Properties of Division of Integers

Q. (a)Write a pair of integers and a positive integer whose sum is $-5$
(b)Write a negative integer and a positive integer whose sum is $8$
(c) )Write a negative integer and a positive integer whose difference is $-3$

Q.

What are the 4 types of sentences?

Q.

Integers are not closed under which operation?

1. Multiplication

2. Division

3. Addition

4. Subtraction

Q.

When we divide a negative integer by a positive integer, we divide them as whole numbers and put a ______ sign before quotient. Fill in the blanks to make the statement true.

Q.

If a, b, c are integers, then (a $÷$ b) $÷$ c = a $÷$ (b $÷$ c)

1. True

2. False

Q.

Evaluate $(-36)÷(-9)$

Q.

Evaluate $(-49)÷\left(49\right)$

Q.

When we divide two integers, we always get an integer.

1. 0 was exactly at the center of the number line

2. 0 was one of the integers

Q. Write down a pair of integers whose sum is $0$.

Q.

When two positive integers are added we get ________integers

Q.

Evaluate the following: $\left(-30\right)÷10$

Q.

While multiplying a positive integer and a negative integer, we multiply them as ________ numbers and put a ________ sign before the product. Fill in the blanks to make the statement true.

Q.

For any integer b, b ÷ (-1) is

1. b

2. 1

3. -b

4. Not defined

Q.

Using the information and your understanding till now, choose from the given options, the properties which hold good for the division of integers?

1. Closure property

2. Commutative property

3. Associative property

4. None of these

Q.

Under which of the following operations, are the integers not closed?

1. Addition

2. Subtraction

3. Multiplication

4. Division

Q.

Dividing Integers. Find the quotient.

$\frac{-6}{-2}$

Q.

Find the value of the expression:
(–45) – (–39) + 42 – 28 – (–152) – 85 + (–9)

1. 46
2. 36
3. 63
4. 66

Q. Which of the following mathematical operations is not closed on integers?

1. Addition
2. Subtraction
3. Multiplication
4. Division

Q. Which of the following statements are true and which are false?

(i) The product of a positive and a negative integer is negative.
(ii) The product of two negative integers is a negative integer.
(iii) The product of three negative integers is a negative integer.
(iv) Every integer when multiplied with −1 gives its multiplicative inverse.
(v) Multiplication on integers is commutative.
(vi) Multiplication on integers is associative.
(vii) Every nonzero integer has a multiplicative inverse as an integer.

Q.

What are inverse operations and give examples?

Q.

Question 105

State whether the statement is True or False.

Integers are closed under division.

Q.

If a' is any integer then a+0=------------- = --------------

Name the additive identity.

Q. Divide:
$\left(ii\right)7.8$ by $100$

Q. The sum of two rational numbers is always a rational number. Which of the following property is illustrated by the given statement?

1. Commutative property
2. Associative property
3. Distributive property
4. Closure property

Q. Which of the following statements are true?
(i) The product of a positive and a negative integer is negative.
(ii) The product of three negative integers is a negative integer.
(iii) Of the two integers, if one is negative, then their product must be positive.
(iv) For all non-zero integers a and b, a × b is always greater than either a or b.
(v) The product of a negative and a positive integer may be zero.
(vi) There does not exist an integer b such that for a> 1, a × b = b × a = b.

Q.

Question 59

Fill in the blanks to make the statement true.

When we divide a negative integer by a positive integer, we divide them as whole numbers and put a ___ sign before quotient.

Q. Write all the integers between -5 and 5, which are divisible by 2 or 3.

Q.

Add the difference of $-202$ and $392$ to the sum of $-189$ and $-79.$

Q. Integers are closed under division.

1. False
2. True

Q. State true or false:
$(-37)÷0=0$