Name: Rational Numbers Between Two Rational Numbers
Uploaded: 2019-07-19
Duration: 9 min 50 s
Description: In this video, we will learn that we can find infinite rational numbers between any two rational numbers. Interested to know more? Just click!

Question

Recall the commutativity of different operations for whole numbers by filling the following table.

Operation	Numbers	Remarks
Addition	$a + b = b + a$	Addition is commutative.
Subtraction	_____	Subtraction is not commutative
Multiplication	_____	Multiplication is commutative.
Division	_____	Division is not commutative.

Accepted Answer

Addition
Example: $5 + 4 = 9$ And $4 + 5 = 9$ . Therefore, $5 + 4 = 4 + 5$

This shows that we can add whole numbers in any order.
Therefore, according to commutative property for addition the sum of two whole numbers is the same, no matter in which order they are added.

Multiplication
Example: $5 \times 4 = 20$ And $4 \times 5 = 20$ . Therefore, $5 \times 4 = 4 \times 5$

This shows that we can multiply whole numbers in any order.
Commutative property for multiplication states that the product of two whole numbers is the same, no matter in which order they are multiplied.

Subtraction
Example: $7 - 5 = 2$ And $5 - 7 = - 2$ . Therefore, $7 - 5 \neq 5 - 7$
Hence, Subtraction is not commutative.
Division
Example: $6 \div 2 = 3$ And $2 \div 6 = 1 / 3$ . Therefore, $6 \div 2 \neq 2 \div 6$
Hence, Division is not commutative.

Hence, the table could be filled in the following way.

Operation Numbers Remarks

Addition $a + b = b + a$ Addition is commutative.

Subtraction $a - b \neq b - a$ Subtraction is not commutative

Multiplication $a \times b = b \times a$ Multiplication is commutative.

Division $a \div b \neq b \div a$ Division is not commutative.

Important Questions on Rational Numbers

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