Last updated on July 4th, 2025
Division is a basic arithmetic operation used for splitting a number into equal parts. The parts of division are dividend, divisor, quotient, and remainder. The result that we get by dividing a number by another is called a quotient. For example, 10 ÷ 5 = 2; here, 2 is the quotient.
A quotient is the result of dividing a number by another number. E.g., in 16 ÷ 8 = 2, 16 is the dividend, 8 is the divisor, 2 is the quotient, and 0 is the remainder.
Depending on the dividend and divisor, a quotient can either be an integer or a decimal.
When we divide a number by another number, we get a quotient. There are different methods to find the quotient, such as:
In this method, we subtract the divisor from the dividend till 0 remains or until the subtraction is no longer possible.
For example, 16 ÷ 4
16 - 4 = 12 —-------------- Step 1
12 - 4 = 8 —-------------- Step 2
8 - 4 = 4 —-------------- Step 3
4 - 4 = 0 —-------------- Step 4
Here, 4 is the quotient. So, 16 ÷ 4 = 4
We use this method to divide a large number. Here, the dividend is written inside the division bracket and the divisor is written outside. Follow these steps to find the quotient using the long division method:
Step 1: The dividend should be inside the bracket, while the divisor should be outside.
For example, dividing 96 by 4, so 96 is written inside and 4 outside the bracket
Step 2: We divide the first digit from the dividend with the divisor.
Dividing 9 by 4, gives us the quotient of 2 and remainder of 1.
Step 3: Subtract
Here, 9 - 8 = 1
Step 4: Bring down the next digit
So, 6 is brought down to form 16
Step 5: Divide again
Dividing 16 by 4, the quotient is 4. So we write 4 next to 2
Step 6: Repetition of step 3, which is subtraction
Here, 16 - 16 = 0
Once we get 0 as the remainder, it means the division is complete.
So, 96 ÷ 4 = 24.
The remainder is the part after dividing a number when the divisor does not completely divide the dividend. It occurs when the divisor does not divide the dividend evenly. Tools like counters, blocks, or beads help students visualize division with remainders.
We can ignore the remainder while writing the final answer because not mentioning the remainder will not affect the result. E.g., when 30 is divided by 4, we get 2 as the remainder and 7 as the quotient. While writing the answer, we can decide to ignore the remainder, and write only the quotient (7) as the answer.
Sometimes, we need to round up the quotient by increasing the dividend. For example, if a box can fit 6 books, then how many boxes are required to fit 50 books? To find the number of boxes required to fit 50 boxes = 50 ÷ 6 = 8.33, so we need 9 boxes to fit all the books.
If the remainder is non-zero, then it means it can be written as a decimal or fraction as it can be divided further. For instance, when dividing 20 by 6, we get 3 as the quotient and 2 as the remainder. In fraction, it can be expressed as 3 2/6, which can be simplified into 3 1/3. In decimal, it is expressed as 3.333.
One of the basic operations in mathematics is division, which we often use in our daily lives. Here are some of the real-life applications of quotients.
Although division is a basic math operation, we can sometimes make mistakes while writing down the quotient or remainder. Here, let us go through some of the common mistakes and methods to avoid them while dividing:
A shopkeeper has 24 apples and wants to pack them equally into 6 baskets. How many apples will be in each basket?
There are 4 apples in each basket
To find the number of apples in each basket, we divide the total number of apples by the number of baskets
So, the number of apples in each basket = 24 ÷ 6 = 4
A factory produces 144 toys in a day and packs them in boxes containing 12 toys each. How many boxes are needed?
The number of boxes needed is 12
To find the number of boxes needed, divide the total number of toys by the number of toys per box:
So, the number of boxes needed = 144 ÷ 12 = 12
A bakery has 10 kg of flour and needs to divide it into 4 equal portions. How much flour is in each portion?
Each portion has 2.5 kg flour
To find how much flour is in each portion, divide the total flour by the number of portions:
So, the amount of flour in each portion = 10 ÷ 4 = 2.5
Find the quotient of 999 ÷ 3
The quotient of 999 ÷ 3 is 333
To find the quotient, divide:
999 ÷ 3 = 333
A farmer harvests 250 oranges and wants to place them in crates, with 50 oranges per crate. How many crates will he need?
The number of crates needed is 5
To find the number of crates, divide the total number of oranges by the number of oranges per crate: 250 ÷ 50 = 5
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.
: She loves to read number jokes and games.