Class 4 — Mathematics
Division: Long Division and Remainders
Class 4
- ✓By the end of this lesson students will be able to understand division as equal sharing and repeated subtraction.
- ✓By the end of this lesson students will be able to identify the dividend, divisor, quotient, and remainder in a division problem.
- ✓By the end of this lesson students will be able to perform long division of 2-digit and 3-digit numbers by a 1-digit divisor.
- ✓By the end of this lesson students will be able to understand the concept of a remainder and its property.
- ✓By the end of this lesson students will be able to verify division results using the formula: Dividend = Divisor × Quotient + Remainder.
Key concepts
Division means sharing equally or grouping equally. It is also a process of repeated subtraction. For example, if you have 12 sweets and want to share them equally among 3 friends, each friend will get 4 sweets. This can be written as 12 ÷ 3 = 4.
In a division problem, we use specific terms:\n* **Dividend**: The number being divided. (e.g., in 12 ÷ 3 = 4, 12 is the Dividend)\n* **Divisor**: The number by which we divide. (e.g., in 12 ÷ 3 = 4, 3 is the Divisor)\n* **Quotient**: The result of the division. (e.g., in 12 ÷ 3 = 4, 4 is the Quotient)\n* **Remainder**: The number left over after division, when the dividend cannot be divided completely by the divisor. (e.g., in 13 ÷ 3 = 4 with 1 left over, 1 is the Remainder)
Long division is a method used to divide larger numbers into smaller groups or parts. It helps us find the quotient and remainder systematically. We write the dividend inside the division symbol and the divisor outside.
The remainder is the part of the dividend that is left over after dividing as much as possible by the divisor. An important property of the remainder is that it must always be smaller than the divisor. If the remainder is 0, it means the division is exact.
To check if our division is correct, we can use a simple formula. This formula helps us confirm the relationship between the dividend, divisor, quotient, and remainder.
Key facts to remember
- 1Division is a process of equal sharing or equal grouping.
- 2Division is also known as repeated subtraction.
- 3The four main terms in division are: Dividend, Divisor, Quotient, and Remainder.
- 4The formula to verify division is: Dividend = Divisor × Quotient + Remainder.
- 5The remainder must always be smaller than the divisor.
- 6When a number is divided by 1, the quotient is the number itself. (e.g., 15 ÷ 1 = 15)
- 7When 0 is divided by any non-zero number, the quotient is 0. (e.g., 0 ÷ 7 = 0)
- 8Division by zero is not defined.
Worked examples
Example 1
Divide 48 by 4.
Answer
Quotient = 12, Remainder = 0.
This is an example of exact division, where the remainder is 0.
Example 2
Divide 75 by 6 and find the quotient and remainder.
Answer
Quotient = 12, Remainder = 3.
Observe that the Remainder (3) is less than the Divisor (6).
Example 3
Divide 257 by 5. Find the quotient and remainder. Also, verify your answer.
Answer
Quotient = 51, Remainder = 2. Verified.
Always ensure the remainder is less than the divisor (2 < 5).
Common mistakes
- ✗Not knowing multiplication tables well, leading to errors in finding the correct quotient digit.
- ✗Making errors in subtraction during each step of long division.
- ✗Forgetting to bring down the next digit of the dividend.
- ✗Writing a remainder that is greater than or equal to the divisor.
- ✗Confusing the positions of the dividend, divisor, and quotient in the long division format.
Exam tips
- ★Memorise your multiplication tables thoroughly, as they are essential for quick and accurate division.
- ★Write down each step of the long division clearly and neatly to avoid errors.
- ★Always check your answer using the verification formula: Dividend = Divisor × Quotient + Remainder.
- ★Double-check your subtraction at each step.
- ★Ensure that your final remainder is always smaller than the divisor.
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