Question

Select the ratio that is equivalent to 12:14.
(a) 6:2
(b) 6:7
(c) 3:8
(d) 5:7

Answer 1

Hint: First, before proceeding for this, we must know that the ratio is defined as the first term written on the left side of the colon comes and the numerator and the second term which is written on the right side of the colon comes in the denominator and the division gives us the ratio. Then, we need to find a common table at which these both numbers can be divided and usually we start with the lowest prime number as 2. Then, we can see that the denominator has the term 7 which is actually itself a prime number that means it will not come in any other table except 1 and itself, by which we get the final ratio.

Complete step by step answer:
In this question, we are supposed to find the equivalent ratio of 12:14.
So, before proceeding for this, we must know that the ratio is defined as the first term written on the left side of the colon comes and the numerator and the second term which is written on the right side of the colon comes in the denominator and the division gives us the ratio.
Now, in this question, we are given with the number for ratio as 12:14 which can be written in $\dfrac{p}{q}$ form as:
$\dfrac{12}{14}$
Now, we need to find a common table at which these both numbers can be divided and usually we start with the lowest prime number as 2.
So, by dividing the numerator and denominator by 2, we get:
$\dfrac{6}{7}$
Now, we can see that the denominator has the term 7 which is actually itself a prime number that means it will not come in any other table except 1 and itself.
So, we can’t further divide the above rational number and it is the final answer.
Then, to get the answer in required form, we write in the ratio form as:
6:7
So, 6:7 is the equivalent ratio of the given numbers as 12:14.
Hence, option (b) is correct.

Note:
Now, to solve these types of questions we need to know some of the basics of the prime numbers that are used above in the question. So, the prime number is the natural number greater than 1 that is not a product of two smaller natural numbers.