Numbers are the main thing to calculate anything. Today, I will teach you rational numbers and provide Chapter 1 solutions. Before reading this, let’s learn again natural numbers, whole numbers, and integers shortly, and then read rational numbers.
What are natural numbers?
We naturally count everything from 1 and go in ascending order and these numbers are positive and do not contain 0. Natural numbers are numbers that are used to count and order things. Counting things is called cardinal and ordering things is called ordinal.
Cardinal Natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, …
Ordinal Natural numbers: 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th, …
What are whole numbers?
All positive natural numbers from 0 to infinity are called whole numbers.
Whole numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, …
What are integers?
These are numbers that include all whole numbers and negative numbers. It can be represented on a number line, where 0 is the number between positive and negative numbers. The number to the left of 0 is called a negative number and the number to the right of 0 is called a positive number.
Integers
What is rational number?
Rational numbers are defined as: Numbers that can be expressed as fractions or p/q where q is not equal to zero are called rational numbers. For example, 2/8 is a rational number, where p is 2 and q is 8.
Well, I welcome you to be promoted in class 8th. Prepare your bag and timetable, then read/learn and examine yourself.
Sum of Rational Numbers
The sum of any two rational numbers a and b are also called rational numbers. Let’s check with some rational numbers
1. 2/5 + 4/8
= (2 × 8 + 4 × 5)/40
= (16 + 20)/40
= 36/40
= 9/10
This sum is showing as p/q, which is called rational number.
Let’s take another example
2. -3/8 + (-4/7)
= ((-3 × 7) + (-4 × 8)) / 56
= (-21 + (-32))/56
= -53/56
Subtraction of Rational Numbers
The subtraction of any two rational numbers a and b are also called rational numbers. Let’s check with some rational numbers.
1. 4/9 – 3/7
= (4 × 7 – 3 × 9) / 63
= (28 – 27)/63
=1/63
This subtraction is showing as p/q, which is called rational numbers.
2. 5/7 – 9/4
= (5 × 4 – 9 × 7) / 28
= (20 – 63)/28
= -43
Multiplication of Rational Numbers
The multiplication of any two rational numbers a and b are also called rational numbers. Let’s check with some rational numbers.
1. 3/5 × 5/8
= (3 × 5)/(5 × 8)
= 15/40
This multiplication is showing as p/q, it is called rational numbers.
2. 4/7 × 3/8
= (4 × 3)/(7 × 8)
= 12/56
Division of Rational Numbers
We know that a 0 is not defined for any rational number a. However, if we do not include zero, then the set of all other rational numbers is closed under division.
Apart from definition and types, I wrote articles for Exercise 1.1 and 1.2 solved answers.
