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

Warm-Up: Quick Mental Division Facts

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

Checking the Warm-Up Answers Together

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

Where We Use Division Daily

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

Learning the Vocabulary of Division

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 Four Steps of Long Division

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!

A Division with No Remainder

Calculate: 4,560 ÷ 12

12)4560

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

Solving 4,560 Divided by 12

    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

Division That Leaves a Remainder

Calculate: 5,678 ÷ 23

23)5678

This one will have a remainder!

Step One: Dividing the First Two Digits

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

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

Step Two: Bringing Down the Next Digit

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

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

Step Three: Finishing the Division

    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 Division Answer Works

The Magic Formula

(Quotient × Divisor) + Remainder = Dividend

Check Example 2:

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

It works!

The Important Rule About Remainders

The remainder must ALWAYS be less than the divisor!

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

If remainder ≥ divisor, divide once more!

Word Problem About Distributing Books

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 = ?

Solving the Book Distribution Problem

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

Answer: 144 books per classroom

Practice Problem: Try It Yourself

Calculate: 5,400 ÷ 15

15)5400

Try this on your own!

Practice Problem 1: The Answer

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

Answer: 360

Practice Problem: Watch for a Remainder

Calculate: 7,896 ÷ 34

34)7896

Will this have a remainder?

Practice Problem 2: The Answer

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

Answer: 232 remainder 8

Word Problem: Packing Coffee into Bags

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 = ?

Solving the Coffee Packing Problem

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

Answer: 350 full bags, with 15 kg left over

Word Problem: Learners per Class

Learners per Class

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

4,680 ÷ 36 = ?

Solving the Learners per Class Problem

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

Answer: 130 learners per class

Common Division 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 with Division

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: Check Your Understanding

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: The Correct 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 Today

• 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: More Practice Problems Ahead

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 the Division Steps for Next Time

Division Steps:

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

Check: (Q × D) + R = Original

Well Done, You've Mastered Division

You can now divide by two-digit numbers!

Next lesson: Mixed Operations (BODMAS/DMAS)

Keep practicing!