Properties of Integers under Division

Q. When we divide one integer by another, the result is not always an integer. The property is invalid in case of division.

1. closure
2. commutative
3. associative

Q. property of integers under division states that 'a' divided by 'b' is not equal to 'b' divided by 'a'.

1. Commutative
2. Closure
3. Distributive

Q.

State whether true or false: For all non-zero integers '$a$' and '$b$', $a\times b$ is always greater than either $a$ or $b$.

1. True

2. False

Q. Which of the following statement(s) is/are true?

1. 
   On dividing an integer by an integer , the result will always be an integer.
2. 
   On dividing an integer by zero, the result will always be zero.
3. 
   On multiplying an integer by zero, the result will always be zero.
4. 
   On dividing an integer by one, the result will always be the integer itself.

Q. Statement 1: Product of two integers with the same sign is always a positive integer.​
Statement 2: Quotient of two integers with the same sign is always a positive integer. ​ ​
Choose the correct option.​

1. Both the statements are true.​
2. Only statement 1 is true.​
3. Only statement 2 is true.​
4. Both the statements are false.​

Q. Match the following for the following properties of integers such that a, b and c are integers.

1. $\ne$ a / (b / a)
2. Commutative Property
3. Closure Property

Q. There are $5$ letters and $5$ directed envelopes.The number of ways in which all the letters can be put in wrong envelope is

1. $59$
2. $119$
3. $44$
4. $40$

Q. property of integers under division states that ($a÷b)$$÷c$ $\ne$ $a÷(b÷c)$ where a, b and c are integers.

1. Closure
2. Distributive
3. Associative

Q.

Division of whole numbers follows the commutative law.

1. True

2. False

Q.

Division of whole numbers does not follow the commutative law.

1. True

2. False

Q.

Division of whole numbers follows the commutative law.

1. True

2. False

Q.

(-5) $÷$ 3 = 3 $÷$ (-5) [Say true or false]

1. False

2. True

Q. What is the result of $(a÷0)÷b$?

1. Undefined
2. 0
3. a
4. b

Q. Fill in the blank with correct sign:
(18 ÷ 3) ÷ (-3)

18 ÷ (3 ÷ (-3))

1. >
2. <
3. =

Q. Which of the statements is/are false?

1. Division follows associative property of integers.
2. Multiplication follows commutative property of integers.
3. Subtraction follows closure property of integers.
4. None of these

Q.

Which among the following properties hold for division?

1. Closure property

2. Commutative property

3. Associative property

4. None of these properties

Q. Statement: Closure property of intergers is valid for division.

1. True
2. False

Q.

For any integer a, a ÷ 0 is

1. not defined

2. a

3. 0

4. 1