BODMAS Mastery Challenge

1. Short Answer (2 pts)

Using the BODMAS rule, simplify the expression: 8 + 2 × (5 - 3) Of 2. Provide detailed steps.

✓ Answer

Step 1: Evaluate the bracket: 5 - 3 = 2 Step 2: Compute the Of operation: 2 Of 2 = 2² = 4 Step 3: Multiply: 2 × 4 = 8 Step 4: Add: 8 + 8 = 16

2. Short Answer (2 pts)

Simplify the expression: (4 + 6) Of 2 ÷ 5 - 3. Outline every step clearly.

✓ Answer

Step 1: Evaluate the bracket: 4 + 6 = 10 Step 2: Compute the Of operation: 10 Of 2 = 10² = 100 Step 3: Divide: 100 ÷ 5 = 20 Step 4: Subtract: 20 - 3 = 17

3. Short Answer (2 pts)

Apply the BODMAS rule to simplify: 3 × (10 - 4) Of 2 + 7. Provide a step-by-step explanation.

✓ Answer

Step 1: Compute the bracket: 10 - 4 = 6 Step 2: Compute the Of operation: 6 Of 2 = 6² = 36 Step 3: Multiply: 3 × 36 = 108 Step 4: Add: 108 + 7 = 115

4. Short Answer (2 pts)

Simplify the expression: (12 - 4) Of 2 ÷ (3 + 1) using BODMAS. Show your working.

✓ Answer

Step 1: Evaluate the first bracket: 12 - 4 = 8 Step 2: Evaluate the second bracket: 3 + 1 = 4 Step 3: Apply Of operation: 8 Of 2 = 8² = 64 Step 4: Divide: 64 ÷ 4 = 16

5. Short Answer (2 pts)

Using BODMAS, simplify: 2 + 3 × (8 - 2) Of 2 - 5. Describe each intermediate step.

✓ Answer

Step 1: Evaluate the bracket: 8 - 2 = 6 Step 2: Apply Of operation: 6 Of 2 = 6² = 36 Step 3: Multiply: 3 × 36 = 108 Step 4: Add and subtract: 2 + 108 = 110, then 110 - 5 = 105

6. Short Answer (2 pts)

Simplify: (7 + 3) Of 2 - 4 × (6 - 4) by applying BODMAS. Provide a detailed breakdown.

✓ Answer

Step 1: Evaluate brackets: 7 + 3 = 10 and 6 - 4 = 2 Step 2: Apply Of operation: 10 Of 2 = 10² = 100 Step 3: Multiply: 4 × 2 = 8 Step 4: Subtract: 100 - 8 = 92

7. Short Answer (2 pts)

Simplify the expression: (15 - 5) × (3 + 1) Of 2 using the BODMAS rule. Explain your process.

✓ Answer

Step 1: Compute the brackets: 15 - 5 = 10 and 3 + 1 = 4 Step 2: Apply Of operation on the second bracket: 4 Of 2 = 4² = 16 Step 3: Multiply: 10 × 16 = 160

8. Short Answer (2 pts)

Using BODMAS, simplify: 5 × (9 - 4) Of 2 + 2. Include all intermediate calculations.

✓ Answer

Step 1: Evaluate the bracket: 9 - 4 = 5 Step 2: Apply Of operation: 5 Of 2 = 5² = 25 Step 3: Multiply: 5 × 25 = 125 Step 4: Add: 125 + 2 = 127

9. Short Answer (2 pts)

Simplify the following using the BODMAS rule: (14 ÷ 2) Of 2 + (3 × 2). Provide a clear explanation of each step.

✓ Answer

Step 1: Compute the first bracket: 14 ÷ 2 = 7 Step 2: Apply Of operation: 7 Of 2 = 7² = 49 Step 3: Compute the second bracket: 3 × 2 = 6 Step 4: Add: 49 + 6 = 55

10. Short Answer (2 pts)

Apply BODMAS to simplify: 10 + (6 - 2) Of 2 ÷ 4. Show each step in your solution.

✓ Answer

Step 1: Evaluate the bracket: 6 - 2 = 4 Step 2: Apply Of operation: 4 Of 2 = 4² = 16 Step 3: Divide: 16 ÷ 4 = 4 Step 4: Add: 10 + 4 = 14

11. Short Answer (2 pts)

Simplify: (20 - 10) Of 2 - 3 × (7 - 2) using the BODMAS rule. Detail every computation stage.

✓ Answer

Step 1: Evaluate brackets: 20 - 10 = 10 and 7 - 2 = 5 Step 2: Apply Of operation: 10 Of 2 = 10² = 100 Step 3: Multiply: 3 × 5 = 15 Step 4: Subtract: 100 - 15 = 85

12. Short Answer (2 pts)

Using BODMAS, simplify: 3 + 2 × (12 - 4) Of 2. Provide a complete explanation.

✓ Answer

Step 1: Evaluate the bracket: 12 - 4 = 8 Step 2: Apply Of operation: 8 Of 2 = 8² = 64 Step 3: Multiply: 2 × 64 = 128 Step 4: Add: 3 + 128 = 131

13. Short Answer (2 pts)

Simplify the expression: (18 - 6) Of 2 ÷ 3 + 7 using BODMAS. Explain each step in detail.

✓ Answer

Step 1: Evaluate the bracket: 18 - 6 = 12 Step 2: Apply Of operation: 12 Of 2 = 12² = 144 Step 3: Divide: 144 ÷ 3 = 48 Step 4: Add: 48 + 7 = 55

14. Short Answer (2 pts)

Apply the BODMAS rule to simplify: 4 × [(9 - 3) Of 2 - 5]. Provide a detailed solution.

