What is BODMAS Rule?

The BODMAS rule is a set of guidelines that helps us solve math problems correctly. BODMAS stands for Brackets, Orders (exponents), Division, Multiplication, Addition, and Subtraction. By following the BODMAS rule, we ensure that everyone gets the same answer when solving math problems.

Have you ever gotten different answers from your friends when solving a math problem? This happens when we don’t follow the same rules. The BODMAS rule helps everyone get the same answer. In this article, you’ll learn what the BODMAS rule is, why it’s important in mathematics, the correct order of operations in BODMAS, and how to apply the BODMAS rule to solve mathematical expressions with many clear examples.

What is the BODMAS Rule?

The BODMAS rule tells us which steps to do first when solving a math problem. Here’s what each letter in BODMAS stands for:

B – Brackets: These are symbols like (), [], and {}. We solve whatever is inside brackets first. Example: In (4 + 2) × 3, we first calculate (4 + 2) = 6, then multiply by 3 to get 18.

O – Orders: These are powers (like 3²), square roots, and indices. Some people call these “indices” in BIDMAS or “exponents” in PEMDAS. Example: In 2³ + 4, we first calculate 2³ = 8, then add 4 to get 12.

D – Division: We divide numbers using the ÷ symbol. Example: In 10 ÷ 2 + 3, we first calculate 10 ÷ 2 = 5, then add 3 to get 8.

M – Multiplication: We multiply numbers using the × symbol. Example: In 4 + 3 × 2, we first calculate 3 × 2 = 6, then add 4 to get 10.

A – Addition: We add numbers using the + symbol. Example: After following the steps above, we perform addition.

S – Subtraction: We subtract numbers using the – symbol. Example: After following the steps above, we perform subtraction.

When we have a mathematical expression with many operators, we follow the BODMAS rule to get the right answer every time.

Why is the BODMAS Rule Important?

The BODMAS rule makes sure everyone gets the same answer. Let’s see what happens without it:

Look at this: 2 + 3 × 4

Without BODMAS: 2 + 3 = 5, then 5 × 4 = 20 With BODMAS: 3 × 4 = 12, then 2 + 12 = 14

The correct answer is 14 because we must do multiplication before addition.

The BODMAS rule is used in:

• School math
• Cooking (when changing recipes)
• Money calculations
• Science experiments
• Computer games and apps

Step-by-Step Application of the BODMAS Rule

Let’s solve some mathematical expressions using the BODMAS rule:

Example 1: 4 + 2 × 3

1. No brackets
2. No orders (exponents/indices)
3. Do multiplication: 2 × 3 = 6
4. Do addition: 4 + 6 = 10 Answer: 10

Example 2: (7 – 3) × 2²

1. Solve brackets: (7 – 3) = 4
2. Solve orders: 2² = 4
3. Do multiplication: 4 × 4 = 16 Answer: 16

Example 3: 12 ÷ 4 × 3

1. No brackets or orders
2. Division and multiplication have the same importance, so work from left to right
3. 12 ÷ 4 = 3
4. 3 × 3 = 9 Answer: 9

Example 4: 20 – 4 × 3 + 2

1. No brackets or orders
2. Do multiplication: 4 × 3 = 12
3. Do addition and subtraction from left to right: 20 – 12 + 2 = 8 + 2 = 10 Answer: 10

Example 5: (8 + 4) ÷ (3 – 1)

1. Solve brackets: (8 + 4) = 12 and (3 – 1) = 2
2. Do division: 12 ÷ 2 = 6 Answer: 6

Example 6: 3² + 4 × (8 – 6)

1. Solve brackets: (8 – 6) = 2
2. Solve orders: 3² = 9
3. Do multiplication: 4 × 2 = 8
4. Do addition: 9 + 8 = 17 Answer: 17

Example 7: 5 + [6 × (4 – 2) – 3]

1. Solve innermost brackets first: (4 – 2) = 2
2. Calculate inside the square brackets: 6 × 2 – 3 = 12 – 3 = 9
3. Do addition: 5 + 9 = 14 Answer: 14

Common Mistakes to Avoid in BODMAS Rule

When using BODMAS, be careful about these mistakes:

1. Forgetting the left-to-right rule: When two operations have the same importance (like division and multiplication), always work from left to right.
2. Forgetting to do brackets first: Always solve what’s inside brackets before anything else.
3. Getting confused with negative numbers: -3² means -(3×3) = -9, not (-3)×(-3) which equals 9.
4. Ignoring multiple types of brackets: When there are many brackets like [3+(4×2)], solve the inner brackets (4×2) first.

