Division of Integers

Division of integers is discussed here. Division of whole numbers is an inverse process of multiplication.

Dividing 20 by 4 means finding an integer which when multiplied with 4 gives us 20, such an integer is 5.

Therefore, we write as 20 ÷ 4 = 5 or, \(\frac{20}{4}\) = 5

Similarly, dividing 45 by -9 means, finding an integer which when multiplied with -9 gives 45, such an integer is -5.

Therefore, we write 45 ÷ (-9) = -5 or, \(\frac{45}{-9}\) = -5

Dividing (-28) by (-4) means, what integer should be multiplied with (-4) to get (-28), such an integer is 7.

Therefore, (-28) ÷ (-4) = 7 or, \(\frac{-28}{-4}\) = 7

Definitions of the following terms used in division:

Dividend- The number to be divided is called dividend.

Divisor- The number which divides is called the divisor.

Quotient- The result of division is called the quotient.

When dividend is negative and divisor is negative, the quotient is positive. When the dividend is negative and the divisor is positive, the quotient is negative.

In division of integers we use the following rules:

Rule 1

The quotient of two integers either both positive or negative is a positive integer equal to the quotient of the corresponding absolute values of the integers.

(i) The quotient of two positive integers is positive. Here, we divide the numerical value of the dividend by the numerical value of the divisor.

For example; (+ 9) ÷ (+ 3) = + 3

(ii) The quotient of two negative integers is positive. Here, we divide the numerical value of the dividend by the numerical value of the divisor and assign (+) sign to the quotient obtained.

For example; (- 9) ÷ (- 3) = + 3

Thus, for dividing two integers with like signs, we divide their values and give plus sign to the quotient.

Rule 2

The quotient of a positive and a negative integer is a negative integer and its absolute value is equal to the quotient of the corresponding absolute values of the integers.

For example; (+ 16) ÷ (- 4) = - 4

Thus, for dividing integers with unlike signs, we divide their values and give minus sign to the quotient.

● Numbers - Integers

Integers

Multiplication of Integers

Properties of Multiplication of Integers

Examples on Multiplication of Integers

Division of Integers

Absolute Value of an Integer

Comparison of Integers

Properties of Division of Integers

Examples on Division of Integers

Fundamental Operation

Examples on Fundamental Operations