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 a number divides another number evenly (without any remainder), then the quotient will be a whole number. For example, 16 ÷ 4 = 4. Here, the remainder is 0.
  
   
• The quotient is a decimal number when the number is not evenly divisible by another number. For example, 16 ÷ 5 = 3.2. It can also be written as 16 ÷ 5 = 3, where quotient = 3, and remainder = 1
   

When we divide a number by another number, we get a quotient. There are different methods to find the quotient, such as: 

 

• Finding Quotients by Repeated Subtraction
  
   
• Finding Quotients by Long Division Method
   

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. 

 

• To share objects among a group of people, we use division. For instance, when sharing a pizza among a group of 3 people, we divide the number of slices by the number of people. 
  
   
• While shopping, to calculate the cost per unit, we use division. 
  
   
• In cooking, to adjust the recipe according to the number of servers, we use division. 
  
   
• For budgeting and calculating the average spending, we use division.