>Rational Numbers>Properties of Rational Numbers

Properties of Rational Numbers

IMPORTANT

Important Questions on Properties of Rational Numbers

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IMPORTANT

Rational Numbers>Properties of Rational Numbers> Q 1

$\{\frac{7}{5} \times (\frac{- 3}{10})\} + \{\frac{7}{5} \times \frac{9}{10}\}$ Find using distributive property.

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Rational Numbers>Properties of Rational Numbers> Q 2

$\{\frac{9}{16} \times 3\} + \{\frac{9}{16} \times (- 19)\}$ Find using distributive property.

EASY

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Rational Numbers>Properties of Rational Numbers> Q 3

Check whether it is a rational number.

$- \frac{2}{3} \div \frac{6}{11} =$ _____.

EASY

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Rational Numbers>Properties of Rational Numbers> Q 4

Check whether it is a rational number.

$\frac{2}{1} \times \frac{19}{13} =$ _____.

EASY

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Rational Numbers>Properties of Rational Numbers> Q 5

Check whether it is a rational number.

$\frac{3}{7} \times \frac{5}{2} =$ _____.

EASY

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Rational Numbers>Properties of Rational Numbers> Q 6

Check whether it is a rational number.

$\frac{48}{9} - \frac{11}{8} =$ _____.

EASY

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Rational Numbers>Properties of Rational Numbers> Q 7

Check whether it is a rational number.

$\frac{2}{3} - \frac{3}{7} =$ _____.

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Rational Numbers>Properties of Rational Numbers> Q 8

Check whether it is a rational number.

$\frac{7}{2} + \frac{2}{7} =$ _____.

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Rational Numbers>Properties of Rational Numbers> Q 9

Fill in the following blanks.

$3 \times$ _____ $= 3$ and _____ $\times 3 = 3$

$- 2 \times$ _____ $= - 2$ and _____ $\times - 2 = - 2$

$\frac{7}{8} \times$ _____ $= \frac{7}{8}$ and _____ $\times \frac{7}{8} = \frac{7}{8}$

What observations have you made in the above multiplications?

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Rational Numbers>Properties of Rational Numbers> Q 10

Complete the following table.

Numbers	Associative under
Numbers	Addition	Subtraction	Multiplication	Division
Natural numbers	Yes
Whole numbers				No
Integers		Yes
Rational Numbers			Yes

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Rational Numbers>Properties of Rational Numbers> Q 11

Complete the table with necessary illustrations and remarks for integers.

Operation	Integers with example	Remark
Addition	Is $2 + [(- 3) + 5)] = [(2 + (- 3)] + 5 ?$ $2 + [(- 3) + 5] = 2 + [- 3 + 5] = 2 + 2 = 4$ $[2 + (- 3)] + 5 = [2 - 3] + 5 = - 1 + 5 = 4$ For any three integers $a, b, c$ $a + (b + c) = (a + b) + c$
Subtraction	Is $6 - (9 - 5) = (6 - 9) - 5 ?$
Multiplication	Is $2 \times [7 \times (- 3)] = (2 \times 7) \times (- 3) ?$
Division	$10 \div [2 \div (- 5)] = [10 \div 2] \div (- 5) ?$ $10 \div [2 \div (- 5)] = 10 \div \frac{2}{- 5} = 10 \times \frac{- 5}{2} = - 25$ Now, $[10 \div 2] \div (- 5) = \frac{10}{2} \div (- 5) = 5 \div (- 5) = \frac{5}{- 5} = - 1$ Thus, $10 \div [2 \div (- 5)] \neq [10 \div 2] \div (- 5)$

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Rational Numbers>Properties of Rational Numbers> Q 12

Complete the table with necessary illustrations and remarks for whole numbers.

Operation	Examples with whole numbers	Remark
Addition	Is $2 + (3 + 0) = (2 + 3) + 0 ?$ $2 + (3 + 0) = 2 + 3 = 5$ $(2 + 3) + 0 = 5 + 0 = 5$ $\Rightarrow 2 + (3 + 0) = (2 + 3) + 0$ $a + (b + c) = (a + b) + c$ for any three whole numbers $a, b, c$
Subtraction	$(2 - 3) - 2 = ? 2 - (3 - 2) = ?$ Is $(2 - 3) - 2 = 2 - (3 - 2) ?$	Subtraction is not associative
Multiplication		Multiplication is associative
Division	Is $2 \div (3 \div 5) = (2 \div 3) \div 5 ?$ $2 \div (3 \div 5) = 2 \div \frac{3}{5} = 2 \times \frac{5}{3} = \frac{10}{3}$ $(2 \div 3) \div 5 = \frac{2}{3} \div 5 = \frac{2}{3} \times \frac{1}{5} = \frac{2}{15}$ $2 \div (3 \div 5) \neq (2 \div 3) \div 5$	Division is not associative

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Rational Numbers>Properties of Rational Numbers> Q 13

Complete the following table.

Numbers	Commutative with respect to
Numbers	Addition	Subtraction	Multiplication	Division
Natural numbers	Yes	No	Yes
Whole numbers				No
Integers
Rational Numbers				No

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Rational Numbers>Properties of Rational Numbers> Q 14

Complete the following table for integers.

Operation	Example	Remark
Addition		Addition is commutative in Integers.
Subtraction	$2, 3$ are integers $2 - (3) = ? (3) - 2 = ? Is 2 - 3) = (3) - 2 = ?$
Multiplication
Division		Division is not Commutative in Integers

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Rational Numbers>Properties of Rational Numbers> Q 15

Complete the following table for whole numbers.

Operation	Example	Remark
Addition	$2, 3$ are whole numbers $2 + 3 = 5$ and $3 + 2 = 5$ , $∴ 2 + 3 = 3 + 2$	Addition is commutative in W.
Subtraction	Is $3 - 2$ equal to $2 - 3$ ?	Subtraction is not commutative
Multiplication
Division	$4 \div 2 = ? 2 \div 4 = ?$ Is $4 \div 2 = 2 \div 4 ?$

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Rational Numbers>Properties of Rational Numbers> Q 16

Fill the blanks in the table.

Numbers	Closure property under
Numbers	Addition	Subtraction	Multiplication	Division
Natural numbers	Yes
Whole numbers				No
Integers		Yes
Rational Numbers			Yes

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Rational Numbers>Properties of Rational Numbers> Q 17

If we exclude zero from the set of integers is it closed under division? Check the same for natural numbers.

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Rational Numbers>Properties of Rational Numbers> Q 18

The product of the rational numbers, $3 \div \frac{17}{13} =$ _____.

EASY

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Rational Numbers>Properties of Rational Numbers> Q 19

Check whether it is a rational number.

$0 + \frac{1}{2} =$ _____.

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Rational Numbers>Properties of Rational Numbers> Q 20

The product of the rational numbers, $\frac{- 2}{3} \div \frac{6}{11} =$ _____.