Division by Two-Digit Numbers

P6 Mathematics - Term I, Topic 3

Lesson 4 of 5

Learning Objectives:

• Divide by 2-digit numbers with/without remainders
• Solve division word problems
• Check division using multiplication

Mental Warm-Up!

1. 72 ÷ 8 = ?
2. 144 ÷ 12 = ?
3. 200 ÷ 10 = ?
4. 360 ÷ 12 = ?

Answers

1. 72 ÷ 8 = 9
2. 144 ÷ 12 = 12
3. 200 ÷ 10 = 20
4. 360 ÷ 12 = 30

When Do We Divide?

• Sharing: Dividing items equally
• Shopping: Finding unit price
• Grouping: Making equal groups
• Average: Finding per-person amounts
• Packing: Items per box/bag

Division Vocabulary

Example: 17 ÷ 5 = 3 remainder 2

• Dividend: 17 (number being divided)
• Divisor: 5 (number dividing by)
• Quotient: 3 (the answer)
• Remainder: 2 (what's left)

The Division Process

Four Steps

1. Divide: How many times does divisor go into dividend?
2. Multiply: Multiply quotient digit by divisor
3. Subtract: Subtract from dividend
4. Bring down: Bring down next digit, repeat

D M S B - Remember this pattern!

Example 1: Division Without Remainder

Calculate: 4,560 ÷ 12

12)4560

Let's work through this step by step...

Example 1: Step-by-Step

    380
   ----
12)4560
   36↓
   ---
    96
    96
   ---
     0

1. 12 into 45? 3 times (3 × 12 = 36)
2. 45 - 36 = 9, bring down 6 → 96
3. 12 into 96? 8 times (8 × 12 = 96)
4. 96 - 96 = 0, bring down 0
5. 12 into 0? 0 times

Answer: 380

Example 2: Division WITH Remainder

Calculate: 5,678 ÷ 23

23)5678

This one will have a remainder!

Example 2: Step 1

    2
   ---
23)5678
   46
   ---
   10

• 23 doesn't go into 5
• 23 into 56? 2 times (2 × 23 = 46)
• 56 - 46 = 10

Example 2: Step 2

    24
   ---
23)5678
   46↓
   ----
   107
    92
   ----
    15

• Bring down 7 → 107
• 23 into 107? 4 times (4 × 23 = 92)
• 107 - 92 = 15

Example 2: Step 3

    246 r 20
    --------
23)5678
   46↓↓
   ----
   107
    92
   ----
    158
    138
    ----
     20

• Bring down 8 → 158
• 23 into 158? 6 times (6 × 23 = 138)
• 158 - 138 = 20

Answer: 246 remainder 20

Checking Your Answer ✓

The Magic Formula

(Quotient × Divisor) + Remainder = Dividend

Check Example 2:

• (246 × 23) + 20 = ?
• 5,658 + 20 = 5,678 ✓

It works!

Important Rule!

About Remainders

The remainder must ALWAYS be less than the divisor!

Examples:

• 17 ÷ 5 = 3 r 2 ✓ (2 < 5)
• 20 ÷ 6 = 3 r 2 ✓ (2 < 6)
• 25 ÷ 7 = 3 r 4 ✓ (4 < 7)

If remainder ≥ divisor, you can divide one more time!

Word Problem 1

Distributing Books

Problem: A school received 3,456 books to distribute equally among 24 classrooms. How many books does each classroom get?

What operation? DIVISION!

3,456 ÷ 24 = ?

Word Problem 1: Solution

    144
    ---
24)3456
   24↓↓
   ----
   105
    96
   ----
    96
    96
    ---
     0

Answer: 144 books per classroom

Practice Problem 1

Calculate: 5,400 ÷ 15

15)5400

Try this on your own!

Practice Problem 1: Answer

    360
    ---
15)5400
   45↓↓
   ----
    90
    90
   ----
     0

Answer: 360

Practice Problem 2

Calculate: 7,896 ÷ 34

34)7896

Will this have a remainder?

Practice Problem 2: Answer

    232 r 8
    -------
34)7896
   68↓↓
   ----
   109
   102
   ----
    76
    68
   ----
     8

Answer: 232 remainder 8

Word Problem 2

Packing Coffee

Problem: A farmer harvested 8,765 kg of coffee to pack in bags of 25 kg each. How many full bags? How much coffee is left over?

8,765 ÷ 25 = ?

Word Problem 2: Solution

    350 r 15
    --------
25)8765
   75↓↓
   ----
   126
   125
   ----
    15
     0
   ----
    15

Answer: 350 full bags, with 15 kg left over

Word Problem 3

Learners per Class

Problem: 4,680 learners are to be divided into 36 equal classes. How many learners per class?

4,680 ÷ 36 = ?

Word Problem 3: Solution

    130
    ---
36)4680
   36↓↓
   ----
   108
   108
   ----
     0

Answer: 130 learners per class

Common Mistakes to Avoid!

1. Wrong estimation of quotient digit
2. Forgetting to bring down the next digit
3. Remainder ≥ divisor (should divide one more time!)
4. Multiplication errors when checking
5. Not aligning numbers properly

Tips for Success!

1. Estimate first (round divisor and dividend)
2. Use multiplication tables to help
3. Check your work: (Q × D) + R = Original
4. Be systematic - don't skip steps
5. Remainder must be < divisor

Quick Assessment ✓

1. What are the four steps of division?

2. How do you check if your division answer is correct?

3. Can the remainder be bigger than the divisor?

Quick Assessment: Answers

1. Divide, Multiply, Subtract, Bring down (DMSB)

2. (Quotient × Divisor) + Remainder = Dividend

3. No! Remainder must be less than divisor

Summary: What We Learned

• Divide by two-digit numbers
• Handle remainders correctly
• Check answers using multiplication
• Solve real-life division problems
• Remember: DMSB (Divide, Multiply, Subtract, Bring down)

Homework

1. 7,890 ÷ 15 = ?
2. 9,876 ÷ 34 = ?
3. 12,456 ÷ 48 = ?
4. Word problem: 5,670 oranges are packed in boxes of 45 each. How many full boxes can be made?

Show all working and check your answers!

Remember!

Division Steps:

1. Divide
2. Multiply
3. Subtract
4. Bring down
5. Repeat!

Check: (Q × D) + R = Original

Well Done!

You can now divide by two-digit numbers!

Next lesson: Mixed Operations (BODMAS/DMAS)

Keep practicing!