Order of Basic Operation – Basic 6 Mathematics Lesson Note (First Term)

What is Order of Operations?

The order of operations tells us which calculations to do first when we have more than one operation in a problem.

BODMAS Rule

B – Brackets ( ) O – Of (powers/indices) D – Division ÷ M – Multiplication × A – Addition + S – Subtraction –

Remember: Always work from left to right when operations have the same priority.

Order of Operations with Whole Numbers

Example 1: 15 + 3 × 4

Step 1: Multiplication first (3 × 4 = 12)

Step 2: Then addition (15 + 12 = 27)

Answer: 27

Example 2: (8 + 2) × 6 – 15

Step 1: Brackets first (8 + 2 = 10)

Step 2: Multiplication (10 × 6 = 60)

Step 3: Subtraction (60 – 15 = 45)

Answer: 45

Example 3: 24 ÷ 6 + 3 × 5

Step 1: Division (24 ÷ 6 = 4)

Step 2: Multiplication (3 × 5 = 15)

Step 3: Addition (4 + 15 = 19)

Answer: 19

Exercise A – Whole Numbers

Solve using BODMAS:

1. 12 + 8 × 2 = ______
2. (15 – 3) ÷ 4 = ______
3. 20 – 6 × 2 + 8 = ______
4. 45 ÷ 9 + 7 × 3 = ______
5. (24 + 6) ÷ 5 – 2 = ______
6. 18 ÷ 2 × 3 + 5 = ______
7. 50 – (12 + 8) ÷ 4 = ______
8. 6 × 7 – 15 ÷ 3 = ______

Order of Operations with Fractions

Example 1: 1/2 + 1/4 × 2

Step 1: Multiplication first (1/4 × 2 = 2/4 = 1/2)

Step 2: Addition (1/2 + 1/2 = 1)

Answer: 1

Example 2: (3/4 – 1/4) × 2/3

Step 1: Brackets first (3/4 – 1/4 = 2/4 = 1/2)

Step 2: Multiplication (1/2 × 2/3 = 2/6 = 1/3)

Answer: 1/3

Example 3: 2/3 ÷ 1/3 + 1/2

Step 1: Division first (2/3 ÷ 1/3 = 2/3 × 3/1 = 2)

Step 2: Addition (2 + 1/2 = 2 1/2)

Answer: 2 1/2

Exercise B – Fractions

Solve using BODMAS:

1. 1/3 + 1/2 × 2 = ______
2. (1/2 + 1/4) ÷ 3 = ______
3. 3/4 – 1/4 × 2 = ______
4. 2/3 × 3/4 + 1/6 = ______
5. (5/6 – 1/3) × 2 = ______
6. 1 1/2 ÷ 3/4 – 1/2 = ______
7. 2/5 + 1/2 × 4/5 = ______
8. (3/4 + 1/4) ÷ 1/2 = ______

Order of Operations with Decimals

Example 1: 2.5 + 1.2 × 3

Step 1: Multiplication first (1.2 × 3 = 3.6)

Step 2: Addition (2.5 + 3.6 = 6.1)

Answer: 6.1

Example 2: (4.8 – 1.8) ÷ 2

Step 1: Brackets first (4.8 – 1.8 = 3.0)

Step 2: Division (3.0 ÷ 2 = 1.5)

Answer: 1.5

Example 3: 6.4 ÷ 1.6 + 2.5 × 2

Step 1: Division (6.4 ÷ 1.6 = 4)

Step 2: Multiplication (2.5 × 2 = 5)

Step 3: Addition (4 + 5 = 9)

Answer: 9

Exercise C – Decimals

Solve using BODMAS:

1. 3.5 + 2.1 × 2 = ______
2. (7.2 – 3.2) ÷ 4 = ______
3. 8.4 – 1.2 × 3 = ______
4. 9.6 ÷ 2.4 + 1.5 = ______
5. (5.5 + 2.5) × 0.5 = ______
6. 12.8 ÷ 3.2 – 1.8 = ______
7. 4.6 + 3.4 × 1.5 = ______
8. (10.5 – 4.5) ÷ 1.5 = ______

Mixed Operations

Example: 15 + 1/2 × 4 – 2.5

Step 1: Multiplication (1/2 × 4 = 2)

