Fill in the blanks in the following table with Yes or No if they follow commutative properties. addition subtraction multiplication division Rational numbers Yes _____ _____ _____ Integers _____ No _____ _____ Whole numbers _____ _____ Yes _____ Natural numbers _____ _____ _____ No

Commutative property or commutative law explains that order of terms does not matter while performing an operation. The commutative property of rational numbers, integers, whole numbers and natural numbers is applicable for addition and multiplication only and not for subtraction and division. Thus, the table could be filled in the following way. addition subtraction multiplication division Rational numbers Yes No Yes No Integers Yes No Yes No Whole numbers Yes No Yes No Natural numbers Yes No Yes No

Recall the associativity of the four operations for whole numbers through this table: Operation Numbers Remarks Addition Addition is associative Subtraction Subtraction is not associative Multiplication a × ( b × c ) = ( a × b ) × c Multiplication is associative Division Division is not associative

The associative property states that you can add or multiply regardless of how the numbers are grouped. The commutative property of rational numbers, integers, whole numbers and natural numbers is applicable for addition and multiplication only and not for subtraction and division. Hence, the table can be filled in the following way. Operation Numbers Remarks Addition a + ( b + c ) = ( a + b ) + c Addition is associative Subtraction a - ( b - c ) ≠ ( a - b ) - c Subtraction is not associative Multiplication a × ( b × c ) = ( a × b ) × c Multiplication is associative Division a ÷ ( b ÷ c ) ≠ ( a ÷ b ) ÷ c Division is not associative

Find - 1 2 + 3 7 + - 4 3 and - 1 2 + 3 7 + - 4 3 . Are the two sums equal?

Given, - 1 2 + 3 7 + - 4 3 and - 1 2 + 3 7 + - 4 3 Solving the first expression. ⇒ - 1 2 + 3 7 + - 4 3 = - 1 2 + 9 - 28 21 = - 1 2 + - 19 21 = - 21 - 38 42 = - 59 42 Solving the second expression. ⇒ - 1 2 + 3 7 + - 4 3 = - 7 + 6 14 + - 4 3 = - 1 14 - 4 3 = - 3 - 56 42 = - 59 42 Here, we could see that the final answers are same. So we can say the sum is equal. This property is called associative property, which states that a + b + c = a + b + c .

Is 2 3 × - 6 7 × 4 5 = 2 3 × - 6 7 × 4 5 ?

Given, to check whether 2 3 × - 6 7 × 4 5 = 2 3 × - 6 7 × 4 5 To verify solve LHS and RHS separately LHS ⇒ 2 3 × - 6 7 × 4 5 = 2 3 × - 24 8 35 = - 16 35 RHS ⇒ 2 3 × - 6 7 × 4 5 = - 12 4 21 7 × 4 5 = - 16 35 Here, LHS = RHS Hence, 2 3 × - 6 7 × 4 5 = 2 3 × - 6 7 × 4 5 This property is called associative property. It states that a × b × c = a × b × c .

Fill in the blanks in the following table with Yes or No if they follow associative properties. addition subtraction multiplication division Rational numbers _____ _____ _____ No Integers _____ _____ Yes _____ Whole numbers Yes _____ _____ _____ Natural numbers _____ No _____ _____

The associative property states that you can add or multiply regardless of how the numbers are grouped. The associative property of rational numbers, integers, whole numbers and natural numbers is applicable for addition and multiplication only and not for subtraction and division. Thus, the table could be filled in the following way. addition subtraction multiplication division Rational numbers Yes No Yes No Integers Yes No Yes No Whole numbers Yes No Yes No Natural numbers Yes No Yes No

Find using distributive. 7 5 × - 3 12 + 7 5 × 5 12

Given, 7 5 × - 3 12 + 7 5 × 5 12 According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. ⇒ 7 5 - 3 12 + 5 12 = 7 5 - 3 + 5 12 = 7 5 2 12 ⇒ 14 60 = 7 30 Hence, the required is 7 30 .

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Fill in the following table and check the commutativity of different operations for integers:

Operation Numbers Remarks

Addition Addition is commutative.

Subtraction $5 - (- 3) \neq - 3 - 5$ Subtraction is not commutative.

Multiplication Multiplication is commutative.

Division Division is not commutative.

Important Questions on Rational Numbers

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IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 1 - Rational Numbers>TRY THESE>Q 1

Fill in the blanks in the following table with Yes or No if they follow commutative properties.

	addition	subtraction	multiplication	division
Rational numbers	Yes	_____	_____	_____
Integers	_____	No	_____	_____
Whole numbers	_____	_____	Yes	_____
Natural numbers	_____	_____	_____	No

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MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 1 - Rational Numbers>Exercise>Q 1

Recall the associativity of the four operations for whole numbers through this table:

Operation	Numbers	Remarks
Addition		Addition is associative
Subtraction		Subtraction is not associative
Multiplication	$a \times (b \times c) = (a \times b) \times c$	Multiplication is associative
Division		Division is not associative

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IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 1 - Rational Numbers>Exercise>Q 2

Find

\frac{- 1}{2} + [\frac{3}{7} + (\frac{- 4}{3})]

and

[\frac{- 1}{2} + \frac{3}{7}] + (\frac{- 4}{3}) .

Are the two sums equal?

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IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 1 - Rational Numbers>Exercise>Q 3

\frac{2}{3} \times (\frac{- 6}{7} \times \frac{4}{5}) = (\frac{2}{3} \times \frac{- 6}{7}) \times \frac{4}{5} ?

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MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 1 - Rational Numbers>TRY THESE>Q 1

Fill in the blanks in the following table with Yes or No if they follow associative properties.

	addition	subtraction	multiplication	division
Rational numbers	_____	_____	_____	No
Integers	_____	_____	Yes	_____
Whole numbers	Yes	_____	_____	_____
Natural numbers	_____	No	_____	_____

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MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 1 - Rational Numbers>THINK, DISCUSS AND WRITE>Q 1

If a property holds for rational numbers, will it also hold for integers? For whole numbers? Which will? Which will not?

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8th Jammu and Kashmir Board

IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 1 - Rational Numbers>TRY THESE>Q (i)

Find using distributive.

\{\frac{7}{5} \times (\frac{- 3}{12})\} + \{\frac{7}{5} \times \frac{5}{12}\}

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IMPORTANT

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 1 - Rational Numbers>TRY THESE>Q (ii)

Find using distributive.

\{\frac{9}{16} \times \frac{4}{12}\} + \{\frac{9}{16} \times \frac{- 3}{9}\}

Important Questions on Rational Numbers

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