Division of Whole Numbers – Basic 6 Mathematics Lesson Note (First Term)

Division of Whole Numbers

Long Division Method

Steps:

1. Divide the first digit(s) of dividend by divisor
2. Multiply and subtract
3. Bring down the next digit
4. Repeat until all digits are used

Example: 2,846 ÷ 7

    406 R 4

   ________

7 ) 2,846

    28↓

    —-

     046

      42

      —

       46

       42

       —

        4

Check: 406 × 7 + 4 = 2,842 + 4 = 2,846 ✓

Division with Larger Numbers

Example: 45,678 ÷ 23

     1,986 R 20

    __________

23 ) 45,678

     23↓

     —-

     226

     207

     —-

     197

     184

     —-

     138

     138

     —-

       0

Exercise A – Whole Number Division

Solve these division problems:

1. 789 ÷ 6 = ______ R ______
2. 2,456 ÷ 8 = ______ R ______
3. 15,678 ÷ 24 = ______ R ______
4. 34,567 ÷ 45 = ______ R ______
5. 56,789 ÷ 67 = ______ R ______

Exercise B – Check Your Answers

Use multiplication to check these divisions:

1. 567 ÷ 9 = 63 Check: 63 × 9 = ______
2. 1,234 ÷ 7 = 176 R 2 Check: 176 × 7 + 2 = ______

Division of Decimal Numbers

Method 1: Dividing Decimals by Whole Numbers

Steps:

1. Place decimal point in quotient directly above dividend decimal
2. Divide as with whole numbers

Example: 45.6 ÷ 8

    5.7

   ______

8 ) 45.6

    40↓

    —-

     56

     56

     —

      0

Method 2: Dividing by Decimals

Steps:

1. Move decimal point in divisor to make it a whole number
2. Move decimal point in dividend the same number of places
3. Divide normally

Example: 67.2 ÷ 2.4

Move decimal 1 place: 672 ÷ 24

     28

   _____

24 ) 672

     48↓

     —-

     192

     192

     —-

       0

Exercise C – Decimal Division

Solve these problems:

1. 78.6 ÷ 6 = __________
2. 156.8 ÷ 8 = __________
3. 45.36 ÷ 12 = __________
4. 89.7 ÷ 3 = __________
5. 234.5 ÷ 5 = __________

Exercise D – Dividing by Decimals

Solve these problems:

1. 84.6 ÷ 2.3 = __________
2. 156.8 ÷ 3.2 = __________
3. 72.45 ÷ 2.5 = __________
4. 91.8 ÷ 1.8 = __________

Real Life Problems

Money Problems

Example: ₦2,400 is shared equally among 8 children. How much does each child get?

Solution: ₦2,400 ÷ 8 = ₦300

Distance and Time Problems

Example: A car travels 456.8 km in 8 hours. What is the average speed per hour?

Solution: 456.8 ÷ 8 = 57.1 km per hour

Exercise E – Money Problems

Solve these real problems:

1. Sharing Money: ₦15,600 is shared equally among 12 students for a school trip. How much does each student contribute? Answer: ₦__________
2. Shop Profit: A trader made ₦84,560 profit in 8 weeks. What was her average weekly profit? Answer: ₦__________
3. Salary Division: Mr. Kola’s annual salary is ₦1,440,000. What is his monthly salary? Answer: ₦__________

Exercise F – Time and Distance

Solve these problems:

1. Travel Speed: A bus covers 368.4 km in 6 hours. What is its average speed? Answer: ______ km/h
2. Work Rate: 24 workers can complete a project in 15 days. How many days will 18 workers take to complete the same project? Answer: ______ days
3. Food Distribution: A bag of rice weighing 78.6 kg is shared equally among 6 families. How much rice does each family get? Answer: ______ kg

Exercise G – Measurement Problems

Solve these problems:

1. Fabric Cutting: A piece of cloth 45.6 meters long is cut into pieces of 2.4 meters each. How many pieces can be made? Answer: ______
2. Water Distribution: 567 liters of water is distributed equally into 21 containers. How much water is in each container? Answer: ______ liters
3. School Supplies: 2,568 exercise books are shared equally among 24 classes. How many books does each class get? Answer: ______

Quantitative Reasoning

Mental Division Strategies

Dividing by 10, 100, 1000:

• Move decimal point left by number of zeros
• 456 ÷ 10 = 45.6
• 456 ÷ 100 = 4.56

Dividing by 5:

• Divide by 10, then multiply by 2
• 85 ÷ 5 = (85 ÷ 10) × 2 = 8.5 × 2 = 17

Dividing by 25:

• Divide by 100, then multiply by 4
• 300 ÷ 25 = (300 ÷ 100) × 4 = 3 × 4 = 12

Exercise H – Mental Division

Use mental strategies:

1. 567 ÷ 10 = ______
2. 2,340 ÷ 100 = ______
3. 85 ÷ 5 = ______ (Use ÷10 then ×2)
4. 400 ÷ 25 = ______ (Use ÷100 then ×4)
5. 750 ÷ 50 = ______ (Use ÷100 then ×2)

Exercise I – Division Patterns

Complete these patterns:

1. 240 ÷ 8 = 30 2,400 ÷ 8 = ______ 24,000 ÷ 8 = ______
2. 56 ÷ 7 = 8 560 ÷ 7 = ______ 5,600 ÷ 7 = ______
3. 45 ÷ 9 = 5 450 ÷ 9 = ______ 4,500 ÷ 9 = ______

Answer Key

Exercise A:

1. 131 R 3
2. 307 R 0
3. 653 R 6
4. 768 R 7
5. 847 R 30

Exercise C:

1. 13.1
2. 19.6
3. 3.78
4. 29.9
5. 46.9

Exercise D:

1. 36.8
2. 49
3. 28.98
4. 51

Exercise E:

1. ₦1,300
2. ₦10,570
3. ₦120,000

Exercise F:

1. 61.4 km/h
2. 20 days
3. 13.1 kg

Exercise G:

1. 19 pieces
2. 27 liters
3. 107 books

Exercise H:

1. 56.7
2. 23.4
3. 17
4. 16
5. 15