# Property of Real Numbers

Updated: 06 Aug 2023

2066

Real numbers form a fundamental mathematical concept encompassing rational and irrational numbers. Understanding the properties of real numbers is essential for solving equations, simplifying expressions, and mastering various mathematical disciplines. In this article, we will engage in a multiple-choice question (MCQ) format to explore and reinforce our knowledge of the property of real number.

## Property of Real Numbers

In this article, “property of real number” refer to closure, commutative, associative, identity, and zero properties. These are vital for solving mathematical problems and building a strong foundation in algebra and beyond. In other words, the properties of real numbers are just one of the basic foundations of mathematics.

### Closure Property of Real Numbers

**1. Closure Property of Addition**

The sum of real numbers is also a real number.**Statement:**

If a, b \in R then a+b \in R**Example:**

7+9=16

Where 16 is a real number.

**2. Closure Property of Subtraction**

The difference between any two real numbers is also a real number.**Statement:**

If a, b \in R then a-b \in R **Example:**

7-9=-2

Where -2 is a real number.

**3. Closure Property of Multiplication**

The Product of real numbers is also a real number.**Statement:**

If a, b \in R then a . b \in R **Example:**

7 \times 9=63

Where 63 is a real number.

**4. Closure Property of Division**

The quotient of any two real numbers is also a real number but it should be noted that the divisor is not zero.**Statement**

For any real numbers a, b \ (where \ b \neq 0 )

If \ a, b \in R \ then \ \frac{a}{b} \in R \ (b \neq 0) **Example:**

\frac{7}{9}=0.7777 \ldots

Where 0.7777 \ldots is a real number.

### Commutative Property of Real Numbers

**1. Commutative Property of Addition:**

According to commutative property of Addition states that, if we change the position or order of two Real Numbers in Adding does not change the final result.**Statement:**

If a, b \in R then a+b=b+a**Example:**

7+9 =9+7

16 =16

**2. Commutative Property of Multiplication**

According to commutative property of Multiplication states that, if we change the position or order of two Real Numbers in Multiplying does not change the final result.**Statement:**

If a, b \in R then a . b=b . a **Example:**

7 \times 9 =9 \times 7

63 =63

**Note:**

Commutative Property w.r.t **Subtraction** and **Division** may not be applicable.**Examples:**

**3. Subtraction**

7-9=9-7

-2 \neq 2

Not Applicable

**4. Division**

\frac{7}{9}=\frac{9}{7}

0.777 \ldots \neq 1.285 \ldots

Not Applicable

### Associative Property of Real Numbers

**1. Associative Property of Addition:**

According to the Associative property of Addition, the order of grouping the real numbers in different ways in Adding does not affect the final result.**Statement:**

If a, b, c \in R then a+(b+c)= (a+b)+c **Example:**

2+(3+5) =(2+3)+5

2+8 =5+5

10 =10

**2. Associative Property of Multiplication**

According to the Associative property of Addition, the order of grouping the real numbers in different ways in Multiplying does not affect the final result.**Statement:**

If a, b, c \in R then a(b c)=(a b) c**Example:**

2(3 \times 5)=(2 \times 3) 5

2(15)=(6) 5

30=30

**Note:**

Associative Property w.r.t **Subtraction** and **Division** may not be applicable.

Examples:

**3. Subtraction**

2-(3-5)=(2-3)-5

2-(-2)=(-1)-5

2+2=-1-5

4 \neq-6

Not Applicable

**4. Division**

2 \div(3 \div 5)=(2 \div 3) \div 5

2 \div 0.6=0.66 \div 5

3.333 \ldots \neq 0.132

Not Applicable

### Distributive Property of Real Numbers

- According to the Distributive Property of Real Numbers over Addition states:

**Statement:**

a \times (b+c)=(a \times b)+(a \times c) **Example:**

2 \times (4+1)=(2 \times 4)+(2 \times 1)

