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Fractions that Cannot Be Reduced
Posted: Thu Sep 03, 2026 5:15 pm
by Jason
Fractions which cannot be reduced have a GCF of 1. You will find when figuring out the GCF that the two or more compared numbers have no numbers in common except 1, but, remember, we never need to factor in 1 into GCF calculations.
What is the below fraction reduced, if it can be reduced?
\(\dfrac{99}{17}\)
\(99 \longrightarrow 3 * 33 \longrightarrow 3 * (3 * 11) \longrightarrow 3^{1} * 3^{1} * 11^{1} \longrightarrow 3^{2} * 11^{1}\)
\(17 \longrightarrow 17^{1}\)
The lowest prime powers, common to all numbers, are:
none
\(GCF = 1\)
\(so\)
\(\dfrac{99}{17} = \dfrac{99}{17}\)
The fraction in this problem cannot be reduced because there is no GCF other than 1.
Re: Fractions that Cannot Be Reduced
Posted: Fri Sep 04, 2026 9:36 am
by Stoic
When I was at school, we went a bit further by saying that this is 5 times 14/17 to make numbers lower.
Re: Fractions that Cannot Be Reduced
Posted: Fri Sep 04, 2026 4:36 pm
by Jason
One bad temptation is to see the prime 17 and assume it can't be reduced - when the numerator might be divisible by 17.
Stoic wrote: Fri Sep 04, 2026 9:36 am
When I was at school, we went a bit further by saying that this is 5 times 14/17 to make numbers lower.
Yeah, that's possible also by dividing the top by bottom.
Re: Fractions that Cannot Be Reduced
Posted: Sat Sep 05, 2026 5:37 pm
by Stoic
When I watched some documentaries, I think that first occurance of fractions appeared in Egypt because they needed it for some dividing problems they had. They also had an interesting way of how they divide two numbers. I think saw that with how computers work, by using similar system.
Re: Fractions that Cannot Be Reduced
Posted: Sat Sep 05, 2026 8:03 pm
by Jason
Stoic wrote: Sat Sep 05, 2026 5:37 pm
When I watched some documentaries, I think that first occurance of fractions appeared in Egypt because they needed it for some dividing problems they had. They also had an interesting way of how they divide two numbers. I think saw that with how computers work, by using similar system.
I don't know much about it except that basic computer memory is based on 1 (true) and 0 (false).
