Mathematics -- Class 4

Topic: Division (Long Division, Remainder, and Checking)
Name: ____________________________Class: 4Date: ________________
Learning Objectives
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:

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 x 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 x 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 x 6 = 6. Subtract: 8 - 6 = 2.

Step 2: Bring down 5. Now we have 25.

Step 3: 25 / 6 = 4. Write 4. Multiply: 4 x 6 = 24. Subtract: 25 - 24 = 1.

Answer: 85 / 6 = 14 remainder 1

Checking Division Using Multiplication

You can always check if your division is correct using this rule:

(Quotient x Divisor) + Remainder = Dividend

Example 3: Check 57 / 4 = 14 remainder 1

Check: (14 x 4) + 1 = 56 + 1 = 57. This matches the dividend. Correct!

Example 4: Check 85 / 6 = 14 remainder 1

Check: (14 x 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
WordMeaning
DividendThe number being divided
DivisorThe number we divide by
QuotientThe answer of the division
RemainderThe amount left over after equal sharing
Long DivisionA step-by-step method to divide bigger numbers

Mathematics -- Class 4 (continued)

Topic: Division -- Key Points and Practice
Key Points to Remember
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 x ) + 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 x 5) + 1 = . Correct?
  2. 49 / 6 = 8 remainder 2. Check: (8 x 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.

DividendDivisorQuotientRemainderCheck: (Q x D) + R
473
635
897
544