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 

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