BODMAS Rule Worksheet - Free Printable

To solve the given problems using the BODMAS rule, we need to follow the order of operations:

BODMAS Rule:
- B: Brackets
- O: Orders (exponents and roots)
- D: Division
- M: Multiplication
- A: Addition
- S: Subtraction

Let's evaluate each expression step by step.

---

1. \( 5 + 3 \times 12 \)

- Step 1: Perform multiplication first.
\[
3 \times 12 = 36
\]
- Step 2: Perform addition.
\[
5 + 36 = 41
\]

Answer: \( \boxed{41} \)

---

2. \( 24 \div 6 + 7^2 \)

- Step 1: Evaluate the exponent.
\[
7^2 = 49
\]
- Step 2: Perform division.
\[
24 \div 6 = 4
\]
- Step 3: Perform addition.
\[
4 + 49 = 53
\]

Answer: \( \boxed{53} \)

---

3. \( 3 \times (27 - 16) \)

- Step 1: Solve the expression inside the brackets.
\[
27 - 16 = 11
\]
- Step 2: Perform multiplication.
\[
3 \times 11 = 33
\]

Answer: \( \boxed{33} \)

---

4. \( 25 - 4 \times (7 + 5) \div 4 + 3 \)

- Step 1: Solve the expression inside the brackets.
\[
7 + 5 = 12
\]
- Step 2: Perform multiplication.
\[
4 \times 12 = 48
\]
- Step 3: Perform division.
\[
48 \div 4 = 12
\]
- Step 4: Perform subtraction and addition from left to right.
\[
25 - 12 + 3 = 13 + 3 = 16
\]

Answer: \( \boxed{16} \)

---

5. \( 64 - 3(13 + 2 \times 12 \div 8 - 3 \times 3) + 11 \)

- Step 1: Solve the innermost expression inside the brackets.
- Perform division and multiplication first:
\[
2 \times 12 \div 8 = 24 \div 8 = 3
\]
\[
3 \times 3 = 9
\]
- Now, perform addition and subtraction inside the brackets:
\[
13 + 3 - 9 = 16 - 9 = 7
\]
- Step 2: Multiply by 3.
\[
3 \times 7 = 21
\]
- Step 3: Perform subtraction and addition outside the brackets.
\[
64 - 21 + 11 = 43 + 11 = 54
\]

Answer: \( \boxed{54} \)

---

6. \( [(45 - 3) \div (3^2 + 5)] \times 2 - 5 \)

- Step 1: Solve the expressions inside the brackets.
- For the numerator:
\[
45 - 3 = 42
\]
- For the denominator:
\[
3^2 = 9
\]
\[
9 + 5 = 14
\]
- Step 2: Perform division.
\[
42 \div 14 = 3
\]
- Step 3: Perform multiplication.
\[
3 \times 2 = 6
\]
- Step 4: Perform subtraction.
\[
6 - 5 = 1
\]

Answer: \( \boxed{1} \)

---

7. \( (2 \times 3^3 \div 9) - 2 \times (6 + 8) \div 7 \)

- Step 1: Solve the exponents.
\[
3^3 = 27
\]
- Step 2: Solve the expressions inside the brackets.
- For the first part:
\[
2 \times 27 \div 9 = 54 \div 9 = 6
\]
- For the second part:
\[
6 + 8 = 14
\]
\[
2 \times 14 \div 7 = 28 \div 7 = 4
\]
- Step 3: Perform subtraction.
\[
6 - 4 = 2
\]

Answer: \( \boxed{2} \)

---

8. \( (120 - 12) \div (36 \div 3) - 22 + 7 \)

- Step 1: Solve the expressions inside the brackets.
- For the numerator:
\[
120 - 12 = 108
\]
- For the denominator:
\[
36 \div 3 = 12
\]
- Step 2: Perform division.
\[
108 \div 12 = 9
\]
- Step 3: Perform subtraction and addition from left to right.
\[
9 - 22 + 7 = -13 + 7 = -6
\]

Answer: \( \boxed{-6} \)

---

9. \( 5 \times 12 \div 10 - (6 \times 4) \div 12 \)

- Step 1: Solve the expressions inside the brackets.
\[
6 \times 4 = 24
\]
- Step 2: Perform multiplication and division from left to right.
\[
5 \times 12 = 60
\]
\[
60 \div 10 = 6
\]
\[
24 \div 12 = 2
\]
- Step 3: Perform subtraction.
\[
6 - 2 = 4
\]

Answer: \( \boxed{4} \)

---

10. \( [96 \div (6^2 - 12) \div 4 - 3] \times 2 + 13 \)

- Step 1: Solve the expression inside the brackets.
- For the exponent:
\[
6^2 = 36
\]
- Perform subtraction:
\[
36 - 12 = 24
\]
- Perform division:
\[
96 \div 24 = 4
\]
\[
4 \div 4 = 1
\]
- Perform subtraction:
\[
1 - 3 = -2
\]
- Step 2: Perform multiplication.
\[
-2 \times 2 = -4
\]
- Step 3: Perform addition.
\[
-4 + 13 = 9
\]

Answer: \( \boxed{9} \)

---

Final Answers:

1. \( \boxed{41} \)
2. \( \boxed{53} \)
3. \( \boxed{33} \)
4. \( \boxed{16} \)
5. \( \boxed{54} \)
6. \( \boxed{1} \)
7. \( \boxed{2} \)
8. \( \boxed{-6} \)
9. \( \boxed{4} \)
10. \( \boxed{9} \)