Dividend Divisor Quotient Remainder Formula

The dividend divisor quotient remainder formula shows the relationship between the dividend, divisor, quotient, and remainder which is one of the main aspects in the division. The division is a process where a number is divided into equal parts leaving behind a remainder if the number cannot be divided further. The division divisor quotient remainder formula is an important rule under division, let's learn more about it along with solving a few examples. 

What Is Dividend Divisor Quotient Remainder Formula? 

The dividend divisor quotient remainder formula consists of the 4 main aspects used in division i.e. dividend, divisor, quotient, and remainder. A dividend is a number that is divided by the divisor. The divisor is the factor that divides the dividend. The result obtained by the division process is called the quotient and the number left behind after the completion of the division is called the remainder. The dividend divisor quotient remainder formula is obtained in the division method.

Dividend Divisor Quotient Remainder Formula

The formula is:

Dividend = Divisor × Quotient + Remainder

This can be verified in the division shown above: 9 = 2 × 4 + 1

Derivation of Dividend Divisor Quotient Remainder Formula

The dividend divisor quotient remainder formula helps in verifying the answer obtained by the division method. Usually, when we divide a number by another number, it results in an answer, such that;

a/b = c where a is the dividend, b is the divisor, and c is the quotient. In other words, it can be written as:

Dividend/Divisor = Quotient

Dividend = Divisor × Quotient

And if any remainder is left, after the division process, then it is written as:

Dividend = Divisor × Quotient + Remainder

Therefore, the dividend divisor quotient remainder formula is Dividend = Divisor x Quotient + Remainder

Examples Using Dividend Divisor Quotient Remainder Formula

Example 1: Find the remainder when the dividend is 75, the divisor is 5 and the quotient is 15. Use the dividend divisor quotient remainder formula. 

Solution: Given, dividend = 75, divisor = 5, quotient = 15 and let the remainder be x

Marking them in the formula: 

Dividend = Divisor × Quotient + Remainder

75 = 5 × 15 + x

75 = 75 + x

x = 75 - 75

x = 0

Therefore, by using the formula we obtained the remainder which is 0. Remainder = 0

Example 2: Find the dividend when the remainder is 1, the divisor is 3, and the quotient is 31.

Solution: Given, remainder = 1, divisor = 3, quotient = 31 and let the dividend be x

Using the dividend divisor quotient remainder formula:

Dividend = Divisor × Quotient + Remainder

Dividend = 3 × 31 + 1

Dividend = 94

Therefore, the dividend is 94 

Example 3: Divide 120 by 5 using the division method and verify it with the dividend divisor quotient remainder formula. 

Solution: First let's divide 120 by 5 using the simple division method: 

120/5 = 24 

Here, 120 is the dividend, 5 is the divisor, 24 is the quotient, and 0 is the remainder. 

Let us verify this answer by using the dividend divisor quotient remainder formula:

Dividend = Divisor × Quotient + Remainder

120 = 5 × 24 + 0

120 = 120 

As we can see that the LHS = RHS, hence the division is correct.