simplify the fraction 126/105

The first thing you have to do is to factorize the number 126 (numerator) and 105 (denominator)

 

 

Let's start with the numerator:

The last digit in 126 is an even number. Therefor the whole number is divisible with 2:

126/2 = 63 The digit sum of 63 is 9, which is divisible with 3, therefor the whole number is divisible with 3:

63/3 = 21 The digit sum of 21 is 3, which is divisible with 3, therefor the whole number is divisible with 3:

21/3 = 7 This number is a prime number (no divisors other than 1 and itself)

 

To sum it up: 126 = 2*3*3*7

 

Now, lets factorize the denominator:

Since the last digit in 105 ends with a zero or a 5, we know that the whole number is divisible with 5:

105/5 = 21 The digit sum of 21 is 3, which is devidable with 3, therefor the whole number is divisible with 3:

21/3 = 7 This number is a prime number (no divisors other than 1 and itself)

 

We conclude that 105 = 3*5*7

 

Now that we have factorized both the nomerator and the denominator, we can restate the fraction:

 

126/105 = (2*3*3*7)/(3*5*7) 

 

Look for factors that occur in both the nomerator (top) and denominator (bottom). Did you find any?

Yup, 3 and 7!

We devide the numerator and the denominator by 3*7 and get:

 

(2*3)/5 = 6/5