Question 1

Calculate: 60 ÷ 5 × 2 + 10 − 8

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 60 ÷ 5 = 12, then 12 × 2 = 24. Step 2: Now we have 24 + 10 − 8. Step 3: Addition and Subtraction (left to right): 24 + 10 = 34, then 34 − 8 = 26.

Question 2

Simplify: 2 + 8 × 5 − 12 ÷ 3

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 8 × 5 = 40 and 12 ÷ 3 = 4. Step 2: Now we have 2 + 40 − 4. Step 3: Addition and Subtraction (left to right): 2 + 40 = 42, then 42 − 4 = 38.

Question 3

How many numbers between 100 and 200 are divisible by 7?

Accepted Answer

Step 1: Find the smallest multiple of 7 ≥ 100: 100 ÷ 7 = 14.28..., so first multiple is 7 × 15 = 105. Step 2: Find the largest multiple of 7 ≤ 200: 200 ÷ 7 = 28.57..., so last multiple is 7 × 28 = 196. Step 3: Count multiples from 7 × 15 to 7 × 28: 28 - 15 + 1 = 14. Therefore, there are 14 numbers.

Question 4

A number when divided by 8 leaves remainder 0. Which statement is definitely true about this number?

Accepted Answer

Step 1: If a number is divisible by 8 (remainder 0), then it is also divisible by all factors of 8. Step 2: Factors of 8 are: 1, 2, 4, 8. Step 3: Therefore, the number must be divisible by 4. Step 4: Check: any multiple of 8 (e.g., 16, 24, 32) is also a multiple of 4.

Question 5

Which of the following numbers is divisible by 11?

Accepted Answer

Step 1: Apply divisibility rule for 11: alternating sum of digits (starting from right) must be divisible by 11. Step 2: For 5742: (2 - 4 + 7 - 5) = 0, which is divisible by 11. Step 3: Verify: 5742 ÷ 11 = 522. Therefore, 5742 is divisible by 11.

Question 6

A number is divisible by both 4 and 6. Which of the following must also divide this number?

Accepted Answer

Step 1: A number divisible by both 4 and 6 must be divisible by their LCM. Step 2: Find LCM(4, 6): 4 = 2², 6 = 2 × 3, so LCM = 2² × 3 = 12. Step 3: Any number divisible by 12 is also divisible by 12 itself, as well as all its factors (1, 2, 3, 4, 6, 12). Therefore, the answer is 12.

Question 7

Find the value of 50 − 30 ÷ 6 + 4 × 3

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 30 ÷ 6 = 5 and 4 × 3 = 12. Step 2: Now we have 50 − 5 + 12. Step 3: Subtraction and Addition (left to right): 50 − 5 = 45, then 45 + 12 = 57.

Question 8

Simplify: 48 ÷ 6 + 12 × 2 − 5

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 48 ÷ 6 = 8 and 12 × 2 = 24. Step 2: Now we have 8 + 24 − 5. Step 3: Addition and Subtraction (left to right): 8 + 24 = 32, then 32 − 5 = 27.

Question 9

Evaluate: 100 − 20 × 3 + 15 ÷ 5

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 20 × 3 = 60 and 15 ÷ 5 = 3. Step 2: Now we have 100 − 60 + 3. Step 3: Subtraction and Addition (left to right): 100 − 60 = 40, then 40 + 3 = 43.

Question 10

What is the value of 36 + 12 ÷ 4 − 3 × 2?

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 12 ÷ 4 = 3 and 3 × 2 = 6. Step 2: Now we have 36 + 3 − 6. Step 3: Addition and Subtraction (left to right): 36 + 3 = 39, then 39 − 6 = 33.

Question 11

Evaluate: 50 − 5 × 6 + 20 ÷ 4 − 3

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 5 × 6 = 30 and 20 ÷ 4 = 5. Step 2: Rewrite as 50 − 30 + 5 − 3. Step 3: Subtraction and Addition (left to right): 50 − 30 = 20, then 20 + 5 = 25, then 25 − 3 = 22. Therefore, answer is 22.

Question 12

Calculate: 36 ÷ 6 × 2 + 10 − 4 × 2

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 36 ÷ 6 = 6, then 6 × 2 = 12. Also, 4 × 2 = 8. Step 2: Rewrite as 12 + 10 − 8. Step 3: Addition and Subtraction (left to right): 12 + 10 = 22, then 22 − 8 = 14. Therefore, answer is 14.

