About Dividend in Math
What is Dividend?
We know that division is an operation in which we divide a number into equal parts. Here the number which is being divided is known as the dividend of the division operation.
In other words while performing the division operation, the number that is divided is called dividend and the number that divides it is called the divisor. We have to note here that the dividend can be a decimal, integer or an algebraic expression.
In fractional form, division is represented by a horizontal line called a fraction bar, and the dividend (numerator) is above the fraction line and divisor (denominator) is below the fraction line.
For example in the fraction \( \frac{a}{b} \),
a \( \rightarrow \) Dividend
b \( \rightarrow \) Divisor
This is read as ‘a over b’ or ‘divide a by b’.
For example:
\( \frac{15}{7} \)
Here \( 15 \) is in numerator and known as dividend and \( 7 \) is in denominator and known as divisor. It can be read as ‘\( 15 \) upon \( 7 \)’.
Terms Used in Division
Any division operation will have four parts to it, which are:
- Dividend: The number that we divide is called the dividend.
- Divisor: The number which divides is called the divisor.
- Quotient: The result we get from the division operation is called the quotient.
- Remainder: The number which is left after the division operation is known as the remainder.
For example, from the image we can see that \( 6 \) is the divisor, \( 135 \) is the dividend, \( 22 \) is the quotient and \( 3 \) is the remainder.
Dividend Formula
The formula to find the dividend is,
\( \text{Dividend}=\text{Divisor}\times \text{Quotient}+ \text{Remainder} \)
Let us apply this formula for the given example to verify the value of the dividend.
Here,
Divisor \( = 6 \)
Quotient \( = 22 \)
Remainder \( = 3 \)
So as per the formula, Dividend \( = 6\times 22+3 \)
\( = 132+3 \)
\( = 135 \)
We get the dividend as \( 135 \), hence verified.
Rapid Recall
Solved Dividend Examples
Example 1: Write the terms used in division for \( 65\div 3 \).
Solution:
Therefore, in \( 65\div 3 \) dividend \( = 65 \), divisor \( = 3 \), quotient \( = 21 \) and remainder \( = 2 \).
Example 2: Mary has \( 100 \) ribbons and she wants to divide them equally into \( 4 \) separate packets. How many ribbons will there be in each packet?
Solution:
Total Number of ribbons \( = 100 \)
Number of packets of ribbons \( = 4 \)
As per question we have to divide \( 100 \) into \( 4 \) groups of equal count, that is, we will have to divide \( 100 \) by \( 4 \), that is,
\( 100\div 4 = 25 \)
So there will be \( 4 \) groups each of count \( 25 \), that is, \( 4 \) packets each having \( 25 \) ribbons.
Example 3: In a division operation if divisor \( = 15 \), quotient \( = 3 \) and remainder \( = 9 \), find the dividend?
Solution:
\( \text{Dividend}=\text{Divisor}\times \text{Quotient}+\text{Remainder} \)
Substitute the given values,
Dividend \( = 15\times 3 + 9 \)
\( = 45 + 9 \)
\( = 54 \)
Therefore, the dividend is \( 54 \).
\( \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \)
There are 4 terminologies used in division operation:
- Dividend
- Divisor
- Quotient
- Remainder
\( \text{Dividend} = \text{Divisor} \times \text{Quotient} \)
\( \text{Dividend} = 16 \times 7 \) [Multiply]
Therefore, \( \text{Dividend} = 112 \)
In the division operation, the number which divides another number is a divisor and the number which is divided is a dividend.
When a division operation is performed the part of the dividend left after the operation is complete is known as the remainder.