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The value which is divided by another value is called a dividend. It is the base for any kind of method involving division to derive an outcome. It is an essential aspect amongst the four engaged in the procedure of division. Colloquially, it is the whole number to be broken into four equal parts through division.
The mathematical operation of the division includes four terms which are divisor, dividend, quotient, and remainder. The other operations in arithmetic include addition, multiplication, and subtraction. The main purpose of the article is to discuss and explain the concept of dividends in detail. The formula related to dividends would also be focused on in the article, in addition to the methods facilitating the retrieval of dividends. The article will also be illustrated with various examples of solutions regarding dividends.
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Key takeaways: Dividend, divisor, quotient/outcome, remainder, division, fraction, divided by, number, value.
What is Dividend?
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A dividend can be an integer, a fraction or an expression denoted through algebra. In terms of algebraic expressions, the dividend is displayed over the divisor along with a slanting line between them which is also termed as fraction bar. An example for division in terms of algebraic expression can be a divided by b presented as a/b where the dividend is a and divisor is b.
An example of a fraction would be \(\frac{6}{2}\). 6 is the dividend and 2 is the divisor in the exemplified fraction. The term for the dividend is the numerator and the term for the divisor is the denominator in terms of a fraction. After the division of the dividend by the divisor, the outcome in the form of the quotient is either in decimals or whole numbers, only in cases where the remainder needs to be 0.
Also Check: Multiplication and Division of Integers
Terms in division
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- Dividend - The value that needs to be divided by the divisor is known as the dividend
- Divisor - The value that is used for the division of the dividend is known as the divisor
- Quotient - The result derived through the division is known as the quotient
- Remainder - The remaining value after the division has been carried out is known as the remainder.
Formula for dividend
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When divisor, quotient and remainder are given, the dividend can be derived.
The formula for dividend is described as follows:
Dividend = Divisor x Quotient + Remainder.
Such a formula is used to verify the outcome derived through division.
For example, when 6 is divided by 2, the formula is applied as follows:
2 x 3 = 6 where 2 is the divisor, 3 is the quotient. The remainder does not need to be added as it is 0.
Also Check: BODMAS Rule
Examples of dividend
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Some examples concerning dividend are as follows:
- 10 divided by 5 results in 2. Here, the dividend is 10
- 30 divided by 3 results in 10. Here, the dividend is 30
- 24 divided by 8 results in 3. Here, the dividend is 24
- 1 divided by 4 results in 0.25. Here, the dividend is 1
Also Check: Number System
Things to remember
- If the dividend is 0, the outcome/quotient is also 0. For example, 0 divided by 10 results in 0, 0 divided by 18 results in 0, 0 divided by 2 results in 0, 0 divided by 5 results in 0 and 0 divided by 1000 results in 0.
- If the divisor is 1, the outcome/quotient is equal to the dividend. For example, 5 divided by 1 result in 5, 500 divided by 1 result in 500, 5 divided by 1 result in 5, 8000 divided by 1 result in 8000 and 25,000 divided by 1 result in 25,000
- If the dividend is equal to the divisor, the outcome/quotient is 1. For example, 12 divided by 12 results in 1, 40 divided by 40 results in 1, 85 divided by 85 results in 1, 120 divided by 120 results in 1 and 5000 divided by 5000 results in 1.
Sample Questions
Q1. What is the outcome when the divisor is 2? (2 marks)
A: If the divisor is 2, the outcome/quotient is half of the dividend. For example, if the dividend is 100 and the divisor is 2, the outcome/quotient is 50. To verify, 50 + 50 = 100. Furthermore, it can also be verified using the formula for dividend by the virtue of which 100 is derived when 50 is multiplied by 2.
Q2. What are the terminologies used in the division apart from dividend? (2 marks)
A: Besides dividend, the terminologies used in the mathematical operation of division include divisor, quotient and remainder. These kinds of terminologies form the elements to ensure that the complete process of division is carried out effectively.
Q3. Find the dividend in the fraction 3/4? (2 marks)
A: In the given fraction 3/4, the dividend is 3. Additionally, 3 and can also be termed as numerator and denominator respectively instead of dividend and divisor. The outcome in this regard would be 0.75 which means a half and a quarter in case the remainder needs to be 0.
Q4. What is the outcome when the divisor is 4? (3 marks)
A: If the divisor is 4, the outcome/quotient is the quarter of the dividend. For example, if the dividend is 500 and the divisor is 4, the outcome/quotient is 125. To verify, 125 + 125 + 125 = 500. Furthermore, it can also be verified using the formula for dividend by the virtue of which 500 is derived when 125 is multiplied by 4.
Q5. If the dividend is x and the divisor is 10 and the outcome/quotient is 100, what is the value of x? (3 marks)
A: When the outcome/quotient is 100 and the divisor is 10, the value of the dividend x would be 1000 because if x/10 = 100, then the value of x can be derived only when 100 is multiplied by 10 which is 1000.
Q6. How to ensure that the remainder in division is 0? (2 marks)
A: The dividend needs to be equally divided by the divisor to ensure that the remainder is 0. If the remainder is not 0, it can be reduced to 0 when the quotient/outcome and the dividend are in decimals instead of whole numbers.
Q7. How to find the square root of the dividend? (2 marks)
A: The square root of the dividend is the value multiplied by itself. Such a value is both the quotient/outcome and the divisor, if and only if the remainder is 0. For example, if the dividend is 9, the square root would be 3 which is not only the divisor but also the quotient/outcome. It can also be stated in such an instance that the dividend is the square of the divisor.
Q8. If the quotient/outcome is 10 and the divisor is 5, what is the dividend? (2 marks)
A: The dividend would be 15 if the divisor is 5 and the quotient/outcome is 10 because 5 multiplied by 10 leads to 15. The value of the dividend will remain the same even if the values of the quotient/outcome and the divisor are swapped.
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