[keayonia]

I need help on reducing fractions please asap ::)

[labman]

Best thing is to look for common factors in both the numerator and denominator. The bigger ones you can find, the faster it will go. However you can grind down even the largest ones taking out 2,3,5,7, etc. until no common factors are left. Don't give up too soon. 39/65 = 3/5.

[eawoodall]

yes you divide by all the prime numbers, until you reach the square root of the number you are testing.

i.e. if you want to know if 135/x is going to reduce you must test every prime below 12 = 2,3,5,7,11. (because 135^(0.5) < 12)
135 mod 2 <> 0. so 2 is not a factor of 135.
135 mod 3 =0 so 3 is a factor. 135 div 3 = 45. 45 mod 3 = 15. 15 mod 3 =5.
135 mod 5 =0 so 135 div 5 = 27.
135 mod 7 <> 0. so 7 is not a factor of 135.
135 mod 11 <>0. so 11 is not a factor of 135.

the prime factors of 135 are =(3,5).
135 = 3^3 * 5^1.
all the factors of 135 = (1,3,5,135).

you do exactly the same with whatever x there is.
then you look at the common primes to each part of the rational number, and you cancel out (both the top and bottom) the maximum shared number of primes (highest power or exponent).

for example

if the bottom (x) was 145: (ie 135/145 was the question)
145 = 5^1 times 29^1.
so the common prime factors of 135 and 145 are 5^1.
dividing both by 5 we get 27/29.

if the bottom were 63: (ie 135/63 was the question_
63 = 3^2 times 7^1.
so the common prime numbers of 135 and 63 are 3^2.
dividing both by 9 we get 15/7.
(sometimes teachers want you to write 15/7 as 1 + 6/7).

[fredg]

Hi,
Do you mean reducing fractions to another fraction?
Such as:
6/12 is the same as 1/2

Or, 8/12 is the same as 2/3.

OK, if that is the case then here is a way to do it:
Take, for example the fraction 14/24

Look to see what is the largest number that will divide into both 14 and 24 and even number of times. The answer is 2, because 2 divided into 14 is 7; and 2 divided into 24 is 12.
So, the answer is 7/12

Try 36/42

Look again to see what number the largest number is that will divide evenly into both 36 and 42.
It is 6.
So, the reduced fraction is 6/7

Best of luck,
fredg

[eawoodall]

yes, and mathematically it is equivalent to take the largest number that is in both the top and bottom, and divide it out, but does not strengthen the prime number theory or practice that most teachers want the students to develop, at the same time. Sometimes the teachers require the student to show the prime numbers involved, and with prime numbers it proves that the number can not be reduced further, no matter how large the number looks.

notice this example:
simplify 113/124
113^(1/2) < 12. So we test all primes below 12.
113 mod 2 <> 0
113 mod 3 <> 0
113 mod 5 <> 0
113 mod 7 <> 0
113 mod 11 <> 0.
113 is not a multiple of 2 or 3 or 5 or 7 or 11, so 113 is prime.
113 = 113^1.
124 = 2^2 * 31^1.
so 113/124 does not reduce. Because there are no prime factors in common.