✓ Answer

Step 1: Evaluate the inner bracket: 9 - 3 = 6 Step 2: Apply Of operation: 6 Of 2 = 6² = 36 Step 3: Subtract: 36 - 5 = 31 Step 4: Multiply: 4 × 31 = 124

15. Short Answer (2 pts)

Simplify the expression: (16 ÷ 2) Of 2 + 3 × (8 - 5) using the BODMAS rule. Give a step-by-step breakdown.

✓ Answer

Step 1: Compute the division: 16 ÷ 2 = 8 Step 2: Apply Of operation: 8 Of 2 = 8² = 64 Step 3: Evaluate the bracket: 8 - 5 = 3 Step 4: Multiply: 3 × 3 = 9 Step 5: Add: 64 + 9 = 73

16. Short Answer (2 pts)

Using the BODMAS rule, simplify: 5 × (7 + 3) Of 2 - 10. Explain each step clearly.

✓ Answer

Step 1: Evaluate the bracket: 7 + 3 = 10 Step 2: Apply Of operation: 10 Of 2 = 10² = 100 Step 3: Multiply: 5 × 100 = 500 Step 4: Subtract: 500 - 10 = 490

17. Short Answer (2 pts)

Simplify: (24 - 8) ÷ 4 Of 2 using BODMAS. Provide the detailed process.

✓ Answer

Step 1: Evaluate the bracket: 24 - 8 = 16 Step 2: Divide by 4: 16 ÷ 4 = 4 Step 3: Apply Of operation: 4 Of 2 = 4² = 16 Note: Alternatively, if the intended operation is to compute (24-8) first then Of 2, then 16 Of 2 = 256 and 256 ÷ 4 = 64. Clarification: Based on BODMAS, Of has higher precedence than division. Therefore, recalculate as: Step 1: 24 - 8 = 16 Step 2: Apply Of operation: 16 Of 2 = 16² = 256 Step 3: Divide: 256 ÷ 4 = 64 Final Answer: 64

18. Short Answer (2 pts)

Simplify the expression: 3 × (14 - 4) Of 2 ÷ 2 + 5 using the BODMAS rule. Explain your steps thoroughly.

✓ Answer

Step 1: Evaluate the bracket: 14 - 4 = 10 Step 2: Apply Of operation: 10 Of 2 = 10² = 100 Step 3: Multiply: 3 × 100 = 300 Step 4: Divide: 300 ÷ 2 = 150 Step 5: Add: 150 + 5 = 155

19. Short Answer (2 pts)

Using BODMAS, simplify: (10 + 2) Of 2 - (18 ÷ 3). Provide a detailed solution.

✓ Answer

Step 1: Evaluate the bracket: 10 + 2 = 12 Step 2: Apply Of operation: 12 Of 2 = 12² = 144 Step 3: Divide: 18 ÷ 3 = 6 Step 4: Subtract: 144 - 6 = 138

20. Short Answer (2 pts)

Simplify the expression: 2 + [(8 - 3) Of 2 × 4] - 7 using the BODMAS rule. Walk through all steps.

✓ Answer

Step 1: Evaluate the inner bracket: 8 - 3 = 5 Step 2: Apply Of operation: 5 Of 2 = 5² = 25 Step 3: Multiply: 25 × 4 = 100 Step 4: Add: 2 + 100 = 102 Step 5: Subtract: 102 - 7 = 95

21. Fill in the Blank (1 pts)

Fill in the blank: In the expression (12-4) Of 2 ÷ 3 + 7, after applying the bracket and Of operations, the intermediate value is _____.

✓ Answer

64

22. Fill in the Blank (1 pts)

Fill in the blank: Simplify (8+2) Of 2 - 3×4. The value of (8+2) Of 2 is _____.

✓ Answer

100

23. Fill in the Blank (1 pts)

Fill in the blank: In the expression 5×(9-4) Of 2 + 2, the term (9-4) Of 2 simplifies to _____.

✓ Answer

25

24. Fill in the Blank (1 pts)

Fill in the blank: For (20-10) Of 2 - 3×(7-2), the computation of (20-10) Of 2 yields _____.

✓ Answer

100

25. Fill in the Blank (1 pts)

Fill in the blank: In the problem 4×[(9-3) Of 2 - 5], the component (9-3) Of 2 evaluates to _____.

✓ Answer

36

26. Fill in the Blank (1 pts)

Fill in the blank: When simplifying (16÷2) Of 2 + 3×(8-5), the (16÷2) Of 2 part computes to _____.

✓ Answer

64

27. Fill in the Blank (1 pts)

Fill in the blank: In (10+2) Of 2 - (18÷3), the intermediate value (10+2) Of 2 is _____.

✓ Answer

144

28. Fill in the Blank (1 pts)

Fill in the blank: For 3×(14-4) Of 2 ÷2 +5, the segment (14-4) Of 2 results in _____.

✓ Answer

100

29. Fill in the Blank (1 pts)

Fill in the blank: In 5×(7+3) Of 2 - 10, the operation (7+3) Of 2 computes to _____.

✓ Answer

100

30. Fill in the Blank (1 pts)

Fill in the blank: In the expression 2+[(8-3) Of 2×4]-7, the result of (8-3) Of 2 is _____.

✓ Answer

25