Maths Activity For Class 8 Rational Numbers

This study material on NCERT Maths Class 8 Rational Numbers covers all the concepts of this chapter thoroughly. You will get the explanation and solution for every sum given in the Class 8 Maths Rational Numbers Questions here. So let us learn what is a rational number first.

What is a Rational Number?

A rational number can be defined as any number which can be represented in the form of p/q where q ≠ 0. Rational numbers are represented by the symbol Q. Rational numbers can be natural numbers, whole numbers, integers, or fractions.

Examples of rational numbers are ½, 5, 0.25, etc.

Rational Numbers for Class 8 project covers the conditions for checking a rational number 

To check if a number is rational or not, verify the below conditions.

• The number should be represented in the form of p/q, where q≠0.

• The ratio p/q can be further simplified and represented in decimal form.

Types of Rational Numbers

• Positive Rational Number

If both the numerator and denominator are of the same signs, then the rational numbers are called positive rational numbers. Example: ⅖,(-4)/(-5)

• Negative Rational Numbers

If numerator and denominator are of opposite signs, then the rational number is called a negative rational number. Example:  (-2)/5

Arithetic Operations on Rational Numbers

Let us discuss how we can perform arithmetic operations on rational numbers, say a/b and c/d.

• Addition of Rational Number- When we add a/b and c/d, we need to make the denominator the same. Hence, we can write it as (ad+bc)/bd.

            Example: 1/2 + 3/4 = (2+3)/4 = 5/4

• Subtraction of Rational Number: Similar to addition, if we subtract a/b and c/d, then also, we need to make the denominator the same, first, and then do the subtraction.

               Example: 1/2 – 3/4 = (2-3)/4 = -1/4

• Multiplication of Rational Numbers: In the case of multiplication, while multiplying two rational numbers, the numerator and denominators of the rational numbers are multiplied, respectively. If a/b is multiplied by c/d, then we write it as  (a × c)/(b × d).

Example: 1/2 × 3/4 = (1 × 3)/(2 × 4) = 3/8

• Division of Rational Number : If a/b is divided by c/d, then it is represented as:

(a/b)÷(c/d) = ad/bc’

Example: 1/2 ÷ 3/4 = (1×4)/(2×3) = 4/6 = ⅔

Multiplicative Inverse of Rational Numbers

The multiplicative inverse of the rational number is defined as the reciprocal of the given fraction.

If the number is a/b then it’s multiplicative inverse will be b/a.

Fact: When a number is multiplied by its own multiplicative inverse the resultant value is equal to 1.

For example, 3/7 is a rational number, then the multiplicative inverse of the rational number 3/7 is 7/3.

Properties of Rational Numbers

As we know a rational number is a subset of the real number, the rational number will obey all the properties of the real number system. Following are some of the important properties of rational numbers.

• If we add, subtract, or multiply any two rational numbers, the results are always a rational number.

• A rational number remains the same if we multiply or divide both the numerator and denominator with the same factor.

• If we add zero to a rational number resultant will be the same number itself.

• Rational numbers are closed under addition, subtraction, and multiplication operations.

Follow the given methods to find the Rational Numbers between two Rational Numbers

Between two rational numbers, there are “n” rational numbers. Now, let us have a look at the two different methods for finding rational numbers.

• Method 1: Find the equivalent fraction for the given rational numbers and then find out the rational numbers in between them. Those numbers should be the required rational numbers.

• Method 2: Find the mean value for the two given rational numbers. The mean value will be the required rational number. In we have  to find more rational numbers, repeat the same process with the old and the newly obtained rational numbers.

Did you Know?

2 cannot be written as a simple fraction. There are many more such numbers, and because they are not rational they are called irrational numbers.

Solved Examples:

1. The sum of the two numbers is -1/3. If one of the numbers is -12/3, find another number.

Solution: Let us write down the given numbers

Sum of two numbers = -1/3

One of the number = -12/3

By using the formula,

Another number = sum of number – given number

= -1/3 – -12/3

Since the denominators are the same we can subtract directly

= (-1+12)/3 = 11/3

Therefore,  the other number is 11/3

2. How to Multiply 6/13 By the Reciprocal of -7/16 ?

Ans: We know reciprocal of a is 1/a , So reciprocal of  -7/16 = 16/-7 = -16/7

According to the question,

6/13 × (Reciprocal of -7/16)

=6/13 × (-16/7)

= -96/91

Hence -96/91 is the final answer.