2 \times 5=8+2

10=10

- According to the Distributive Property of Real Numbers over Subtraction states:

**Statement:**

a \times (b-c)=(a \times b)-(a \times c) **Example:**

2 \times (4-1)=(2 \times 4)-(2 \times 1)

2 \times 3=8-2

6=6

### Additive Identity of Real Number

Zero (0) is called Additive Identity because adding “0” to any real number, the result will be the real number itself.**Statement:**

If a \in R then a+0=0+a=a**Examples:**

- 3+0=3
- 3+0=0+3=3
- -5+0=-5
- 9+0=9
- \frac{2}{3}+0=\frac{2}{3}
- 9.5+0=9.5

### Multiplicative Identity of Real Number

1 is called Multiplicative Identity because multiplying “1” to any real number, the result will be the real number itself.**Statement:**

If a \in R then a \times 1=1 \times a=a**Examples:**

- 3×1=3
- 3 \times 1=1 \times 3=3
- -5 \times 1=-5
- 9 \times 1=9
- \frac{2}{3} \times 1=\frac{2}{3}
- 9.5 \times 1=9.5

### Additive Inverse of Real Number

If we add a real number to its opposite real number, the result will always be zero (0).**Statement:**

If a \in R then a+a^{\prime}=a^{\prime}+a=0 then a^{\prime} is called additive inverse of a

OR

a+(-a)=-a+a=0

10+(-10)=-10+10=0

**Example:**

- 2+(-2)=0
- 3+(-3)=0
- -5+5=5-5=0
- -20+20=0
- 10-10=0
- -\frac{2}{3}+\frac{2}{3}=0
- \frac{2}{3}+\left(-\frac{2}{3}\right)=0
- \sqrt{2}+(-\sqrt{2})=0
- 9.5-9.5=0

### Multiplicative Inverse of Real Number

If we multiply a real number to its reciprocal real number, the result will always be “1”.**Statement:**

If a \in R then a . a^{-1}=a^{-1} . a=1 then a^{-1} is called multiplicative inverse of a .

OR

a \cdot \frac{1}{a}=\frac{1}{a} \cdot a=1

OR

a \times \frac{1}{a}=1

10 \cdot \frac{1}{10}=\frac{1}{10} \cdot 10=1 **Examples:**

- -5\times \frac{1}{-5}=1
- 5 \cdot \frac{1}{5}=1
- -3 \times \frac{1}{-3}=1
- -3\left(\frac{1}{-3}\right)=1
- \frac{1}{3} \times 3=1
- \frac{5}{3} \times \frac{3}{5}=1
- \left(\frac{5}{3}\right)\left(\frac{3}{5}\right)=1
- \left(-\frac{5}{3}\right)\left(-\frac{3}{5}\right)=1
- \left(\frac{-5}{3}\right)\left(\frac{-3}{5}\right)=1
- \sqrt{2}\left(\frac{1}{\sqrt{2}}\right)=1
- 9.5\left(\frac{1}{9.5}\right)=1

### Reflexive Property

Every real number or value is equal to itself. e.g. a=a which means that a itself equal to a .**Example**

- 5 =5
- \frac{1}{5} =\frac{1}{5}
- -3 =-3
- -3.8 =-3.8
- \sqrt{2} =\sqrt{2}
- 5.9+\sqrt{2} =5.9+\sqrt{2}
- x+y =x+y

### Symmetric Property

By interchanging the sides of an equation doesn’t effect the result. e.g. a=b then b=a does not effect the result. In other words, Left side equal to right side of an equation.

- Right side equal to left side of an equation

**Example**

- 9+7=16 then 16=9+7
- x=16 or 16=x
- x+y=z or z=x+y
- x+2=z or z=x+2
- a-5=b or b=a-5
- 5.9+\sqrt{2}=x or x=5.9+\sqrt{2}

**Note:**

If x=y then x may be replaced by y or y may be replaced by x in any equation.

### Trichotomy Property

By comparing two real numbers, there will be one possibility from the following.

