how do 83/100 simplify to 5/6
It doesn't. 100 is not divisible by 6, nor is 83 divisible by 5.
5/6 = .8333333333 .....
83/100 = .8300000000000......
so
5/6 is a little bigger than 83/100
and they are only the same to two significant figures.
To simplify the fraction 83/100 to 5/6, follow these steps:
Step 1: Prime factorize both the numerator and the denominator.
83: 83 is a prime number, so its prime factorization is just 83.
100: Divide 100 by its prime factors until you can't divide it anymore.
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factorization of 100 is 2² × 5², which can be written as 2 × 2 × 5 × 5.
Step 2: Cancel out any common factors between the numerator and the denominator.
Since there are no common factors between 83 and any of the prime factors of 100 (2, 2, 5, 5), we cannot cancel any common factors.
Step 3: Divide the numerator and the denominator by their greatest common divisor (GCD) to simplify the fraction.
The GCD of 83 and 100 is 1 (since 83 is a prime number).
Divide the numerator and the denominator by 1:
83 ÷ 1 = 83
100 ÷ 1 = 100
Step 4: Write the simplified fraction.
The simplified fraction of 83/100 is 83/100 since there are no common factors to cancel out.
Therefore, 83/100 cannot be simplified to 5/6.
To simplify the fraction 83/100 to 5/6, you need to find the greatest common divisor (GCD) of the numerator (83) and the denominator (100), and then divide both numerator and denominator by this GCD. Here's how you can do it step by step:
Step 1: Identify the GCD of 83 and 100.
The factors of 83 are 1 and 83.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The only common factor between 83 and 100 is 1 since 83 is a prime number.
Step 2: Divide both the numerator and denominator by their GCD, which is 1.
83 ÷ 1 = 83
100 ÷ 1 = 100
So, the fraction 83/100 is already in its simplest form because the numerator and denominator do not share any common factors other than 1.