Question 1

Simplify: (144 ÷ 12) × 5 + 18 ÷ 3 − 8

Accepted Answer

Step 1: Solve division and multiplication from left to right: 144 ÷ 12 = 12. Step 2: 12 × 5 = 60. Step 3: 18 ÷ 3 = 6. Step 4: Now solve addition and subtraction from left to right: 60 + 6 = 66. Step 5: 66 − 8 = 58. Therefore, the answer is 58.

Question 2

What is the value of √256 + √144 − √100?

Accepted Answer

Step 1: Calculate √256 = 16 (since 16 × 16 = 256). Step 2: Calculate √144 = 12 (since 12 × 12 = 144). Step 3: Calculate √100 = 10 (since 10 × 10 = 100). Step 4: Now compute 16 + 12 − 10 = 28 − 10 = 18. Therefore, the answer is 18.

Question 3

Simplify: (7² − 5²) ÷ (7 + 5)

Accepted Answer

Step 1: Calculate 7² = 49. Step 2: Calculate 5² = 25. Step 3: Subtract: 49 − 25 = 24. Step 4: Calculate denominator: 7 + 5 = 12. Step 5: Divide: 24 ÷ 12 = 2. Therefore, the answer is 2. [Note: This uses the difference of squares formula: a² − b² = (a + b)(a − b), so (49 − 25)/(7 + 5) = (7 − 5)(7 + 5)/(7 + 5) = 7 − 5 = 2]

Question 4

If 3/5 of a number is 45, what is the number?

Accepted Answer

Step 1: Let the number be x. Step 2: Set up equation: (3/5) × x = 45. Step 3: Multiply both sides by 5/3: x = 45 × (5/3). Step 4: Calculate: x = (45 × 5) ÷ 3 = 225 ÷ 3 = 75. Therefore, the answer is 75.

Question 5

What is the value of √256 + ∛27 − √100?

Accepted Answer

Step 1: Calculate √256 = 16 (since 16 × 16 = 256). Step 2: Calculate ∛27 = 3 (since 3 × 3 × 3 = 27). Step 3: Calculate √100 = 10 (since 10 × 10 = 100). Step 4: Combine: 16 + 3 − 10 = 9. Therefore, the answer is 9.

Question 6

Simplify: (8 × 9) ÷ (6 ÷ 2) + 5

Accepted Answer

Step 1: Solve the numerator: 8 × 9 = 72. Step 2: Solve the denominator: 6 ÷ 2 = 3. Step 3: Divide: 72 ÷ 3 = 24. Step 4: Add 5: 24 + 5 = 29. Therefore, the answer is 29.

Question 7

Simplify: (144 ÷ 12) × 5 + 36 ÷ 6 − 8

Accepted Answer

Step 1: Solve division first: 144 ÷ 12 = 12 and 36 ÷ 6 = 6. Step 2: Substitute: 12 × 5 + 6 − 8. Step 3: Multiply: 12 × 5 = 60. Step 4: Add and subtract left to right: 60 + 6 = 66, then 66 − 8 = 58. Therefore, the answer is 58.

Question 8

Simplify: (8 × 15) ÷ (6 × 4) + 12

Accepted Answer

Step 1: Calculate numerator: 8 × 15 = 120. Step 2: Calculate denominator: 6 × 4 = 24. Step 3: Divide: 120 ÷ 24 = 5. Step 4: Add: 5 + 12 = 17. Therefore, the answer is 17.

Question 9

Simplify: 1248 ÷ 26 × 4 – 120 + 35

Accepted Answer

Step 1: Perform division first: 1248 ÷ 26 = 48. Step 2: Multiply: 48 × 4 = 192. Step 3: Subtract: 192 – 120 = 72. Step 4: Add: 72 + 35 = 107. Therefore, the answer is 107.

Question 10

What is 25% of 320?

Accepted Answer

Step 1: Convert percentage to decimal: 25% = 25/100 = 0.25. Step 2: Multiply: 0.25 × 320 = 80. Alternatively, 25% = 1/4, so 320 ÷ 4 = 80. Therefore, the answer is 80.