- a=b
- a < b
- a > b

Examples:

- 6=6
- 3 < 6
- 7 > 5

### Transitive Property of Real Number

**1. Transitive Property of Equality**

If a equal to b under a rule and b equal to c under the same rule then a equal to c is known as transitive property.**Statement:**

a=b and b=c then a=c **Example:**

x+y=z and z=a+b then x+y=a+b

x=5+y and 5+y=z then x=z

**2. Transitive Property of Inequality**

- If a greater than b under a rule and b greater than c under the same rule then a greater than c is known as transitive property of inequality.

**Statement:**

If a > b and b > c then a > c **Example:**

If 7 > 5 and 5 > 2 then 7 > \mathbf{2}

- If a less than b under a rule and b less than c under the same rule then a less than c is known as transitive property of inequality.

**Statement:**

If a < b and b < c then a < c**Example:**

If 3 < 5 and 5 < 7 then 3 < 7

### Addition Property of Real Numbers

**Addition Property of Equality**

If we add the same number or expression on both sides of an equation, the equation does not change which means both the sides remain equal.**Statement:**

a=b then a+c=b+c **Examples:**

1. x=5 then

x+2=5+2

x+2=7

2. x-3=7

Add 3 on Both sides

x-3+3=7+3

x=10

**Addition Property of Inequality**

If we add the same number or expression on both sides of an inequality, the inequality does not change.

- If a > b then a+ c > b+c

**Examples:**

1. 5 > 3

then 5+2 > 3+2

So 7 > 5

2. 5 > 3

then 5+7 > 3+7

So 12 > 10

3. x-3 > 5

Add 3 on B.S

x-3+3 > 5+3

x > 8

- If a < b then a+c < b+c

**Examples:**

1. 3 < 5

then 3+2 < 5+2

So 5 < 7

2. x-3 < 5

Add 3 on B.S

x-3+3 < 5+3

x < 8

### Subtraction Property of Real Number

**Subtraction Property of Equality**

If we Subtract the same number or expression from both sides of an equation, the equation does not change means both the sides remain equal.**Statement:**

a=b then a-c=b-c **Examples:**

1. x=5 then x-2=5-2

2. x+3=7

Subtract 3 from Both sides

x+3-3=7-3

x=4

**Subtraction Property of Inequality**

If we Subtract the same number or expression from both sides of an inequality, the inequality does not change.

- If a > b then a - c > b- c

**Example:**

1. 5 > 3

then 5-2 > 3-2

2. 5 > 3

then 5-7 > 3-7

So -2 > -4

3. x+3 > 5

Subtract 3 from B.S

x+3-3 > 5-3

x > 2

- If a < b then a-c < b-c

**Examples:**

1. 3 < 5

then 3-2 < 5-2

2. x < 5

then x-2 < 5-2

3. x+3 < 5

Subtract 3 from B.S

x+3-3 < 5-3

x < 2

4. y+5 < 17

Subtract 5 from Both sides

x+5-5 < 17-5

y < 12

### Multiplication Property of Real Numbers

**Multiplication Property of Equality**

If we Multiply the same number or expression on both sides of an equation, the equation does not change which means both the sides remain equal.**Statement:**

a=b then a \times c=b \times c **Examples:**

1. x=5

then x \times 2=5 \times 2

So 2x = 10

2. \frac{x}{3}=7

Multiply 3 on Both sides

\frac{x}{3} \times 3=7 \times 3

x=21

**Multiplicative Property of Inequality**

- If we multiply an inequality by a positive number, then the inequality sign is always remained same.
- When c > 0 :

- If a < b then a c < b c
- If a > b then a c > b c

**Examples:**

1. 5 > 3

then 5 \times 2 > 3 \times 2

So 10 > 6

2. 5 < 7

then 5 \times 2 < 7 \times 2

So 10 > 14

3. \frac{x}{3} > 5

Multiply B.S by 3

\frac{x}{3} \times 3 > 5 \times 3

x > 15

2 x > 24

- If we multiply an inequality by a negative number, then the inequality sign is always changed.
- When c < 0 :