Question 13

Simplify: 144 ÷ 12 + 8 × 3 − 5 + 2

Accepted Answer

Step 1: Apply BODMAS — Division and Multiplication first (left to right). 144 ÷ 12 = 12 and 8 × 3 = 24. Step 2: Rewrite as 12 + 24 − 5 + 2. Step 3: Addition and Subtraction (left to right): 12 + 24 = 36, then 36 − 5 = 31, then 31 + 2 = 33. Therefore, answer is 33.

Question 14

Evaluate: 5 + 3 × 4 − 2 ÷ 2 + 6

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 3 × 4 = 12 and 2 ÷ 2 = 1. Step 2: Rewrite as 5 + 12 − 1 + 6. Step 3: Addition and Subtraction (left to right): 5 + 12 = 17, then 17 − 1 = 16, then 16 + 6 = 22. Therefore, answer is 22.

Question 15

What is the value of 100 − 20 × 3 + 15 ÷ 3?

Accepted Answer

Step 1: Apply BODMAS — Multiplication and Division first (left to right). 20 × 3 = 60 and 15 ÷ 3 = 5. Step 2: Rewrite as 100 − 60 + 5. Step 3: Subtraction and Addition (left to right): 100 − 60 = 40, then 40 + 5 = 45. Therefore, answer is 45.

Question 16

Simplify: 2 × (15 + 5) − 8 ÷ 4 + 3

Accepted Answer

Step 1: Apply BODMAS — Brackets first. 15 + 5 = 20. Step 2: Rewrite as 2 × 20 − 8 ÷ 4 + 3. Step 3: Multiplication and Division (left to right): 2 × 20 = 40 and 8 ÷ 4 = 2. Step 4: Rewrite as 40 − 2 + 3. Step 5: Subtraction and Addition (left to right): 40 − 2 = 38, then 38 + 3 = 41. Therefore, answer is 41.

Question 17

Calculate: 100 ÷ 5 × 2 + 30 − 8 × 3 + 12 ÷ 4

Accepted Answer

Step 1: No brackets. Step 2: Apply division and multiplication left to right: 100 ÷ 5 = 20, then 20 × 2 = 40; 8 × 3 = 24; 12 ÷ 4 = 3. Step 3: Rewrite: 40 + 30 − 24 + 3. Step 4: Perform addition and subtraction left to right: 40 + 30 = 70, then 70 − 24 = 46, then 46 + 3 = 49. Therefore, answer is 49.

Question 18

Solve: 72 ÷ 8 + 9 × 4 − 15 + 6 × 3 ÷ 2

Accepted Answer

Step 1: No brackets. Step 2: Apply division and multiplication left to right: 72 ÷ 8 = 9; 9 × 4 = 36; 6 × 3 = 18, then 18 ÷ 2 = 9. Step 3: Rewrite: 9 + 36 − 15 + 9. Step 4: Perform addition and subtraction left to right: 9 + 36 = 45, then 45 − 15 = 30, then 30 + 9 = 39. Therefore, answer is 39.

Question 19

Simplify: 5 × 8 − 12 ÷ 3 + 7 × 2 − 10 + 6 ÷ 2

Accepted Answer

Step 1: No brackets. Step 2: Apply multiplication and division left to right: 5 × 8 = 40, 12 ÷ 3 = 4, 7 × 2 = 14, 6 ÷ 2 = 3. Step 3: Rewrite: 40 − 4 + 14 − 10 + 3. Step 4: Perform addition and subtraction left to right: 40 − 4 = 36, then 36 + 14 = 50, then 50 − 10 = 40, then 40 + 3 = 43. Therefore, answer is 43.

Question 20

Evaluate: 18 + 6 ÷ 2 × 3 − 4 + 5 × 2

Accepted Answer

Step 1: No brackets present. Step 2: Apply division and multiplication left to right: 6 ÷ 2 = 3, then 3 × 3 = 9, and 5 × 2 = 10. Step 3: Rewrite: 18 + 9 − 4 + 10. Step 4: Perform addition and subtraction left to right: 18 + 9 = 27, then 27 − 4 = 23, then 23 + 10 = 33. Therefore, answer is 33.

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