Practice Questions Using the BODMAS Rule

Try these arithmetic expressions using the BODMAS rule:

1. 5 + 2 × 4
2. (6 + 3) × 2
3. 8 ÷ 4 + 2
4. 3² + 5 × 2
5. 24 ÷ (3 + 3)
6. 7 – 2 + 5 × 3
7. 4 × [5 + (3 – 1)]
8. 18 ÷ 3 ÷ 2
9. 2³ – 4 × 2
10. (7 – 3)² + 5

Answers with BODMAS explanation:

1. 5 + 2 × 4 = 5 + 8 = 13 (Multiplication before addition)
2. (6 + 3) × 2 = 9 × 2 = 18 (Brackets first, then multiplication)
3. 8 ÷ 4 + 2 = 2 + 2 = 4 (Division before addition)
4. 3² + 5 × 2 = 9 + 10 = 19 (Orders and multiplication before addition)
5. 24 ÷ (3 + 3) = 24 ÷ 6 = 4 (Brackets first, then division)
6. 7 – 2 + 5 × 3 = 7 – 2 + 15 = 5 + 15 = 20 (Multiplication first, then addition and subtraction from left to right)
7. 4 × [5 + (3 – 1)] = 4 × [5 + 2] = 4 × 7 = 28 (Inner brackets first, then outer brackets, then multiplication)
8. 18 ÷ 3 ÷ 2 = 6 ÷ 2 = 3 (Division from left to right)
9. 2³ – 4 × 2 = 8 – 8 = 0 (Orders first, then multiplication, then subtraction)
10. (7 – 3)² + 5 = 4² + 5 = 16 + 5 = 21 (Brackets first, then orders, then addition)

BODMAS and Other Names

The BODMAS rule has different names in different countries:

• PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) is used in the United States.
• BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction) is used in some parts of the UK.

All these rules mean the same thing! They just use different words for the same ideas.

BODMAS History

Who invented the BODMAS rule? No one person created it. The rule grew over many years as math developed. By the early 1900s, everyone agreed to use the same order of operations to avoid confusion.

How Does the BODMAS Rule Work with Different Types of Numbers

The BODMAS rule works with all kinds of numbers:

• Negative numbers: Be careful with signs. -5² means -(5×5) = -25, but (-5)² means (-5)×(-5) = 25. Example: 3 + (-2)² = 3 + 4 = 7 Example: 3 + -2² = 3 + -(2×2) = 3 + -4 = -1
• Fractions: Solve the top and bottom of the fraction separately using BODMAS. Example: (2 + 3) ÷ (8 – 6) = 5 ÷ 2 = 2.5
• Decimals: Treat them just like whole numbers. Example: 1.5 × 2.5 + 0.5 = 3.75 + 0.5 = 4.25
• Mixed operations: Handle complex expressions step by step. Example: √9 + 4 × (10 ÷ 2 – 3) = 3 + 4 × (5 – 3) = 3 + 4 × 2 = 3 + 8 = 11

Solving Equations Without BODMAS

Can you solve math problems without BODMAS? Yes, but it’s harder! You would need to put brackets around everything to show the order. For example:

• Without BODMAS: 2 + 3 × 4 = ?
• With lots of brackets: 2 + (3 × 4) = 2 + 12 = 14

This is why BODMAS is so helpful – it saves time and makes math clearer.

Real-Life Applications of the BODMAS Rule

The BODMAS rule isn’t just for math class. It’s used in many real-life situations:

• Budgeting: Calculating how much money you’ll save or spend Example: If you save $5 per week for 4 weeks, plus a $20 bonus: 5 × 4 + 20 = 20 + 20 = $40
• Cooking: Changing recipe amounts Example: If a recipe needs 2 cups of flour × 1.5 + ¼ cup for dusting = 3 + ¼ = 3¼ cups total
• Building things: Measuring the right amounts of materials Example: If you need 3 tiles for each of 4 rows, plus 2 extra tiles: 3 × 4 + 2 = 12 + 2 = 14 tiles
• Playing games: Many video games use BODMAS for calculating scores Example: If you get 2 points per enemy × 5 enemies + 10 bonus points = 10 + 10 = 20 points
• Science experiments: Getting accurate results Example: If a chemical reaction produces 2 grams per hour × 3 hours + 1 gram initial amount = 6 + 1 = 7 grams total
• Computer programming: All programming languages use order of operations Example: In Python: result = 2 * (3 + 4) would calculate 3 + 4 first, then multiply by 2

Learning Tricks for BODMAS

To remember BODMAS easily, try these tricks:

• Make a sentence: “Big Octopuses Don’t Make Awful Soup”
• Draw a BODMAS ladder with Brackets at the top step
• Use colored cards for each operation
• Sing a BODMAS song
• Make hand signs for each operation

BODMAS Worksheets and Resources

Want more practice? Here are good resources:

• Online tools: Khan Academy, Math-Drills.com, IXL.com
• Free worksheets: PrintableMaths.com, K5Learning.com
• BODMAS games: There are many fun games online that help practice order of operations
• BODMAS apps: Search for “order of operations” in app stores

Logic-based Mathematics Problems Using the BODMAS Rule

Try these fun logic puzzles that test your understanding of the BODMAS rule:

