Question

find a rational number between 1/2 and 3/4​

Answer 1

Answer:

you can use this simple formula :

If we want to insert n rational numbers between rational numbers a and b

Then d=(b-a)/(n+1)

Then the n ration numbers will be:

a+d, a+2d,………………………………….till a+n*d

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Here given a=1/2 , b=3/4 and n=5

so d=(3/4–1/2)/(5+1)=(1/4)/6=1/24

Thus 1st number=a+d=1/2+1/24=13/24

2nd no.= 13/24+1/24=14/24

Hence 3rd 4th and 5th numbers are:

15/24,16/24 and 17/24

If we like then the numbers can be written in simple fraction form:

So 5 rational no. are: 13/24,14/24,15/24,16/24, and 17/24

OR 13/24 ,7/12,5/8,2/3 and 17/24

Note: You can check the next no =17/24+1/24=18/24=3/4=b

This verifies our solution too

Answer 2

Answer:

5/8 is the number between 1/2 and 3/4.

Explanation:

Rational numbers are the numbers which are in the form of p/q where q never equals to zero. Any number that can be expressed as a ratio or fraction is a rational number. All the integers, whole numbers are rational numbers. The rational numbers are to be denoted as Q.

To find a rational number between any two rational numbers, follow these steps:

Find the mean of the given two numbers for which we have to add the two numbers and then divide the sum by 2.

$\frac{ \frac{1}{2} + \frac{3}{4} }{2 } = \frac {\frac{2 + 3}{4} }{2} \\ = \frac{ \frac{5}{4} }{2}$

$\frac{5}{4} \div 2 \\ \frac{5}{4} \times \frac{1}{2} = \frac{5}{8}$

so, 5/8 is the rational number between the two given numbers.

The real numbers consists of the set of rational numbers and the irrational numbers. The numbers which are not rational are called irrational numbers. The real numbers can be classified as terminating, non terminating and non terminating non repeating expansions. The rational numbers have terminating expansions while the irrational numbers have non terminating expansions.