Maybe that was too much info but it's still good to know anyway.