- If a < b then a c > b c
- If a > b then a c < b c

**Examples:**

1. 5 > 3

then 5 \times-2 < 3 \times-2

So -10 < -6

2. 5 < 7

then 5 \times-2 > 7 \times-2

So -10 > -14

3. \frac{x}{-3} < 5

Multiply B.S by -3

\frac{x}{-3} \times-3 > 5 \times-3

x > -15

### Division Property of Real Number

**Division Property of Equality**

If we Divide the same number or expression to both sides of an equation, the equation does not change means both the sides remain equal.**Statement:**

If a=b then \frac{a}{c}=\frac{b}{c}

Examples:

1. x=5

then \frac{x}{3}=\frac{5}{3}

2. 2 x=-24

Divide Both sides by 2

\frac{2 x}{2}=\frac{-24}{2}

x=-12

**Division Property of Inequality**

- If we divide an inequality by a positive number, then the inequality sign is always remained same.
- When c > 0:

- If \ a < b \ then \ \frac{a}{c} < \frac{b}{c}
- If \ a > b \ then \ \frac{a}{c} > \frac{b}{c}

**Examples:**

1. 18 > 12

Then \frac{18}{3} > \frac{12}{3}

So 6 > 4

2. 8 < 12

Then \frac{8}{4} < \frac{12}{4}

So 2 < 3

3. 2 x > 24

Divide B.S by 2

\frac{2 x}{2} > \frac{24}{2}

x > 12

- If we divide an inequality by a negative number, then the inequality sign is always changed.
- When c < 0 :

- If a > b then \frac{a}{c} < \frac{b}{c}
- If a < b then \frac{a}{c} > \frac{b}{c}

**Examples:**

1. 18 > 12

Then \frac{18}{-3} < \frac{12}{-3}

So -6 < -4

2. 8 < 12

Then \frac{8}{-4} > \frac{12}{-4}

So \ -2 > -3

3. -2 x < 24

Divide B.S by -2

\frac{-2 x}{-2} > \frac{24}{-2}

x > -12

## Cancellation Property of Real Numbers

### Cancellation Property of Addition

**1. Cancellation Property of Equality (Addition):**

The cancellation property of addition states that if the same real number is added to both sides of an equation, the number can be “cancelled” from both sides of an equation.**Statement:**

For any real numbers a, b \& \ c

If a+c=b+c then a=b **Examples:**

1. 2 x+5 =9+5

2 x =9

2. 9 x+15 =y+15

9 x =y

**2. Cancellation Property of Inequality (Addition)**

The cancellation property of addition states that if the same real number is added to both sides of an inequality, the number can be “cancelled” from both sides of an inequality.

Statement

For any real numbers a, b \& \ c

- If a+c > b+c then a > b
- If a+c < b+c then a < b

**Examples:**

1. x+5 > 9+5

x > 9

2. 9 x+15 < y+15

9 x < y

### Cancellation Property of Subtraction

**1. Cancellation Property of Equality (Subtraction)**

The cancellation property of Subtraction states that if the same real number is subtracted from both sides of an equation, the number can be “cancelled” from both sides of an equation.**Statement:**

For any real numbers a, b \& \ c .

