Let N denote the set of all natural numbers and R be the relation on N\times N defined by (a, b) R (c, d)\Longleftrightarrow ad (b+c)=bc(a+d) . Check weather R is an equivalence relation.

Let R be defined on N\times N as (a, b) R (c, d)\Longleftrightarrow ad (b+c)=bc(a+d) . ....(1)Reflexivity:We can write ab(b+a)= ba(a+b) for all a, b\in N Since, sum and product of natural numbers obeys commutative propertyHence, by def (1), we can write (a,b) R (a,b) for all (a,b) \in N\times N Hence, R is reflexive.Symmmetry :Let (a,b) R (c,d) \Rightarrow ad(b+c)=bc(a+d) \Rightarrow da(c+b)=cb(d+a) (Since, sum and product of natural numbers obeys commutative property)or cb(d+a)=da(c+b) \Rightarrow (c,d) R(a,b) Hence, R is symmetric Transitivity :Let (a,b) ,(c,d) , (e,f) \in N\times N Let (a,b)R (c,d) and (c,d)R(e,f) ad(b+c)=bc(a+d) and cf(d+e)=de(c+f) \Rightarrow \dfrac{ab}{a-b} =\dfrac{cd}{c-d} and \dfrac{cd}{c-d}=\dfrac{ef}{e-f} \Rightarrow \dfrac{ab}{a-b}=\dfrac{ef}{e-f} \Rightarrow af(b+e) =be(a+f) \Rightarrow (a,b)R(e,f) Hence , R is transitive \therefore R is Equivalence Relation.

Solve Study Textbooks

Join / Login

>>Class 6
>>Maths
>>Whole Numbers
>> $Properties of Whole Numbers$

Properties of Whole Numbers

Revise with Concepts

Properties of Whole Number Operations

ExampleDefinitionsFormulaes

Learn with Videos

Q: Which of the following statements is incorrect?

The difference of two whole numbers is not necessarily a whole number. The statement whole numbers are closed under subtraction is an incorrect statement.

Q: The property represented by a \times (b + c) = a \times b + a \times c is

Distributive property say that multiplication an division can be distributed over parenthesis.a x (b+c) = a x b + a x cSo correct answer will be option C

Q: A student multiplied 7236 by 65 instead of multiplying by 56 . By how much was his answer greater than the correct answer?

(Hint: Do you need to do both the multiplications?)Difference between 65 and 56=9 Difference in the answer =7236\times 9 7236 \times 9 _________ 65124 _________Therefore, His answer was greater than the correct answer by 65,124 .

Q: Find the product using suitable properties. 854\times 102 .

854\times 102=854\times (100+2) =854\times 100+854\times 2 (Distributive property) =85400+1708 =87108 .

Q: The property represented by a + b = b + a is

Commutative property of addition: Changing the order of addends does not change the sum. For example, a+b=b+a So correct answer will be option B

Q: Verify whether commutative property is satisfied for addition, subtraction, multiplication and division of the following pairs of rational numbers.(i) 4 and \dfrac {2}{5} (ii) \dfrac {-3}{7} and \dfrac {-2}{7}

(i)Addition 4+\dfrac{2}{5}=\dfrac{20+2}{5}=\dfrac{22}{5} \dfrac{2}{5}+4=\dfrac{2+20}{5}=\dfrac{22}{5} Commutative property is satisfied.Subtraction 4-\dfrac{2}{5}=\dfrac{20-2}{5}=\dfrac{18}{5} \dfrac{2}{5}-4=\dfrac{2-20}{5}=\dfrac{-18}{5} Commutative property is not satisfied.Multiplication \dfrac{2}{5}\times 4=\dfrac{8}{5} 4\times \dfrac{2}{5}=\dfrac{8}{5} Commutative property is satisfied.Division 4\div \dfrac{2}{5}=4\times \dfrac{5}{2}=\dfrac{20}{2} \dfrac{2}{5}\div 4=\dfrac{2}{5}\times \dfrac{1}{4}=\dfrac{2}{20} Commutative property is not satisfied.(ii)Addition \dfrac{-3}{7}+\left ( \dfrac{-2}{7} \right )=\dfrac{-3-2}{7}=\dfrac{-5}{7} \dfrac{-2}{7}+\left ( \dfrac{-3}{7} \right )=\dfrac{-2-3}{7}=\dfrac{-5}{7} Commutative property is satisfied.Subtraction \dfrac{-3}{7}-\left ( \dfrac{-2}{7} \right )=\dfrac{-3+2}{7}=\dfrac{-1}{7} \dfrac{-2}{7}-\left ( \dfrac{-3}{7} \right )=\dfrac{-2+3}{7}=\dfrac{1}{7} Commutative property is not satisfied.Multiplication \dfrac{-2}{7}\times \dfrac{-3}{7}=\dfrac{6}{7} \dfrac{-3}{7}\times \dfrac{-2}{7}=\dfrac{6}{7} Commutative property is satisfied.Division \dfrac{-3}{7}\div \dfrac{-2}{7}=\dfrac{-3}{7}\times \dfrac{7}{-2}=\dfrac{3}{2} \dfrac{-2}{7}\div \dfrac{-3}{7}=\dfrac{-2}{7}\times \dfrac{7}{-3}=\dfrac{2}{3} Commutative property is not satisfied.

