Factor each number down to prime numbers. A prime number is divisible only by itself and by 1:
26 = 2*13
54 = 2*3*3*3
45 = 3*3*5
117 = 3*3*13
26 45 2*13 3*3*5
--- * ---- = ------------- * ----------
54 117 2*3*3*3 3*3*13
Now cancel all like terms in the numerator and denominator. You can cancel one 2, the 13, and two 3's:
26 45 2*13 3*3*5 5 5
--- * ---- = ------------- * ----------- = --------- = ----
54 117 2*3*3*3 3*3*13 3*3*3 27
--- * ---- = ------------- * ----------- = --------- = ----
54 117 2*3*3*3 3*3*13 3*3*3 27
Peter H.
Hi Krystian,
The method that Philip P. has given us is guaranteed to give the correct answer, the most simplified expression. It always works. Your suggestion - replacing 45 with 9*5 - sometimes will work, sometimes not. In this specific problem, it will work but only
if you also realize that 117 is 9*13, and thus cancel the 9's. I suggest that you try the method from Philip; that is, factor each number to prime numbers. It works!
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06/02/14
Philip P.
tutor
When you gain a little experience, you will not need to factor down to prime numbers. So you are not wrong in using 9*5 vice 3*3*5 for 45. But since you stated that you were having trouble finding common factors, the sure thing to do is to factor to
prime numbers. It always works, as Peter stated.
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06/02/14
Krystian P.
06/02/14