Rational Numbers – Solved Examples
Example 1: Check which of the following is irrational or rational: 1/2, 13, -4, √3, and π.
Solution:
Rational numbers are numbers that can be expressed in the form of p/q, where q is not equal to 0.
1/2, 13, and -4 are rational numbers as they can be expressed as p/q.
√3, and π are irrational numbers as they can not be expressed as p/q.
Example 2: Check if a mixed fraction, 3(5/6) is a rational number or an irrational number.
Solution:
Simplest form of 3(5/6) is 23/6
Numerator = 23, which is an integer
Denominator = 6, is an integer and not equal to zero.
So, 23/6 is a rational number.
Example 3: Determine whether the given numbers are rational or irrational.
(a) 1.33 (b) 0.1 (c) 0 (d) √5
Solution:
a) 1.33 is a rational number as it can be represented as 133/100.
b) 0.1 is a rational number as it can be represented as 1/10.
c) 0 is a rational number as it can be represented as 0/1.
d) √5 is an irrational number as it can not be represented as p/q.
Example 4: Simplify (2/3) × (6/8) ÷ (5/3).
Solution:
(2/3) × (6/8) ÷ (5/3) = (2/3) x (6/8) × (3/5)
= (2 × 6 × 3)/(3 × 8 × 5)
= 36/120 = 3/10
Example 5: Arrange following rational numbers in ascending order: 1/3, -1/2, 2/5, and -3/4.
Solution:
Common denominator for 3, 2, 5, and 4 is 60. Thus
1/3 = 20/60
-1/2 = -30/60
2/5 = 24/60
-3/4 = -45/60
With common denominator, rational number with greatest numerator is greatest.
⇒ -30/60 < -45/60 < 20/60 < 24/60
Thus, ascending order of given rational numbers is: -1/2 < -3/4 < 1/3 < 2/5
Rational Numbers: Definition, Examples, Worksheet
Rational Numbers are numbers written in terms of the ratio of two integers, where the denominator is not zero. In maths, Rational numbers are a type of real numbers that can be written in the form of p/q, where q ≠ 0. Any fraction is a rational number provided its denominator should not be zero.
Examples of Rational Numbers include 12/21, 34/2, -22 etc. In other words, a rational number is any number that can be written in the form of a/b, where a and b are integers and b is not equal to zero.
In this article, we have provided everything related to Rational numbers including, definitions, examples, types, a list of rational numbers, and how to identify rational numbers.
Table of Content
- What is a Rational Numbers?
- Examples of Rational Numbers
- Representation of Rational Numbers
- Types of Rational Numbers
- How to Identify Rational Numbers?
- List of Rational Numbers in Number System
- Arithmetic Operations on Rational Numbers
- Addition of Rational Numbers
- Subtraction of Rational Numbers
- Multiplication of Rational Numbers
- Division of Rational Numbers
- Equivalent Rational Numbers
- Decimal Expansion of Rational Numbers
- Multiplicative Inverse of a Rational Number
- Rational Numbers Properties
- Find Rational Numbers between Two Rational Numbers?
- Representing Rational Numbers on Real Line
- Rational and Irrational Numbers