What is 12:70 in simplest form

General
1

what is 12:70 in simplest form

2

What is 12:70 in simplest form?

Answer:

To simplify the ratio 12:70, it’s important to find the greatest common divisor (GCD) of the numbers 12 and 70. A ratio is simplified when it is expressed in its lowest terms, meaning both numbers can no longer be divided by any common factor other than 1.

Step 1: Identify the Greatest Common Divisor (GCD)

  • Factors of 12: 1, 2, 3, 4, 6, 12
  • Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

The common factors of 12 and 70 are 1 and 2. The greatest of these factors is 2, which is the GCD.

Step 2: Divide Both Numbers by the GCD

To simplify the ratio, divide both the numerator and denominator by their GCD:

  • Divide 12 by 2:
    $$ \frac{12}{2} = 6 $$

  • Divide 70 by 2:
    $$ \frac{70}{2} = 35 $$

Thus, when both numbers are divided by 2, the simplest form of the ratio is 6:35.

Final Answer:

The simplest form of the ratio 12:70 is 6:35.