1. What comes first in BODMAS: square roots or division? Answer: Square roots are part of “Orders,” which come before division in BODMAS.
2. Is 8 – 3 + 2 the same as 8 + 2 – 3? Why or why not? Answer: Yes, they’re the same. After handling any brackets, orders, multiplication, and division, we do addition and subtraction from left to right, giving 7 in both cases.
3. Add brackets to make this true: 2 + 3 × 4 – 1 = 15 Answer: 2 + (3 × 4) – 1 = 2 + 12 – 1 = 14 – 1 = 13 (not 15) To make it equal 15: (2 + 3) × (4 – 1) = 5 × 3 = 15
4. Which is larger: 2³ + 1 or 3 × 3? Answer: 2³ + 1 = 8 + 1 = 9, and 3 × 3 = 9. They are equal!
5. Find the missing number: 4 + 2 × ? = 14 Answer: 4 + 2 × ? = 14 2 × ? = 10 ? = 5
6. Make this equation true by adding just one pair of brackets: 6 ÷ 3 × 2 + 4 = 8 Answer: Without brackets: 6 ÷ 3 × 2 + 4 = 2 × 2 + 4 = 4 + 4 = 8 (already true!) With brackets: 6 ÷ (3 × 2) + 4 = 6 ÷ 6 + 4 = 1 + 4 = 5 (now false)
7. Does 4 × 3 – 2 × 3 equal (4 – 2) × 3? Use BODMAS to explain. Answer: 4 × 3 – 2 × 3 = 12 – 6 = 6, and (4 – 2) × 3 = 2 × 3 = 6. Yes, they’re equal!

Clarifications and Misconceptions about the BODMAS Rule

Here are answers to common questions about how to apply the BODMAS rule correctly:

Is division always performed before multiplication in BODMAS? No! Division and multiplication have the same importance in the order of operations. You do them from left to right as they appear in the expression. Example: 10 ÷ 5 × 2 = 2 × 2 = 4 (not 10 ÷ 10 = 1) Example: 10 × 5 ÷ 10 = 50 ÷ 10 = 5 (not 10 × 0.5 = 5)

Does addition come before subtraction in the BODMAS rule? No! Addition and subtraction have the same importance. Do them from left to right as they appear. Example: 10 – 5 + 2 = 5 + 2 = 7 (not 10 – 7 = 3) Example: 10 + 5 – 8 = 15 – 8 = 7 (not 10 + (-3) = 7)

Do you use the BODMAS rule even if there are no brackets in the expression? Yes! Even without brackets, you still follow the rest of the rule (ODMAS). The order of operations always applies. Example: 4 + 3 × 2 = 4 + 6 = 10 (multiplication before addition)

What does “Order” mean in BODMAS (e.g., powers, roots, or indices)? “Order” refers to powers (like squares and cubes), roots (like square roots), and indices. These are all calculated second, after brackets. Example: √16 + 2³ = 4 + 8 = 12 (square root and cube are both “orders”)

What happens if there are multiple types of brackets in an expression? When there are multiple types of brackets, solve the innermost brackets first, then work outwards. Example: 5 × {2 + [3 × (4 – 2)]} = 5 × {2 + [3 × 2]} = 5 × {2 + 6} = 5 × 8 = 40

How does the BODMAS rule handle operations inside brackets? Inside brackets, you apply BODMAS again! It’s like a mini-problem inside the main problem. Example: 3 × (4 + 2 × 3) = 3 × (4 + 6) = 3 × 10 = 30

The BODMAS rule helps everyone get the same answer when solving math problems. Remember:

1. Brackets first
2. Orders (powers and roots) next
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

Practice using BODMAS every day, and soon it will become easy! Mathematical problems will make more sense, and you’ll be more confident in math.

BODMAS Related FAQs

What is BODMAS?

BODMAS is an acronym that represents the order of operations in mathematics, ensuring that mathematical expressions are simplified consistently. It stands for Brackets, Order (powers and roots), Division, Multiplication, Addition, and Subtraction. Following BODMAS is crucial to obtain correct results when dealing with complex mathematical expressions.

How to solve BODMAS questions?

To solve BODMAS questions, follow this order: 1. Brackets first, 2. Order (powers and roots), 3. Division and Multiplication from left to right, 4. Addition and Subtraction from left to right.

What is the role of brackets in BODMAS?

Brackets are the highest priority in the BODMAS rule. You should always start by solving operations within brackets first. If there are nested brackets, work from the innermost brackets outward.

How do I handle powers and square roots (Order) in BODMAS?

After dealing with brackets, you should address powers and square roots. These are also part of the Order category in BODMAS. Powers and roots should be evaluated before division, multiplication, addition, and subtraction.

How do I remember the BODMAS rule easily?

You can remember the BODMAS rule by using a mnemonic or acronym like Please Excuse My Dear Aunt Sally (for PEMDAS) or simply by remembering the sequence: Brackets, Order, Division, Multiplication, Addition, Subtraction.