[Math] The steps of simplifying a fraction

fractions

So I'm in an Adult Education class for my GED and I'm trying hard to study on my Math which is the only subject I have trouble with. I only have "barely" a 6th grade education to Math so I'm having a lot of trouble totally understanding it all.

I'm trying to learn how to simplify fractions on Khan Academy which is the current task we're learning in the class. I am not getting any of it. I'm trying to answer the question

Simplify to lowest terms.

36/60

I tried to Google the answer to see if I can find an explaination how to do this and found one on Y/A but the question was how to simplify 60/36 instead. I assume it was the same steps.

You're looking to get rid of the common factors, and inspection is
probably easiest here.

First try 6 as a factor, so

(60/6) /(36/6) = 10/6

10/6 is even, so divide by 2

(10/2) / (6/2) = 5/3

OK, that's pretty simple, and both sides are prime, so the only thing
you could do further is change

5/3 = (3 + 2)/3 = 3/3 + 2/3 = 1 2/3

5/3 or 1 2/3 – take your pick as to the simplest!

I'm still not understanding it.

I understand that:

  • Find the number that goes into both 36 and 60
  • Multiply the number and count how many times it goes into 36/60
  • ???

I'm just not sure what to do after that. What is the next step?

Best Answer

The complete general way is to prime factorize the numerator and denominator. To factorize a number into primes is to find a product of primes that equals the given number. This may seem slightly challenging, but as long as the numbers aren't that large, it is usually not too difficult.

Let me give you an example of a prime factorization of, say, $78$. We first note that it is an even number, so $2$ is a factor, i.e. $78 = 2\cdot 39$. Since $2$ is prime we can not reduce that futher, but $39$ is not. We find the factors of $39 = 3\cdot13$. Therefore $78 = 2\cdot3\cdot13$, where all the factors are now prime.

In the fraction we just cancel each common prime factor, i.e. $$\require{cancel}\frac{36}{60}=\frac{2\cdot 18}{2\cdot 30}=\frac{2\cdot2\cdot9}{2\cdot2\cdot15}= \frac{\cancel{2\cdot2\cdot3}\cdot3}{\cancel{2\cdot2\cdot3}\cdot5}=\frac{3}{5}.$$

Related Question