What is the Division Formula?

Division is one of the top four important arithmetic operations (i.e., Addition, subtraction, multiplication, division). Division operation is used to split the number into equal parts. The symbolic representation for division is '÷' and '/'. a divided by b can be represented as a÷b or a/b. The formula of division is given by

Dividend/Divisor = Quotient

Where, 

Dividend is the number that to be divided.

Divisor is the number to be divided with.

Quotient is the result of division operation.

Also, there is a verification process to be used to check whether the result of the division is true or not. The formula for this verification of division is given by

Dividend = (Divisor × Quotient) + Remainder

Even any of the missing terms can be calculated from the other three terms.

The Division Formula is a fundamental concept in algebra that allows us to express the result of polynomial division as a equation. It's particularly useful when dividing polynomials by linear factors and helps in understanding the relationship between factors and roots of polynomials. This formula is essential for solving various algebraic problems and is widely used in higher mathematics.

What is the Division Formula?

The Division Formula, also known as the Polynomial Remainder Theorem, states that when a polynomial P(x) is divided by (x - a), the remainder is equal to P(a). In other words, if P(x) = (x - a)Q(x) + R, where Q(x) is the quotient and R is the remainder, then R = P(a). This formula provides a quick way to find the remainder without performing long division.

Sample Questions

Question 1: Perform Division between numbers 6 and 3.

Solution:

Given,

Dividend = 6

Divisor = 3

Dividend/divisor = 6/3

= 2.

So, 6÷3 = 3

Question 2: What is the result of 25 ÷ 5?

Solution:

Given

Dividend = 25

Divisor = 5

Quotient = Dividend/Divisor

= 25/5

= 5

So, Quotient = 5

Question 3: A boy had birthday and he had a packet of chocolate containing 100 chocolates which need to be distributed to 50 students in a class. How many chocolates each student gets in the class.

Solution:

Given

Total Chocolates (Dividend) = 100

Total Children (Divisor) = 50

Number of chocolates each got = Dividend/Divisor

= 100/50

= 2

Number of chocolates each student got is 2.

Question 4: What is the Dividend if the divisor, quotient and remainder are 10,2,4 respectively.

Solution:

Given

Divisor = 10

Quotient = 2

Remainder = 4

From formula-> Dividend = (Divisor×Quotient)+Remainder

Dividend can be calculated by substituting other 3 term values.

Dividend = (10 × 2) + 4

= 20 + 4

= 24

Hence, Dividend = 24

Question 5: Find the Divisor if the dividend=25, quotient=7 and remainder=4.

Solution:

Given,

Dividend = 25

Quotient = 7

Remainder = 4

Dividend = (Divisor×Quotient)+Remainder

Dividend-Remainder = Divisor×Quotient

Divisor = (Dividend-Remainder)/Quotient

= (25-4)/7

= 21/7

= 3

Hence, Divisor = 3

Summary

The Division Formula, or Polynomial Remainder Theorem, is a powerful tool in algebra that simplifies the process of finding remainders when dividing polynomials by linear factors. It states that the remainder of a polynomial P(x) divided by (x - a) is equal to P(a). This formula not only streamlines calculations but also provides insights into polynomial behavior, factor relationships, and root finding. By applying this principle, students can solve complex polynomial problems more efficiently and gain a deeper understanding of algebraic structures.