If a-c=b-c then a=b **Examples:**

1. 2 x-5 =9-5

2 x =9

2. 9 x-15 =y-15

9 x =y

**2. Cancellation Property of Inequity (Subtraction)**

The cancellation property of Subtraction states that if the same real number is subtracted from both sides of an inequality, the number can be “cancelled” from both sides of an inequality.**Statement**

For any real numbers a, b \& \ c

- If a+c > b+c then a > b
- If a+c < b+c then a < b

**Examples:**

1. x-5 > 9-5

x > 9

2. 9 x-15 < y-15

9 x < y

### Cancellation Property of Multiplication

**1. Cancellation Property of Equality (Multiplication)**

The cancellation property with respect to Multiplication states that if the same non-zero real number is multiplied on both sides of an equation, the number can be “cancelled” from both sides of an equation.**Statement:**

For any real numbers a, b \& \ c \ (where \ \ c \neq 0)

If a \times c=b \times c then a=b

OR

If a . c=b . c then a=b

OR

If a c=b c then a=b **Examples:**

1. 2 x \times 5=9 \times 5

2 x=9

2. 9 x .15=y .15

9 x=y

3. 3 x=12

3 x=4 \times 3

x=4

4. 4 y=4

y=1

**2. Cancellation Property of Inequality (Multiplication)**

- The cancellation property of Multiplication states that if the same non-zero Positive real number is multiplied on both sides of an inequality, the number can be “cancelled” from both sides of an inequality and the inequality sign remain unchanged.

Statement

For any real numbers a, b \& \ c \ (where \ \ c \neq 0)

- When c > 0 :

- If a \times c > b \times c then a > b
- If a \times c < b \times c then a < b

**Examples:**

1. x \times 5 > 9 \times 5

x > 9

2. 9 x .15 < y .15

9 x < y

- The cancellation property of Multiplication states that if the same non-zero Negative real number is multiplied on both sides of an inequality, the number can be “cancelled” from both sides of an inequality and the inequality sign is reversed.

**Statement:**

For any real numbers a, b \& \ c \ (where \ \ c \neq 0)

- When c < 0 :

- If a \times c > b \times c then a < b
- If a \times c < b \times c then a > b

**Examples:**

1. x \times-5 > 9 \times-5

x < 9

2. -9 x < -9 y

x > y

### Cancellation Property of Division

**1. Cancellation Property of Equality (Division)**

The cancellation property of Division states that if the same non-zero real number is divided to both sides of an equation, the number can be “cancelled” from both sides of an equation.**Statement:**

For any real numbers a, b \& \ c \ (where \ \ c \neq 0)

\frac{a}{c}=\frac{b}{c} then a=b

OR

If a \div c=b \div c then a=b **Examples:**

1. \frac{2 x}{5}=\frac{y}{5}

2 x=y

2. \frac{9 y}{4}=\frac{1}{4}

9 y=1

3. \frac{2 x}{5}=\frac{7}{-5}

\frac{2 x}{5}=-\frac{7}{5}

2 x=-7

**2. Cancellation Property of Inequality (Division)**

- The cancellation property of Division states that if the same non-zero Positive real number is divided to both sides of an inequality, the number can be “cancelled” from both sides of an inequality and the inequality sign remain unchanged.

Statement

For any real numbers a, b \& \ c \ (where \ \ c \neq 0)

- When c > 0:

- { If } \ \frac{a}{c} > \frac{b}{c} \ { then } \ a > b
- { If } \ \frac{a}{c} < \frac{b}{c} \ { then } \ a < b

Examples:

1. \frac{2 x}{5} < \frac{y}{5}

2 x < y

2. \frac{9 y}{4} > \frac{1}{4}

9 y > 1

3. \frac{2 x}{5} > \frac{7}{-5}

\frac{2 x}{5} > -\frac{7}{5}

2 x > -7

- The cancellation property of Division states that if the same non-zero Negative real number is Divided to both sides of an inequality, the number can be “cancelled” from both sides of an inequality and the inequality sign is reversed.

Statement

For any real numbers a, b \& \ c \ (where \ \ c \neq 0)

- When c < 0:

- If \frac{a}{c} > \frac{b}{c} then a < b
- If \frac{a}{c} < \frac{b}{c} then a > b

**Examples:**

1. \frac{8}{-4} > \frac{12}{-4}

8 < 12

2. \frac{18}{-3} < \frac{12}{-3}

18 > 12

## Properties of Real Numbers MCQs

MCQs provide an engaging and effective way to reinforce our understanding of the properties of real numbers.

