Subscribe to our YouTube channel for the latest videos, updates, and tips.


How to Find Rational Numbers?

How to find rational numbers between two given rational numbers?

If m and n be two rational numbers such that m < n then 1/2 (m + n) is a rational number between m and n.


1. Find out a rational number lying halfway between 2/7 and 3/4.

Solution:


Required number = 1/2 (2/7 + 3/4) 

= 1/2 ((8 + 21)/28) 

= {1/2 × 29/28) 

= 29/56

Hence, 29/56 is a rational number lying halfway between 2/7 and 3/4.

2. Find out a rational number lying between -1/3 and 1/2.

Solution:

Required number = 1/2 (-1/3 + 1/2)

= 1/2 ((-2 + 3)/6)

= {1/2 × 1/6)

= 1/12

Hence, 1/12 is a rational number lying between 1/3 and 1/2.



3. Find out ten rational numbers lying between -3/11 and 8/11.

Solution:

We know that -3 < -2 < -1 < 0 < 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8

Therefore, -3 /11< -2/11 < -1/11 < 0/11 < 1/11 < 2/11 < 3/11 < 4/11 < 5/11 < 6/11 < 7/11 < 8/11

Hence, -2/11, -1/11, 0/11, 1/11, 2/11, 3/11, 4/11, 5/11, 6/11 and 7/11 are the ten rational numbers lying between -3/11 and 8/11.



4. Find out three rational numbers lying between 3 and 4.

Solution:


A rational number between 3 and 4 is 1/2 (3 + 4) = 7/2.

Then, 3 < 7/2 < 4

A rational number between 3 and 7/2 = 1/2 {3 + 7/2} = 1/2 (3/1 + 7/2)

= 1/2 ((6 + 7)/2) = (1/2 × 13/2) = 13/4

A rational number between 7/2 and 4 = 1/2 {7/2 + 4} = 1/2 (7/2 + 4/1)

= 1/2 ((7 + 8)/2) = {1/2 × 15/2} = 15/4

Therefore, 3 < 13/4 < 7/2 < 15/4 < 4

Hence, 13/4, 7/2 and 15/4 are the three rational numbers lying between 3 and 4.

Rational Numbers

Introduction of Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Rational Numbers in Descending Order

Representation of Rational Numbers on the Number Line

Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Addition of Rational Numbers

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Same Denominator

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Rational Expressions Involving Addition and Subtraction

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Product of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational  Number

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

To Find Rational Numbers







8th Grade Math Practice 

From How to Find Rational Numbers to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. How to Divide Decimals? | Dividing Decimals by Decimals | Examples

    May 06, 25 01:23 AM

    Dividing a Decimal by a Whole Number
    Dividing Decimals by Decimals I. Dividing a Decimal by a Whole Number: II. Dividing a Decimal by another Decimal: If the dividend and divisor are both decimal numbers, we multiply both the numbers by…

    Read More

  2. Multiplying Decimal by a Whole Number | Step-by-step Explanation|Video

    May 06, 25 12:01 AM

    Multiplying decimal by a whole number is just same like multiply as usual. How to multiply a decimal by a whole number? To multiply a decimal by a whole number follow the below steps

    Read More

  3. Word Problems on Decimals | Decimal Word Problems | Decimal Home Work

    May 05, 25 01:27 AM

    Word problems on decimals are solved here step by step. The product of two numbers is 42.63. If one number is 2.1, find the other. Solution: Product of two numbers = 42.63 One number = 2.1

    Read More

  4. Worksheet on Multiplying Decimals | Product of the Two Decimal Numbers

    May 05, 25 01:05 AM

    Practice the math questions given in the worksheet on multiplying decimals. Multiply the decimals to find the product of the two decimal numbers, same like multiplying whole numbers.

    Read More

  5. Multiplication of a Decimal by 10, 100, 1000 | Multiplying decimals

    May 05, 25 12:23 AM

    Multiplication of a Decimal by 10, 100, 1000
    The working rule of multiplication of a decimal by 10, 100, 1000, etc... are: When the multiplier is 10, 100 or 1000, we move the decimal point to the right by as many places as number of zeroes after…

    Read More

Rational Numbers - Worksheets

Worksheet on Rational Numbers

Worksheet on Equivalent Rational Numbers

Worksheet on Lowest form of a Rational Number

Worksheet on Standard form of a Rational Number

Worksheet on Equality of Rational Numbers

Worksheet on Comparison of Rational Numbers

Worksheet on Representation of Rational Number on a Number Line

Worksheet on Adding Rational Numbers

Worksheet on Properties of Addition of Rational Numbers

Worksheet on Subtracting Rational Numbers

Worksheet on Addition and Subtraction of Rational Number

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Properties of Multiplication of Rational Numbers

Worksheet on Division of Rational Numbers

Worksheet on Properties of Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

Worksheet on Operations on Rational Expressions

Objective Questions on Rational Numbers