Step 2: Work left to right (15 + 2 – 2.5)

Step 3: Addition (15 + 2 = 17)

Step 4: Subtraction (17 – 2.5 = 14.5)

Answer: 14.5

Exercise D – Mixed Numbers

Solve these mixed problems:

1. 8 + 1/4 × 8 – 1.5 = ______
2. (12 – 2.5) × 1/2 + 3 = ______
3. 15.6 ÷ 4 + 2/3 × 6 = ______
4. 20 – (3.5 + 1/2) × 2 = ______
5. 1/3 × 12 + 5.4 – 2.8 = ______

Real Life Applications

Example: Shopping Problem

Kemi bought 3 books at ₦450 each and 2 pens at ₦75 each. She paid with ₦2,000. How much change did she get?

Solution: Change = 2,000 – (3 × 450 + 2 × 75) = 2,000 – (1,350 + 150) = 2,000 – 1,500 = ₦500

Exercise E – Word Problems

Solve using order of operations:

1. School Supplies: Tunde bought 4 notebooks at ₦120 each and 6 pencils at ₦25 each. If he paid ₦650, how much change did he get? Answer: ₦______
2. Cooking Recipe: A recipe needs 2.5 cups of flour, plus 1/4 cup for every 2 people. How much flour is needed for 8 people? Answer: ______ cups
3. Sports Score: Team A scored 3 goals in each of 4 matches, plus 2 extra goals in the final. Team B scored 15 goals total. What is the difference in their scores? Answer: ______

Exercise F – Time and Money

Solve these problems:

1. Work Schedule: A worker earns ₦1,200 per day. He worked 5 days and got a bonus of ₦800. If he spent ₦4,500, how much money does he have left? Answer: ₦______
2. Journey Cost: Bus fare is ₦150 per person plus ₦25 for each bag. If 3 people travel with 2 bags each, what is the total cost? Answer: ₦______
3. Party Planning: Drinks cost ₦200 each for 15 guests, food costs ₦350 per person, and decorations cost ₦1,500 total. What is the total cost? Answer: ₦______

Exercise G – Order Practice

Write the steps you would follow (don’t solve):

1. Problem: 24 ÷ (8 – 2) + 3 × 5 Step 1: ________________ Step 2: ________________ Step 3: ________________
2. Problem: 2/3 × (1/2 + 1/4) – 1/6 Step 1: ________________ Step 2: ________________ Step 3: ________________

Exercise H – Error Correction

These solutions are wrong. Find the correct answers:

1. Wrong: 15 + 3 × 4 = 18 × 4 = 72 Correct: ______
2. Wrong: (8 + 2) ÷ 5 – 1 = 10 ÷ 4 = 2.5 Correct: ______
3. Wrong: 2.4 + 1.6 × 2 = 4.0 × 2 = 8.0 Correct: ______

Exercise I – Complex Problems

Solve these challenging problems:

1. 25 – (3 × 4 + 8) ÷ 4 = ______
2. 1/2 × (3/4 + 1/4) + 2/3 = ______
3. (15.6 + 4.4) ÷ 5 – 1.2 = ______
4. 48 ÷ 6 × 2 + (15 – 7) = ______
5. 3.5 × 2 + 1/4 × 8 – 5 = ______

Answer Key

Exercise A:

1. 28
2. 3
3. 16
4. 26
5. 4
6. 32
7. 45
8. 37

Exercise B:

1. 4/3 or 1 1/3
2. 1/4
3. 1/4
4. 5/6
5. 1
6. 1 1/2
7. 3/5
8. 2

Exercise C:

1. 7.7
2. 1.0
3. 4.8
4. 5.5
5. 4.0
6. 2.2
7. 9.7
8. 4.0

Exercise D:

1. 8.5
2. 7.75
3. 7.5
4. 12
5. 6.6

Exercise E:

1. ₦500
2. 3.5 cups
3. 1 goal difference

Exercise F:

1. ₦2,300
2. ₦600
3. ₦9,750

Exercise H:

1. 27
2. 1
3. 5.6

Exercise I:

1. 20
2. 1 1/6
3. 2.8
4. 24
5. 4