Practicing with MCQs can deepen our comprehension of real numbers and enhance our problem-solving skills, making our mathematical journey more enjoyable and rewarding. So, keep exploring and mastering the properties of real numbers to unlock the beauty of mathematics. Let’s embark on this exciting journey of discovery.

**1. The set of Real number is the union of two ________ sets.**

O Zero

O New

O Disjoint

O None of these

## Show Answer

** Disjoint
Explanation:
**

**2. Q \cap Q^{\prime}= ________**

O Q

O Q^{\prime}

O \emptyset

O All of them

## Show Answer

** \emptyset
Explanation:
The intersection of Rational and Irrational set is empty set.
**

**3. The sum of two real number is also a real number is called ________ property w.r.t Addition.**

O Closure

O Commutative

O Associative

O None of these

## Show Answer

** Closure
Explanation:
Statement for Closure Property.
**

**4 . The ________ of two real number is also a real number is called closure property.**

O Product

O Commutative

O Associative

O None of these

## Show Answer

** Product
Explanation:
In Closure property the product of two real number is alway be a real number.
**

**5. Example of closure property:**

O 7+9=16

O 7 \times 9=63

O Both a & b

O None of these

## Show Answer

** Both a & b
Explanation:
In Closure property, the sum and product of two real numbers must be the real number. Thus both a & b obey closure property.
**

**6. Commutative property w.r.t addition is ________**

O a+b=b+c

O a+c=b+c

O a+b+c=a+b

O a+b=b+c

## Show Answer

** a+b=b+c
Explanation:
General form of Commutative property w.r.t Addition.
**

**7. Commutative property w.r.t multiplication is ________**

O a b=b c

O a c=b c

O a b c=a b

O a b=b c

## Show Answer

** a b=b c
Explanation:
General form of Commutative property w.r.t Multiplication.
**

**8. Commutative property is ________**

O a+b=b+a

O a b=b a

O Both a & b

O None of these

## Show Answer

** Both a & b
Explanation:
Both a & b Showed the Commutative property of Addition and Multiplication respectively.
**

**9. Associative property w.rt Addition is ________**

O a(bc)=(ab)c

O a+(b+c)=(a+b)+c

O Both a & b

O None of these

## Show Answer

** a+(b+c)=(a+b)+c
Explanation:
General form of Associative property w.r.t Addition.
**

**10. Zero is called ________**

O Additive identity

O Additive inverse

O Both a & b

O None of these

## Show Answer

** Additive identity
Explanation:
Zero (0) is called Additive identity because adding “0” to a number does not change that number.
**

**11. a+0=0+a=a is**

O Additive identity

O Additive inverse

O Both a & b

O None of these

## Show Answer

Explanation:

Zero (0) is called Additive identity because adding “0” to a number does not change that number.

**12. The product of real number and zero is________**

O a

O That number

O Imaginary

O Zero

## Show Answer

** Zero
Explanation:
Any number multiplied to zero is always be zero.
**

**13. 1 is called ________ w.r.t multiplication.**

O Multiplicative identity

O Imaginary

O Multiplicative inverse

O None of these

## Show Answer

** Multiplicative identity
Explanation:
1 is called Multiplicative identity because multiplying “1” to a number does not change that number.
**

**14. a \times 1=1 \times a=a is ________ property.**

O Multiplicative identity

O Imaginary

O Multiplicative inverse

O None of these

## Show Answer

Explanation:

1 is called Multiplicative identity because multiplying “1” to a number does not change that number.

