Properties of Integers

The product of two __________ is again an integer.

In general, a × b is an __________, for all integers a and b.

(–30) × 12 = __________.

Multiplication is __________ for integers.

(–15) × (–10) = __________.

(–17) × 0 = __________.

We know that division is the inverse operation of ______.

(–1) × (–1) = ______.

2 × (– 6) = ______.

When dividing a negative integer by a positive integer, we divide them as whole numbers and then put a ______ sign before the quotient.

(–8) × (–9) = ______.

(–3) × (–7) = ______.

(–8) × 4 = ______.

5 × (– 9) = ______.

When a positive integer is divided by a ______ integer, the quotient obtained is negative and vice-versa.

The product of an ______ number of negative integers is positive.

Integers show a property called ______ property under addition and multiplication.

The ______ 1 is the identity under multiplication, i.e., 1 × a = a × 1 = a for any integer a.

The properties of commutativity, associativity under addition and multiplication, and the ______ property help us to make our calculations easier.

Integers are ______ for addition and subtraction, i.e., a + b and a – b are again integers, where a and b are any integers.

Multiplication of integers is ______ for integers, i.e., a × b = b × a for any integers a and b.

Division of a ______ integer by another negative integer gives positive as quotient.

Integers are closed under addition and subtraction, meaning that the result of adding or subtracting two integers is always an integer.
Addition is commutative, meaning that the order of the integers being added does not change the result (a + b = b + a).
Addition is associative, meaning that the order in which integers are added does not change the result ((a + b) + c = a + (b + c)).
Integer 0 is the identity under addition, meaning that adding 0 to any integer does not change the value (a + 0 = 0 + a = a).

Integers are closed under multiplication, meaning that the product of two integers is always an integer.
Multiplication is commutative, meaning that the order of the integers being multiplied does not change the result (a × b = b × a).
Multiplication is associative, meaning that the order in which integers are multiplied does not change the result ((a × b) × c = a × (b × c)).
The integer 1 is the identity under multiplication, meaning that multiplying any integer by 1 does not change the value (1 × a = a × 1 = a).

Integers exhibit the distributive property, meaning that a × (b + c) = a × b + a × c.

Division is the inverse operation of multiplication.
When a positive integer is divided by a negative integer, the quotient is negative, and vice versa.
When a negative integer is divided by another negative integer, the quotient is positive.

The product of two integers is always an integer.
Multiplication is commutative for integers, meaning that the order of the integers being multiplied does not change the result.
Division statements can be written corresponding to multiplication statements for integers.