Division is the basic operation in mathematics. It is important to understand the concept of division.
Example: Suppose we have 12 chocolates and we want to distribute them equally among our 4 friends. How many chocolates do we give to each of our friends? To find this we divide 12 by 4 and the answer is 3. So, we will give 3 chocolates to each of our friends.
Division operation involves different terms such as dividend, divisor, quotient, and remainder. The dividend is the number we want to divide, the divisor is the number we divide by, the quotient is the result of the division, and the remainder is the leftover value if the division is not exact.
In this article, we are going to discuss these terms and we will also discuss some practice problems on division.
Table of Content
Terms Related to Division
In any division, there are 4 required terms:
- Dividend
- Divisor
- Quotient
- Remainder
Dividend
The dividend is the number that we want to divide. It is the total amount or quantity that is being divided into smaller parts.
For example, In the division problem 12 ÷ 4 = 3, the dividend is 12.
Divisor
The divisor is the number by which we divide the dividend. It is the total amount of how many equal parts the dividend should be divided into.
For example, In the division problem 12 ÷ 4 = 3, the divisor is 4.
Quotient
The quotient is the result of the division. It tells us how many times the divisor fits into the dividend or how much each part is after dividing the dividend by the divisor.
For example, In the division problem 12 ÷ 4 = 3, the quotient is 3.
Remainder
The remainder is left value after dividing the dividend by the divisor. When dividends are not split evenly by the divisor, then the leftover part is the remainder.
Example: When we divide 13 ÷ 4, the remainder is 1.
Division Equation: Dividend = Divisor × Quotient + Remainder
The relationship formula between dividend, divisor, and quotient is:
Dividend = Divisor × Quotient + Remainder
If we rearrange the formula to find the value of the other three terms using the same formula:
- Divisor = (Dividend - Remainder)/Quotient
- Quotient = (Dividend - Remainder)/Divisor
- Remainder = Dividend − Divisor × Quotient
Types of Division
There are different types of division. The classification of division is done on the basis whether we get remainder at the end or not. Some main types of division are:
- Exact Division
- Division with Remainder
- Long Division
- Short Division
Exact Division (Remainder = 0)
When the divisor divides the dividend perfectly, meaning there is no remainder left then it is known as exact division. The quotient we get is a whole number. If the remainder is zero then the formula relationship is:
- Dividend = Divisor × Quotient
- Divisor = Dividend /Quotient
- Quotient = Dividend/Divisor
Example: Divide 36 by 6.
Solution:
Step 1: Write Down the Division Problem
We first write down the dividend, followed by the division symbol (÷), and then the divisor.
Example:
36 ÷ 6
Here, 36 is the dividend, and 6 is the divisor.
Step 2: Divide the Dividend by the Divisor
Now perform the division and find out the quotient. We ask ourselves how many times 6 fits into 36.
Calculation:
6 fits into 36 exactly 6 times because:
6 × 6 = 36
So, the quotient is 6.
Step 3: Calculate the Remainder
Next, we subtract the product of the divisor and quotient from the dividend to find the remainder.
Calculation:
36 - 36 = 0
Since there is nothing left after subtraction, the remainder is 0.
Step 4: Write Down the Quotient and Remainder
Now, we can write down the result of the division.
Result:
36 ÷ 6 = 6
The quotient is 6 and the remainder is 0. This is an example of exact division, where the division is perfect and nothing is left over.
Division with Remainder
Division with a remainder occurs when a number (dividend) is not perfectly divisible by another number (divisor), resulting in a quotient and a leftover value called the remainder. The remainder is the part that cannot be evenly divided by the divisor.
Example: Divide 14 by 3.
Solution:
Dividend: 14
Divisor: 3
Quotient: 4 (since 3 fits into 14 four times)
Remainder: 2 (because
(14 - (3 \times 4) = 2)) The equation representing this division is:
14 =
(3 \times 4) + 2 This shows that 14 divided by 3 gives a quotient of 4 and a remainder of 2, illustrating the concept of division with a remainder.
Long Division
Long division is a method used when we are dividing larger numbers that can not easily be divided in our head i.e. it cannot be divided without using pen and paper.
