Formula to Find Quotient and Remainder with Solved Examples
Division can be defined as splitting large numbers into smaller groups having equal numbers each. The number of smaller groups obtained is called the quotient of a number. The quotient is the result obtained at the end of division like how sum, difference and product are for addition, subtraction and multiplication, respectively.
Dividing Cake using Division
Division is one of the most important mathematical operations used during calculations to obtain equal parts of the given whole of something. So when you are required to cut a whole cake into 12 slices of equal sizes, as you have 12 friends to share it with, you’re applying division.
What Should I Know to do Division?
If you have an idea of the other 3 mathematical operations listed below and a basic knowledge of divisibility you can master division too!
Multiplication tables till 9
Subtraction
Divisibility rules till 9 (This is optional to know if the number would produce a remainder or not)
What is Division?
Division is a process by which a large number is split into smaller groups each containing an equal number of parts in each group. It involves the multiplication and subtraction of some form to obtain the result known as the quotient. Another important aspect of division is the remainder which is the number that is left out after the process of division. Shown below is the symbol of division which is a line with dots placed above and below.
Division Symbol
How to Find the Quotient of a Given Perfectly Divisible Number?
For perfectly divisible numbers, we carry out the division till we obtain a remainder of 0 as illustrated below. We are to divide 625 by 5 as follows:
Division of 625 by 5
Here, the quotient obtained is 125 and the remainder obtained is 0. The simple division is carried out till a remainder of 0 is obtained in the case of a perfectly divisible number.
How to Find the Quotient and Remainder of a Given Number?
The above case illustrated is when the given number is perfectly divisible by the divisor. If the number given is not divisible by the divisor, a remainder is often obtained. To understand this case, we are going to divide 100 by 8 as follows:
Division of 100 by 8
Here, the quotient obtained is 12 and the remainder obtained is 4. Simple division is carried out till a remainder obtained is lesser than the divisor in case of a number that is not divisible by the divisor.
Solved Examples
1. Find the quotient and remainder obtained when 420 is divided by 7.
Ans: We carry out the division as follows:
Division of 420 by 7
The quotient is found to be 60 and the remainder is found to be 0.
2. Divide 67 by 7.
Ans:
Division of 67 by 7
The quotient is 9 and the remainder will be 4.
3. Divide 888 by 7.
Ans:
Division of 888 by 7
The quotient is 126 and the remainder is 6.
Practice Problems
1. Divide 506 by 7 and give the quotient and remainder.
Ans: Quotient - 72, remainder - 2.
2. Divide 782 by 5 and give the quotient and remainder.
Ans: Quotient - 156, remainder - 2.
3. Divide 932 by 4 and give the quotient and remainder.
Ans: Quotient - 233, remainder - 0.
4. Divide 327 by 2 and give the quotient and remainder.
Ans: Quotient - 163, remainder - 1.
5. Divide 144 by 3 and give the quotient and remainder.
Ans: Quotient - 48, remainder - 0.
Summary
Division is a basic mathematical operation where a larger number is split into smaller numbers containing equal groups. The result obtained at the end of the division is known as the quotient. The number that is left out at the end of the process of division which cannot be divided any further is called the remainder.
If the larger number divided by the smaller number is perfectly divisible by it, then we only obtain a quotient and the remainder is usually 0. If the larger number divided by the smaller number is not divisible by it, then we obtain a quotient and the remainder is the number that is left out at the end.
FAQs on Understanding Quotient and Remainder in Division
1. What is quotient and remainder in division?
The quotient is the result obtained when one number is divided by another, and the remainder is the amount left over after division. In a division statement:
Dividend ÷ Divisor = Quotient with a Remainder.
For example:
- 17 ÷ 5 = 3 remainder 2
- Here, 3 is the quotient and 2 is the remainder.
2. What is the formula to find quotient and remainder?
The formula relating dividend, divisor, quotient, and remainder is Dividend = Divisor × Quotient + Remainder.
This is known as the Division Algorithm and always satisfies:
- 0 ≤ Remainder < Divisor
- 23 ÷ 4 = 5 remainder 3
- Check: 4 × 5 + 3 = 23
3. How do you find the quotient and remainder of a number?
You find the quotient by dividing the dividend by the divisor and the remainder is what is left after division.
Steps:
- Divide the dividend by the divisor.
- Write the whole number result as the quotient.
- Multiply the divisor by the quotient.
- Subtract from the dividend to get the remainder.
- 29 ÷ 6
- 6 × 4 = 24
- 29 − 24 = 5
4. What is the Division Algorithm?
The Division Algorithm states that for any integers a and b (b ≠ 0), there exist unique integers q and r such that a = bq + r where 0 ≤ r < b.
Here:
- a = Dividend
- b = Divisor
- q = Quotient
- r = Remainder
5. Can the remainder be greater than the divisor?
No, the remainder is always less than the divisor.
According to the division rule:
- 0 ≤ Remainder < Divisor
- 15 ÷ 4 cannot have remainder 5 because 5 ≥ 4.
6. What is the quotient and remainder when 45 is divided by 8?
When 45 is divided by 8, the quotient is 5 and the remainder is 5.
Calculation:
- 8 × 5 = 40
- 45 − 40 = 5
- 45 = 8 × 5 + 5
7. What happens when the remainder is zero?
If the remainder is zero, the division is exact and the dividend is completely divisible by the divisor.
Example:
- 36 ÷ 9 = 4 remainder 0
- Dividend = Divisor × Quotient
8. What is the difference between quotient and remainder?
The quotient is the whole number result of division, while the remainder is the leftover part after division.
Key differences:
- Quotient shows how many times the divisor fits into the dividend.
- Remainder shows what is left.
- Quotient can be zero or positive.
- Remainder is always less than the divisor.
9. How do you check if your quotient and remainder are correct?
You can verify your answer using the formula Dividend = Divisor × Quotient + Remainder.
Steps to check:
- Multiply divisor by quotient.
- Add the remainder.
- See if the result equals the dividend.
- 52 ÷ 7 = 7 remainder 3
- Check: 7 × 7 + 3 = 52 ✓
10. What are some common mistakes when finding quotient and remainder?
Common mistakes include incorrect multiplication, subtraction errors, and writing a remainder greater than the divisor.
Watch out for:
- Forgetting that Remainder < Divisor.
- Arithmetic mistakes in multiplication.
- Not verifying using the division formula.
- Confusing quotient with remainder.