**15. The product of 1 and a number is________**

O 10

O Zero

O That number

O None of these

## Show Answer

** That number
Explanation:
1 is called Multiplicative identity because multiplying “1” to any number does not change that number.
**

**16. The sum of two numbers is zero (0) is called________**

O Additive identity

O Additive inverse

O Both a & b

O None of these

## Show Answer

** Additive inverse
Explanation:
Definition of Additive inverse
**

**17. If a+a^{\prime}=a^{\prime}+a=0 \ then \ a^{\prime} is called ________ of a .**

O Additive identity

O Additive inverse

O Both a & b

O None of these

## Show Answer

** Additive inverse
Explanation:
When a real number and its opposite, the result will always be 0.
**

**18. If a+(-a)=-a+a=0 \ then \ -a is called of ________ a .**

O Additive identity

O Additive inverse

O Both a & b

O None of these

## Show Answer

** Additive inverse
Explanation:
When a real number and its opposite, the result will always be 0.
**

**19. The product of two numbers is 1 is called________**

O Multiplicative identity

O Imaginary

O Multiplicative inverse

O None of these

## Show Answer

** Multiplicative inverse
Explanation:
When a real number is multiplied by its inverse or reciprocal, the result will always be 1.
**

**20. If a \cdot a^{-1}=a^{-1} \cdot a=1 \ then \ a^{-1} is called ________ of a .**

O Multiplicative identity

O Imaginary

O Multiplicative inverse

O None of these

## Show Answer

** Multiplicative inverse
Explanation:
When the Product of two numbers is “1” then it is said to be Multiplicative inverse.
**

**21 If a \cdot \frac{1}{a}=\frac{1}{a}, a=1 \ then \ \frac{1}{a} is called of ________ a .**

O Multiplicative identity

O Imaginary

O Multiplicative inverse

O None of these

## Show Answer

Explanation:

When the Product of two numbers is “1” then it is said to be Multiplicative inverse.

**22. Distributive Property of Multiplication over Addition is ________**

O a(b+c)=ab+ac

O (b+c)a=ba+ca

O Both a & b

O None of these

## Show Answer

** Both a & b
Explanation:
Both a & b showed the Distributive Property of Multiplication over Addition
**

**23. If a=a , then it is ________ property.**

O Transitive

O Symmetric

O Reflexive

O None of these

## Show Answer

** Reflexive
Explanation:
Every number is equal to itself is known as Reflexive property.
**

**24. If a=b , then also b=a , it is ________ property.**

O Transitive

O Symmetric

O Reflexive

O None of these

## Show Answer

** Symmetric
Explanation:
By interchanging the sides of an equation doesn’t effect the result is known as symmetric Prperty.
**

**25. If a=b \ and \ b=c then a=c , it is ________ property.**

O Transitive

O Symmetric

O Reflexive

O None of these

## Show Answer

** Transitive
Explanation:
If a equal to b under a rule and b equal to c under the same rules then a equal to c is known as transitive property.
**

**26. If y=x^2 \ then \ also \ x^2=y , it is ________ property.**

O Transitive

O Symmetric

O Reflexive

O None of these

## Show Answer

Explanation:

By interchanging the sides of an equation doesn’t effect the result is known as symmetric Prperty.

**27. I x+y=z \ and \ z=a+b then x+y=a+b , it is ________ property.**

O Transitive

O Symmetric

O Reflexive

O None of these

## Show Answer

Explanation:

If a equal to b under a rule and b equal to c under the same rules then a equal to c is known as transitive property.

**28. If 3=3 , then it is ________ property.**

O Transitive>

O Symmetric

O Reflexive

O None of these

## Show Answer

** Reflexive
Explanation:
Every number is equal to itself is known as Reflexive property.
**

**29. If a=b , then also a+c=b+c , it is ________ property of equality.**

O Additive

O Multiplicative

O Both a & b

O None of these

## Show Answer

** Additive
Explanation:
If we add the same number or expression on both sides of an equation, the equation does not change which means both the sides remain equal.
**

**30. If a=b then also ac=bc , it is ________ property of equality.**

O Additive

O Multiplicative

O Both a & b

O None of these

## Show Answer

** Multiplicative
Explanation:
If we Multiply the same number or expression on both sides of an equation, the equation does not change which means both the sides remain equal.
**

