102 LearnersLast updated on July 6th, 2025
Dividend
In the division process, the number being divided by a divisor is known as the dividend. The remainder will be zero when a number is fully divisible by the divisor. If the dividend is not completely divisible by the divisor, the remainder will be a non-zero value. The dividend is one of the key elements in division, as it helps to split the given resources into equal parts. In this article, let us explore the dividend and its properties in detail.
What is a dividend?
The dividend is the total quantity that is to be divided into equal parts.
For example, Allen has 20 books and wants to distribute them among his 5 friends. He divides the books so that all 5 people receive the same number of books.
Here, the number of books = 20
Number of friends = 5
Hence, the dividend is 20, and the divisor is 5.
20 ÷ 5 = 4
4 is the quotient.
Thus, each of Allen’s friends receives 4 books.
How to identify a dividend?
The number that gets divided by another is the dividend. In division, the dividend is divided into equal parts.
- The first way is the division equation, in which the number that appears before the division symbol is the dividend.
- The second method is the long division method, and the number inside the long division symbol is called the dividend.
- Finally, the top number of the fraction is known as the dividend.
Dividend Formula
Dividend is one of the most important elements of the division process, where we have to follow the formula to get the correct result.
The formula for finding the dividend is:
Dividend = (Divisor × Quotient) + Remainder
Here is an example to understand the formula:
The divisor = 5
Quotient = 2
Remainder = 0
Find the dividend.
Using the formula, we can find the dividend as follows:
- Dividend = (Divisor × Quotient) + Remainder
- Dividend = (5 × 2) + 0 = 10
Therefore, the value of the dividend is 10.
Terms Used in Division
The division process consists of four parts. They are:
- Dividend: A number that is being divided by a divisor.
- Divisor: A number that divides the dividend.
- Quotient: The final result obtained when the divisor divides the dividend.
- Remainder: It is the leftover integer that we get after division. If the dividend is completely divisible by the divisor, the remainder is zero. If it is not completely divisible, the remainder will be a non-zero number.
Refer to this image for a clearer understanding of the terms used in division.
Difference Between Dividend and Divisor
Understanding the difference between dividend and divisor helps students differentiate the two elements easily. In division, the dividend and divisor are essential to perform the process.
| Features | Dividend | Divisor |
|
Definition |
The number that is being divided by the divisor. | The number by which the dividend is divided. |
| Importance | The dividend is divided into equal parts by the divisor. | The divisor decides the number of parts into which the dividend is divided. |
| Position |
It comes before the division symbol. |
It comes after the division symbol. |
| Example | In 12 ÷ 2, 12 is the dividend and 2 is the divisor | In 16 ÷ 2, 2 is the divisor and 16 is the dividend. |
Tips and Tricks to Master Dividend
Understanding the concept of dividends helps students solve mathematical problems easily and avoid confusion in calculations. Given below are some tips and tricks to keep in mind:
- When the divisor is greater than the dividend, the quotient will be a decimal number or a fraction.
For example, 89 ÷ 100 = 0.89
- If a number is divided by itself, the quotient is 1, and the remainder is zero.
For instance, 26 ÷ 26 = 1
- If we divide a dividend by 1, the answer will be the dividend itself.
For example, 45 ÷ 1 = 45
- If the remainder is zero, it means that the dividend is completely divisible by the divisor.
For instance, 12 ÷ 2
6 as the quotient.
0 as the remainder.
Common Mistakes and How to Avoid Them in Dividend
Practicing division helps students master the concept and solve mathematical problems accurately. However, students make some mistakes when working with dividends and divisors. Here are some common mistakes and helpful solutions to avoid these errors.
Mistake 1
Misunderstanding between the dividend and the divisor
The dividend is the number that gets divided by the divisor. If students fail to recall the difference, they may get incorrect answers. For example, the given expression is 12 ÷ 4 = 3
Here, 12 is the dividend, 4 is the divisor, and 3 is the quotient.
Mistake 2
Ignoring the remainder
Students should not avoid the remainder in the division process. If a number gets completely divided, then the remainder is 0 or otherwise, it will be a non-zero number. For instance, 19 ÷ 3 gives 6 as the quotient and 1 as the remainder.
Mistake 3
Not placing the dividend and the divisor correctly
If they misplace the elements, the result becomes incorrect. For example, the dividend is 9 and the divisor is 3, so the quotient is 3 (9 ÷ 3 = 3).