Q: Find the product 8739 \times 102 using distributive property.

8739\times 102 =8739\times(100+2) =8739\times100+8739\times2 =873900+17478 =891,378

Q: Find the value of the following. 3845\times 5\times 782+769\times 25\times 218 .

3845\times 782+769\times 25\times 218 =3845\times 5\times 782+769\times 5\times 5\times 218 =3845\times 5\times 782+3845\times 5\times 218 =3845\times 5\times (782+218) =19225\times 1000=19225000 .

Q: Whole numbers are commutative under which of the following operations?

Whole numbers are commutative under addition and multiplication.For exampleTake two whole numbers 2 and 5. Addition =2+5=7 also 5+2=7 , You can add whole nos. in any order which gives same results. Subtraction 2-5=-3 also 5-2=3 Multiplication =2\times 5=10 also 5\times 2=10 You can multiply whole nos. in any order which gives same results.Division =2\div 5=0.4 also 5\div2=2.5 Whole numbers are commutative under addition and multiplication.

Properties of Natural and Whole Numbers

15 mins

Quick Summary With Stories

View solution

Whole numbers are commutative under which of the following operations?

Easy

View solution

Revise with Concepts

Properties of Whole Number Operations

Learn with Videos

Quick Summary With Stories

Closure Property of Whole Numbers.

Commutative Properties of Whole Numbers.

Associative Property of Whole Numbers

One as a Multiplicative Identity.

Properties of Whole Number Operations

Additive and Multiplicative Identity of Whole Numbers

Important Questions

Let N denote the set of all natural numbers and R be the relation on N×N defined by (a,b)R(c,d)⟺ad(b+c)=bc(a+d). Check weather R is an equivalence relation.

Which of the following statements is incorrect?

The property represented by a×(b+c)=a×b+a×c is

A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer?

Find the product using suitable properties. 854×102.

The property represented by a+b=b+a is

Verify whether commutative property is satisfied for addition, subtraction, multiplication and division of the following pairs of rational numbers. (i) 4 and 52​ (ii) 7−3​ and 7−2​

Find the product 8739×102 using distributive property.

Find the value of the following. 3845×5×782+769×25×218.

Whole numbers are commutative under which of the following operations?

Let $N$ denote the set of all natural numbers and $R$ be the relation on $N \times N$ defined by $(a, b) R (c, d) ⟺ a d (b + c) = b c (a + d)$ . Check weather $R$ is an equivalence relation.

The property represented by $a \times (b + c) = a \times b + a \times c$ is

A student multiplied $7236$ by $65$ instead of multiplying by $56$ . By how much was his answer greater than the correct answer?

Find the product using suitable properties.
$854 \times 102$ .

The property represented by $a + b = b + a$ is

Verify whether commutative property is satisfied for addition, subtraction, multiplication and division of the following pairs of rational numbers.
(i) $4$ and $\frac{2}{5}$
(ii) $\frac{- 3}{7}$ and $\frac{- 2}{7}$

Find the product $8739 \times 102$ using distributive property.

Find the value of the following.
$3845 \times 5 \times 782 + 769 \times 25 \times 218$ .