**31. If a+c=b+c then a=b , it is Cancellation property w.r.t ________**

O Addition

O Multiplication

O Both a & b

O None of these

## Show Answer

** Addition
Explanation:
In this, cancelled the non-zero common factor from both side of the equation by Adding or Subtraction.
**

**32. If ac=bc then a=b , it is Cancellation property w.r.t ________**

O Addition

O Multiplication

O Both a & b

O None of these

## Show Answer

** Multiplication
Explanation:
In this, cancelled the non-zero common factor from both side of the equation by Multiplication or Divison.
**

**33. Trichotomy property is used for ________ two numbers.**

O Increasing

O Decreasing

O Comparing

O Equating

## Show Answer

** Comparing
Explanation:
See MCQs No. 34
**

**34. Trichotomy property must be true for ________**

O a=b

O a > b

O a < b

O All of them

## Show Answer

** All of them
Explanation:
Trichotomy property is used for compare two numbers.
**

**35. Trichotomy property must be true for________**

O 5=5

O 3 < 5

O Both a & b

O None of these

## Show Answer

** Both a & b
Explanation:
Trichotomy property is used for compare two numbers.
**

**36. If a > b \ and \ b >c \ then \ a > c , it is ________ property of inequality.**

O Additive

O Multiplicative

O Transitive

O All of them

## Show Answer

** Transitive
Explanation:
If a greater than b under a rule and b greater than c under the same rule then a greater than c is known as transitive property of inequlity.
**

**37. If a < b \ and \ b < c \ then \ a < c, it is ________ property.**

O Additive

O Multiplicative

O Transitive

O All of them

## Show Answer

** Transitive
Explanation:
If a less than b under a rule and b less than c under the same rule then a less than c is known as transitive property of inequlity.
**

**38. If a > b then a+c > b+c , it is ________ property of inequlity.**

O Additive

O Multiplicative

O Transitive

O All of them

## Show Answer

** Additive
Explanation:
If we add the same number or expression on both sides of an inequality, but the result will remain the same. i.e. left side is greater than right side.
**

**39. If a < b then a+c < b+c , it is ________ property.**

O Additive

O Multiplicative

O Transitive

O All of them

## Show Answer

** Additive
Explanation:
If we add the same number or expression on both sides of an inequality, but the result will remain the same. i.e. left side is less than right side.
**

**40. If x > 5 then ________**

O x \times 2 > 5 \times 2

O x \times 2 < 5 \times 2

O Both a & b

O None of these

## Show Answer

** x \times 2 > 5 \times 2
Explanation:
If we multiply the same number or expression on both sides of an inequality, but the result will remain the same. i.e. left side is greater than right side.
Note:
The number should be positive.
**

**41. If x > 5 then ________**

O x \times -2 > 5 \times -2

O x \times -2 < 5 \times -2

O Both a & b

O None of these

## Show Answer

** x \times -2 < 5 \times -2
Explanation:
If we multiply the same Negative number to both sides of an inequality, the result will changed. i.e. left side becomes less than right side.
**

**42. For c > 0 \ and \ a < b then Multiplicative property ________**

O ac < bc

O ac > bc

O Both a & b

O None of these

## Show Answer

** ac < bc
Explanation:
If we multiply the same Positive number to both sides of an inequality, the result will remain same. i.e. left side is less than right side.
**

**43. For c < 0 \ and \ a < b then Multiplicative property ________**

O ac < bc

O ac > bc

O Both a & b

O None of these

## Show Answer

** ac > bc
Explanation:
If we multiply the same Negative number to both sides of an inequality, the result will changed. i.e. left side becomes greaer than right side.
**

**44. For c < 0 \ and \ a > b then Multiplicative property ________**

O ac < bc

O ac > bc

O Both a & b

O None of these

## Show Answer

** ac < bc
Explanation:
If we multiply the same Negative number to both sides of an inequality, the result will changed. i.e. left side becomes less than right side.
**

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