In Mathematics, the dividend is the value that is divided by another value to get the result. The dividend is the base of any division method. The dividend is one of the four important parts of the division process. It is the whole which is to be divided into different equal parts. For example, if 10 divided by 2 is 5, then 10 is the dividend here, which is divided into two equal parts whereas 2 is the divisor, the quotient is 5 and the remainder is 0.
In arithmetic operations, when we perform the division method, we can observe four related terms, they are dividend, divisor, quotient, remainder. In Mathematics, there are four basic operations. They are addition, subtraction, multiplication and division. These fundamental operations have been taught in our primary classes. The division process is one of the basic arithmetic operations. In this article, we are going to discuss the term “Dividend” in Maths, with many solved examples.
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What is Dividend?
The meaning of dividend is a value that is to be divided by another value. It can be an integer, fraction or algebraic expression. The division frequently is shown in algebra by putting the dividend over the divisor with a horizontal line between them. This horizontal line is also called a fraction bar. For example, x divided by y can be represented as x/y and this can be read as “divide x by y” or “x over y”. Here, x is the dividend and y is the divisor.
Let us take the fraction 5/6. In this fraction, 5 is the dividend and 6 is a divisor. The dividend is known as a numerator, and the divisor is known as the denominator in fractions. When the dividend is divided by a divisor, we get a result in either integer form or decimal form.
For example, 35/7 = dividend/divisor = numerator/denominator
Terms Used in Division
In every division process, there are two necessary parts. One is a dividend, and the other is a divisor.
- Dividend: The number or value or amount that we divide is known as a dividend. For example, if we have to distribute 10 toffies among 5 children, then we need to divide the 10 toffies by 5, which will result in 2 toffies for each child. Hence, the value 10 is the dividend here.
- Divisor: The number which divides the dividend is known as a divisor
- Quotient: The result obtained from the division process is known as a quotient
- Remainder: The number left over after the division process is known as the remainder
Consider an example 64 ÷ 2 = 32
Here,
Dividend = 64
Divisor = 2
Quotient = 32
Examples of Dividend
Let us see some examples of dividend here.
- 20÷4 = 5; 20 is the dividend
- 100÷4 = 25; 100 is the dividend
- 24÷3 = 8; 24 is the dividend
- 1/2 = 0.5; 1 is the dividend
Dividend Formula
The formula to find the dividend in Maths is:
Dividend = Divisor x Quotient + Remainder
Usually, when we divide a number by another number, it results in an answer, such that;
x/y = z
Here, x is the dividend, y is the divisor and z is the quotient.
Dividend/Divisor = Quotient
Hence, we can write;
Dividend = Divisor x Quotient
And if any remainder is left, after the division process, then;
Dividend = Divisor x Quotient + Remainder
How to Find the Dividend?
To find the dividend, go through the below steps.
If the divisor and quotient value is given, the dividend can be easily found by multiplying the divisor and quotient.
Dividend = Divisor x Quotient + Remainder
Hence, put the values of divisor and quotient (also remainder if given), in the above formula to find the dividend.
Let us understand in a better way with the help of solved problems.
Solved Problems on Dividend
Let us learn here how to find the dividend with the help of an example.
Example 1:
Find the dividend for the following x / 6 = 5 and also verify the answer.
Solution :
Given: x / 6 = 5
We know that
Dividend / Divisor = Quotient
Therefore,
Dividend = Quotient x Divisor
x = 5 x 6
x = 30
Therefore, the dividend, x is 30.
Verification:
x / 6 = 5
Now substituting the value of x,
30/6 = 5
5 = 5
Therefore, L.H.S = R.H.S
Hence verified.
In case, if the divisor, quotient and the remainder value are given, the dividend can be found as follows:
Step 1: Multiply the divisor and quotient.
Step 2: Add the remainder value to the result obtained from step 1.
Example 2:
Find the dividend, if the quotient is 6, the divisor is 9, and the remainder is 2.
Solution:
Given: Divisor = 9, quotient = 6, Remainder= 2
Step 1: Multiply 9 and 6
(9 x 6 = 54)
The product is 54.
Step 2: Add product and remainder.
(54+2 = 56)
Hence, the dividend is 56.
Verification:
If 56 is divided by 9, we get the quotient 6 and remainder 2.
(i.e) 56/9 = 6 + 2
Where 6 is quotient and 2 is a remainder.
Practice Problems
Find the dividend value “x” and also verify the answer:
- x / 3 = 10
- x / 7 = 7
- x / 5 = 125
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Frequently Asked Questions on Dividend
What is the dividend in Maths?
In mathematics, the dividend is the number to be divided in the division operation. It is whole, which is divided into parts.
What is the formula to find dividend?
The formula for finding the dividend is:
Dividend = Divisor x Quotient + Remainder
Find the dividend, if the quotient is 68 and the divisor is 9.
If the quotient is 68, and the divisor is 9, then the dividend is 612. Because
Dividend = Divisor x Quotient
Therefore, dividend = 68 x 9 = 612.
What are the different terminologies used in the division process?
The different terminologies used in the division process are:
Dividend
Divisor
Quotient
Remainder
Find the value of a, if a/2 = 15.
The value of a is 30. As a = 15 x 2, which is equal to 30.
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