If students replace the dividend and divisor, like 3 ÷ 9 = 0.333, the result will be different.
Mistake 4
Forgetting the formula for the dividend
Always remember the formula for finding the dividend to avoid calculation errors. The formula is:
Dividend = (Divisor × Quotient) + Remainder
If students forget the formula and apply it incorrectly, they will get the wrong dividend.
Mistake 5
Dividing the dividend by zero
Remember that when a number gets divided by 0, the result will always be undefined. This means that no number can be divisible by zero, and the answer will be meaningless. For example, 6 ÷ 0 is undefined.
Real-Life Applications of Dividend
Dividend, divisor, quotient, and remainder are the four main elements of division. The concept of dividends plays an essential role in various real-life situations, such as:
- Distribution and sharing: If we wish to divide 20 pencils among 10 students, the total number of pencils each student gets can be found using division. Here, the dividend is 20, whereas the divisor is 10, and the result is 2. Therefore, each student will receive 2 pencils.
- Banking and financial transactions: The profits of a company are equally shared among the shareholders, and the management uses the profit as dividends to calculate the share of each shareholder.
- Time management: If students need to prepare for their examinations, they can allocate their time accordingly to avoid timing issues. For example, if a student needs to study 10 hours a day, and he has 5 subjects, he can devote 2 hours to each subject.
- Cooking and serving: When we serve a 12-piece pizza to 4 people, the number of pieces represents the dividend, and the number of people is the divisor. Hence, each of them will get 3 pieces.
Solved Examples of Dividend
Problem 1
Find the dividend if the divisor is 8, the quotient is 2, and the remainder is 0.
16 is the dividend
Explanation
Here, divisor = 8
Quotient = 2
Remainder = 0
Using the formula, we can find the dividend.
Dividend = (Divisor × Quotient) + Remainder
Now, let us substitute the values.
Dividend = (8 × 2) + 0 = 16
Thus, the dividend is 16.
Problem 2
Vickey has 98 candies and wants to pack them into boxes, with 7 candies per box. How many boxes will he need?
14 boxes
Explanation
Total candies = 98
Number of candies per box = 7
Here, the dividend is 98.
The divisor is 7.
Here, we can use the division formula:
Dividend ÷ Divisor = Quotient
Now, let us substitute the values:
98 ÷ 7 = 14
Thus, Vickey will need 14 boxes.
Next, we can use the dividend formula to verify the result.
Dividend = (Divisor × Quotient) + Remainder
Dividend = 14 × 7 = 98
Since the product matches the original dividend, the answer is correct.
Problem 3
A textile factory produces 1488 jeans in 24 hours. How many jeans are produced in 1 hour?
The factory produces 62 jeans per hour.
Explanation
The total number of jeans produced = 1,488
Time taken = 24 hours
Now, let’s find the number of jeans produced in 1 hour.
Using the division formula, we can find the answer.
Jeans per hour = Total jeans produced ÷ Total time in hours
Let us substitute the values:
Jeans per hour = 1488 ÷ 24 = 62
Therefore, jeans produced per hour are 62.
Problem 4
A number when divided by 12 gives a quotient of 18. Find the dividend.
216 is the dividend.
Explanation
The divisor = 12
Quotient = 18
Using the dividend formula, we can find the answer.
Dividend = (Divisor × Quotient) + Remainder
Dividend = 12 × 18 = 216
The dividend is 216.
Problem 5
Sarah bakes 20 cakes and wants to pack them into 4 boxes. How many cakes will each box contain?
5 cakes.
Explanation
Total cakes = 20
Total boxes = 4
Here, 20 is the dividend, and 4 is the divisor.
To find the quotient, we can use the division formula.
Dividend ÷ Divisor = Quotient
20 ÷ 4 = 5
Thus, each box will contain 5 cakes.
Next, we can verify the answer.
The formula for the dividend is:
Dividend = (Divisor × Quotient) + Remainder
Dividend = (4 × 5) + 0 = 20
Here, the answer matches the original dividend.
Therefore, each box will have 5 cakes.
FAQs on Dividend
1.Define a dividend in a division.
2.What is the formula for finding a dividend?
3.How to identify the dividend in a fraction?
4.List the terms used in division.
5. Is it possible for a quotient to be a decimal?
6.How can children in Canada use numbers in everyday life to understand Dividend?
7.What are some fun ways kids in Canada can practice Dividend with numbers?
8.What role do numbers and Dividend play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Dividend skills?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
