# RATIONAL NUMBERS BETWEEN TWO RATIONAL NUMBERS

## About "Rational numbers between two rational numbers"

Rational numbers between two rational numbers

Let us consider the two rational numbers a/b and c/d. Here a, b, c and d are integers and also b ≠ 0, d ≠ 0.

We can find many rational numbers between a/b and c/d using the two methods given below.

1. Formula method

2. Same denominator method

Let us discuss these two methods in detail.

## Formula method

Let ‘a’ and ‘b’ be any two given rational numbers. We can find many rational numbers q1, q2, q3,...in between a and b as follows : The numbers q2, q3 lie to the left of q1. Similarly, q4, q5 are the rational numbers between ‘a’ and ‘b’ lie to the right of q1 as follows: Important note :

Average of two numbers always lies between them.

## Same denominator method

Let ‘a’ and ‘b’ be two rational numbers.

(i) Convert the denominator of both the fractions into the same denominator by taking LCM. Now, if there is a number between numerators there is a rational number between them.

(ii) If there is no number between their numerators, then multiply their numerators and denominators by 10 to get rational numbers between them.

To get more rational numbers, multiply by 100, 1000 and so on.

Important note :

By following different methods one can get different rational numbers between ‘a’ and ‘b’.

## Rational numbers between two rational numbers

Example 1 :

Find a rational number between 3/4 and 4/5

Solution :

Formula method :

Let a = 3/4 and b = 4/5

Let q be the rational number between 3/4 and 4/5.

Then, we have

q  =  1/2 x (a + b)

q  =  1/2 x (3/4 + 4/5)

q  =  1/2 x (15 + 16) / 20

q  =  1/2 x 31/20

q  =  31/40

Hence, the rational number between 3/4 and 4/5 is 31/40.

Same denominator method :

Let a = 3/4 and b = 4/5

L.C.M of the denominator (4, 5) is 20.

So, we can write "a" and "b" as given below

a  =  3/4 x 5/5  =  15/20

and

b  =  4/5 x 4/4  =  16/20

To find a rational number between 15/20 and 16/20 , we have to multiply the numerator and denominator by 10.

Then, we have

15/20 x 10/10  =  150/200

16/20 x 10/10  =  160/200

Therefore, the rational numbers between 150/200 and 160/200 are 151/200, 152/200, 153/200, 154/200, 155/200, 156/200, 157/200, 158/200 and 159/200

Example 2 :

Find two rational numbers between -3/5 and 1/2.

Solution :

Let a = -3/5 and b = 1/2

Let q1 and q2 be the rational number between -3/5 and 1/2.

First, let us get q1.

q1  =  1/2 x (a + b)

q1  =  1/2 x (-3/5 + 1/2)

q1  =  1/2 x (-6 + 5) / 10

q1  =  1/2 x (-1/10)

q1  =  -1/20

Now, let find q2.

q2  =  1/2 x (a + q1)

q2  =  1/2 x (-3/5 - 1/20)

q2  =  1/2 x (-12 - 1) / 20

q2  =  1/2 x (-13/20)

q2  =  -13/40

Hence, the two rational number are -1/20 and -13/40.

Note :

The two rational numbers can be inserted as

-3/5 < -13/40 < -1/20 < 1/2

After having gone through the stuff given above, we hope that the students would have understood "Rational numbers between two rational numbers".

Apart from the stuff given above, if you want to know more about "Rational numbers between two rational numbers", please click here

Apart from "Rational numbers between two rational numbers", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 