For Example:
125 (Dividend) = 4 (Divisor) × 31 (Quotient) + 1 (Remainder)
Short Division
Short division is a faster way of dividing when the divisor is a simple number and the division can be done easily without writing.
For Example:
36 (Dividend) = 6 (Divisor) × 6 (Quotient) + 0 (Remainder)
Conclusion
Division is a basic arithmetic operation that splits a number (dividend) into equal parts based on another number (divisor). The result is called the quotient, and any leftover part is the remainder. Key terms include dividend, divisor, quotient, and remainder, all linked by the formula: Dividend = Divisor × Quotient + Remainder.
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Solved Examples of Dividend and Divisor and Quotient
Q1: Divide 56 by 8.
Solution:
Given Dividend: 56
Divisor: 8
Quotient: 56 ÷ 8 = 7
When we divide 56 by 8, the quotient is 7.
Q2: The divisor is 9, the quotient is 11, and the remainder is 4. Find the dividend.
Solution:
Given Divisor: 9
Quotient: 11
Remainder: 4
Dividend: (9 × 11) + 4
= 99 + 4
= 103
The dividend is 103 when divided by 9, giving a quotient of 11 and a remainder of 4.
Q3: The dividend is 75, the quotient is 8, and the remainder is 3. Find the divisor.
Solution:
Dividend: 75
Quotient: 8
Remainder: 3
Divisor: 75 - 3/8 = 72/8 = 9
The divisor is 9 when the dividend is 75, the quotient is 8, and the remainder is 3.
Q4: Divide 1024 by 32 and find the quotient and remainder.
Solution:
Dividend: 1024
Divisor: 32
Quotient: 1024 ÷ 32 = 32
Remainder: 1024 − (32 × 32) = 1024 − 1024 = 0
When we divide 1024 by 32, the quotient is 32, and the remainder is zero.
Q5: Divide 0 by 9.
Solution:
Dividend: 0
Divisor: 9
Quotient: 0 ÷ 9 = 0
The quotient is zero.
When we divide 0 by any number (except zero), the quotient is always 0.
Q6: Divide 23 by 4 and find the remainder.
Solution:
Dividend: 23
Divisor: 4
Quotient: 23 ÷ 4 = 5 (with a remainder)
Remainder: 23 − (4 × 5) = 23 − 20 = 3
When we divide 23 by 4, the quotient is 5 and the remainder is 3.
Q7: Geek has 95 apples. She wants to divide them equally among 4 friends. How many apples will each friend get, and how many will be left over?
Solution:
To find the number of apples each friend will get (quotient):
Quotient = 95/4 = 23 apples per friend
Remainder = 95 − (23 × 4) = 95 − 92 = 3 apples left over
So, each friend will get 23 apples, and 3 apples are left over.
Q8: A library has 120 books and wants to distribute them equally among 8 schools. How many books will each school receive?
Solution:
finding the number of books each school will receive:
We calculate the quotient:
Quotient = 120/8
= 15 books per school.
So, each school will receive 15 books.
Practice Questions on Dividend and Remainder -
Q1: Divide 81 by 9.
Q2: The divisor is 8, the quotient is 7, and the remainder is 6. Find the dividend.
Q3: The dividend is 64, the quotient is 4, and the remainder is 0. Find the divisor.
Q4: Divide 100 by 25 and find the quotient and remainder.
Q5: Divide 0 by 7.
Q6: Divide 75 by 6 and find the remainder.
Q7: A farmer has 95 oranges. He wants to distribute them equally among 5 baskets. How many oranges will each basket have, and how many will be left over?
Q8: A teacher has 144 pencils and wants to give them equally to 12 students. How many pencils will each student receive?
Q9: Divide 200 by 15 and find the quotient and remainder.
Q10: The divisor is 11, the quotient is 5, and the remainder is 2. Find the dividend.
Answer Key
- Quotient = 9
- Dividend = 62
- Divisor = 16
- Quotient = 4, Remainder = 0
- Quotient: 0 ÷ 7 = 0
- Remainder: 75 ÷ 6 = 12 remainder 3
- Quotient: 95 ÷ 5 = 19 oranges per basket, Remainder = 0
- Quotient = 12 pencils per student
- Quotient = 13 remainder 5
- Dividend = 57