What is a Quotient?
In an arithmetic division operation, the quotient is derived when two numbers are divided. The number which is getting divided is known as the dividend. The divisor is the number that divides the dividend. When the divisor does not divide the dividend completely, we get a remainder.
How can we represent the Division Method in different ways?
The division method can be represented in the following ways:
Dividend = Quotient × Divisor + Remainder
Or
Dividend = Quotient × Divisor (when there is no remainder)
As a result, Quotient = Dividend ÷ Divisor
We can represent the above equation in the following way:
From the above image, we can see that the numerator is the dividend and the denominator is the divisor.
The quotient is generally larger or smaller than the divisor, but it is always smaller than the dividend. The following image demonstrates the representation:
How to find the Quotient of any Number?
The quotient is obtained after the process of division is completed. We must first identify which number is the dividend and which number is the divisor. The problem equation is written as, Dividend ÷ Divisor from which we will get the quotient.
Solved Quotient Examples
Example 1 : A team of 10 researchers received $5600 funding for their research project in Manhattan. How much was awarded to each researcher?
Solution:
The total amount of funding received = $5600
The total number of researchers = 10
Here, we need to determine how much money was given to each researcher. So, we will divide 5600 by 10 to get the quotient value.
5600 ÷ 10 = 560
Therefore, $560 was given to each researcher.
Example 2 : Divide 78 by 8.
Solution:
We will use the long division method to find the quotient for this sum.
After division, we get 9 as the quotient and 6 as the remainder.
Example 3 : Find the quotient for 48 ÷ 4.
Solution:
We will use the long division method to find the quotient for the sum.
After division, we obtain 12 as the quotient with no remainder.
Example 4 : When the dividend is 6, the divisor is 4, and the remainder is 2, find the quotient.
Solution:
According to the formula for division,
Dividend = Quotient x Divisor + Remainder
So, Quotient \( (Q) = \frac{\text{Dividend – Remainder}}{\text{Divisor}} \)
Now, substitute the values in the formula,
\( (Q) = \frac{6 – 2}{4} = \frac{4}{4} = 1 \)
Thus, the quotient is 1.
The value of the dividend that the divisor can no longer divide is known as the remainder.
For example: 25 ÷ 4 = 6 as quotient and 1 as remainder
A quotient is obtained from a division process, whereas a product is the result of multiplying numbers. The quotient obtained is smaller than the dividend and divisor, while the product is larger than the numbers being multiplied.
The different terminologies of the division process are:
- Dividend
- Divisor
- Quotient
- Remainder
The quotient doesn’t necessarily need to be a whole number. It can be either a whole number or a decimal number.