Learning Objectives
- Understand division with remainder.
- Perform long division of 2-digit numbers by 1-digit numbers.
- Check division using the rule: Quotient × Divisor + Remainder = Dividend.
- Solve word problems that involve division with remainder.
A Friendly Introduction
In Class 3, you learned that division means sharing equally. You divided small numbers and found exact answers. But what happens when things do not divide equally?
Imagine you have 17 laddoos and want to share them equally among 5 friends. Each friend gets 3 laddoos, but 2 laddoos are left over. That leftover amount is called the remainder. In Class 4, we will learn how to handle remainders and divide bigger numbers using long division.
Understanding Division with Remainder
When we divide a number and it does not split equally, the amount left over is the remainder. The remainder is always less than the divisor.
Think: If you divide 14 by 4, can the remainder be 5? Why or why not?
Parts of a Division:
In 17 ÷ 5 = 3 remainder 2:
- Dividend = 17 (the number being divided)
- Divisor = 5 (the number we divide by)
- Quotient = 3 (the answer)
- Remainder = 2 (what is left over)
Long Division Step by Step
Long division helps us divide bigger numbers in an organised way. Follow these steps: Divide, Multiply, Subtract, Bring down.
Example 1: Divide 57 by 4
Step 1: Divide the tens digit. 5 ÷ 4 = 1. Write 1 in the quotient.
Step 2: Multiply. 1 × 4 = 4. Write 4 below 5.
Step 3: Subtract. 5 − 4 = 1.
Step 4: Bring down the 7. Now we have 17.
Step 5: Divide. 17 ÷ 4 = 4. Write 4 in the quotient.
Step 6: Multiply. 4 × 4 = 16. Subtract. 17 − 16 = 1.
Answer: 57 ÷ 4 = 14 remainder 1
Example 2: Divide 85 by 6
Step 1: 8 ÷ 6 = 1. Write 1. Multiply: 1 × 6 = 6. Subtract: 8 − 6 = 2.
Step 2: Bring down 5. Now we have 25.
Step 3: 25 ÷ 6 = 4. Write 4. Multiply: 4 × 6 = 24. Subtract: 25 − 24 = 1.
Answer: 85 ÷ 6 = 14 remainder 1
[Image: Long Division — Step by Step. A worked-out bus-stop method example of 4536 ÷ 6, showing quotient 756, remainder 0. Context: "Ravi has ₹4536. He divides equally among 6 friends." Each Divide–Multiply–Subtract–Bring down step shown clearly.]
Checking Division Using Multiplication
You can always check if your division is correct using this rule:
(Quotient × Divisor) + Remainder = Dividend
Example 3: Check 57 ÷ 4 = 14 remainder 1
Check: (14 × 4) + 1 = 56 + 1 = 57. This matches the dividend. Correct!
Example 4: Check 85 ÷ 6 = 14 remainder 1
Check: (14 × 6) + 1 = 84 + 1 = 85. This matches the dividend. Correct!
Think: If the check does not give back the dividend, what does that tell you?
Key Words
| Word | Meaning |
|---|
| Dividend | The number being divided |
| Divisor | The number we divide by |
| Quotient | The answer of the division |
| Remainder | The amount left over after equal sharing |
| Long Division | A step-by-step method to divide bigger numbers |
Key Points to Remember
- The remainder is always less than the divisor.
- Long division steps: Divide, Multiply, Subtract, Bring down.
- To check: (Quotient × Divisor) + Remainder = Dividend.
- If the remainder is 0, the division is exact (no leftover).
- In word problems, think carefully about what the remainder means.
Practice Questions
A. Fill in the Blanks
1. In 29 ÷ 6 = 4 remainder 5, the dividend is and the divisor is .
2. The remainder is always than the divisor.
3. To check division: (Quotient × ) + Remainder = .
4. 45 ÷ 7 = remainder .
5. If 36 ÷ 9 = 4 remainder 0, the division is .
B. Solve Using Long Division
1. 68 ÷ 5 = remainder
2. 73 ÷ 3 = remainder
3. 94 ÷ 7 = remainder
4. 86 ÷ 4 = remainder
5. 59 ÷ 8 = remainder
C. Check the Division (write Yes or No)
1. 76 ÷ 5 = 15 remainder 1. Check: (15 × 5) + 1 = . Correct?
2. 49 ÷ 6 = 8 remainder 2. Check: (8 × 6) + 2 = . Correct?
D. Multiple Choice Questions
1. What is the remainder when 37 is divided by 5?
(a) 1(b) 2(c) 3(d) 7
2. Which of the following is correct for 50 ÷ 8?
(a) 6 R 0(b) 6 R 2(c) 7 R 2(d) 5 R 10
3. If Quotient = 9, Divisor = 4, Remainder = 3, what is the Dividend?
(a) 36(b) 39(c) 43(d) 34
E. Word Problems
1. A farmer has 75 mangoes. He packs them into bags of 8. How many full bags can he make? How many mangoes are left over?
2. A teacher has 52 notebooks to distribute equally among 6 students. How many notebooks does each student get? How many are left with the teacher?
3. Rina has 95 rupees. She wants to buy pencils that cost 4 rupees each. How many pencils can she buy? How much money will be left?
Fun Activity — Division Detective
Complete the table. Use long division to find the quotient and remainder, then check your answer using multiplication.
| Dividend | Divisor | Quotient | Remainder | Check: (Q × D) + R |
|---|
| 47 | 3 | | | |
| 63 | 5 | | | |
| 89 | 7 | | | |
| 54 | 4 | | | |