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Real Number System

Rational numbers on number line

Rational numbers can be represented on number line in the similar manner like fractions and integers.

Negative rational numbers are marked to the left of 0 while positive rational numbers are marked to the right of 0.

Example:

Represent on number line.

Solution:

The given rational number is negative. Therefore, it will lie to the left of 0.

The space between –1 and 0 is divided into 5 equal parts. Therefore, each part represents .

Marking at 2 units to the left of 0, we obtain the number line as shown below.

Natural numbers are a collection of all positive numbers starting from 1. Whole numbers are a collection of all natural numbers including 0. Integers are the set of numbers comprising of all the natural numbers 1, 2, 3 ...  and their negatives −1, −2, −3 ..., and the number 0. Rational numbers are the numbers that can be written in form, where p and q are integers and q ≠ 0 Closure property Whole numbers are closed under addition and multiplication. However, they are not closed under subtraction and division. Integers are also closed under addition, subtraction and multiplication. However, they are not closed under division. Rational numbers: Rational numbers are closed under addition.

Example: is a rational number.

Rational numbers are closed under subtraction.

Example: is rational number.

Rational numbers are closed under multiplication.

Example: is a rational number.

Rational numbers are not closed under division.

Example: 2 ÷ 0 is not defined.

Commutativity W…

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