Question

List three rational numbers between 1/3 and 1/7

Answer 1

LCM OF 3and 7= 21
1×7/3×7 and 1×3/7×3
7/21 and 3/21
therefore three rational no. are
4/21,5/21,6/21

it doesnt matter the first no. is small we have to just find the no. between them

Answer 2

Concept

Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The collection of rational numbers is denoted by the letter Q. In other words, a number can be stated as a fraction in which the numerator and denominator are both integers if it can be expressed as a rational number.

Given

the numbers are 1/3 and 1/7

Find

To find out the three rational numbers between he given numbers.

Solution

First, we create the numbers with the same denominator.

1/3 & 1/7

common denominator = LCM of 3 and 7

                                     = 3 × 7

                                     = 21

So,

1/3 = 1/3 × 7/7 = 7/21

1/7 = 1/7 × 3/3 = 3/21

We know that,

3 < 4 < 5 < 6 < 7

Therefore, 3/21 < 4/21 < 5/21 < 6/21 < 7/21

⇒ 1/3 < 4/21 < 5/21 < 6/21 < 1/3

Hence , 3 rational numbers between 1/3 and 1/7 are: 4/21 , 5/21 and 6/21

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