Question 11

If 40% of a number is 96, what is 65% of that number?

Accepted Answer

Step 1: Let the number be x. Then 0.40x = 96. Step 2: Solve for x: x = 96 ÷ 0.40 = 240. Step 3: Find 65% of 240: 0.65 × 240 = 156.

Question 12

If 40% of a number is 240, what is 65% of that number?

Accepted Answer

Step 1: Let the number be x. Given: 40% of x = 240. Step 2: 0.40 × x = 240, so x = 240 ÷ 0.40 = 600. Step 3: Find 65% of 600: 0.65 × 600 = 390. Therefore, the answer is 390.

Question 13

Simplify: [48 ÷ 6 + 12 × 2 - (18 - 6)] ÷ 5

Accepted Answer

Step 1: Solve the bracket first: (18 - 6) = 12. Step 2: Expression becomes: [48 ÷ 6 + 12 × 2 - 12] ÷ 5. Step 3: Perform division and multiplication left to right: 48 ÷ 6 = 8 and 12 × 2 = 24. Step 4: Expression becomes: [8 + 24 - 12] ÷ 5. Step 5: Solve inside bracket: 8 + 24 - 12 = 20. Step 6: Final division: 20 ÷ 5 = 4. Therefore, the answer is 4.

Question 14

A number when divided by 12 gives a quotient of 18 and a remainder of 7. What is the number?

Accepted Answer

Step 1: Use the division algorithm: Dividend = (Divisor × Quotient) + Remainder. Step 2: Substitute values: Number = (12 × 18) + 7 = 216 + 7 = 223.

Question 15

A number when divided by 8 gives quotient 15 and remainder 3. What is the number?

Accepted Answer

Step 1: Use the division algorithm: Dividend = Divisor × Quotient + Remainder. Step 2: Number = 8 × 15 + 3. Step 3: Number = 120 + 3 = 123. Therefore, the answer is 123.

Question 16

Simplify: √(1296) + ∛(1728) − ⁴√(256) + (0.5)⁻² − 2³

Accepted Answer

Step 1: √(1296) = 36 (since 36² = 1296). Step 2: ∛(1728) = 12 (since 12³ = 1728). Step 3: ⁴√(256) = 4 (since 4⁴ = 256). Step 4: (0.5)⁻² = (2)² = 4 (reciprocal and square). Step 5: 2³ = 8. Step 6: Combine: 36 + 12 − 4 + 4 − 8 = 40. Therefore, answer is 40.

Question 17

Simplify: [∛(1728) + ∛(512)] ÷ [∛(343) - ∛(125)] × ∛(64)

Accepted Answer

Step 1: Calculate cube roots: ∛1728 = 12 (since 12³=1728), ∛512 = 8 (since 8³=512), ∛343 = 7 (since 7³=343), ∛125 = 5 (since 5³=125), ∛64 = 4 (since 4³=64). Step 2: Substitute: [12 + 8] ÷ [7 - 5] × 4 = 20 ÷ 2 × 4. Step 3: Following left-to-right order: 20 ÷ 2 = 10. Step 4: 10 × 4 = 40.

Question 18

Simplify: [(2⁴ × 3³) ÷ (2² × 3)] × (2 × 3²) ÷ (2³ × 3)

Accepted Answer

Step 1: Simplify (2⁴ × 3³) ÷ (2² × 3) = 2^(4-2) × 3^(3-1) = 2² × 3² = 4 × 9 = 36. Step 2: Multiply by (2 × 3²) = 2 × 9 = 18. So 36 × 18 = 648. Step 3: Divide by (2³ × 3) = 8 × 3 = 24. So 648 ÷ 24 = 27.

Question 19

Simplify: (144 ÷ 12 + 8) × (15 - 3 × 2) ÷ (20 - 5 × 3)

Accepted Answer

Step 1: Solve the first bracket using BODMAS: 144 ÷ 12 = 12, then 12 + 8 = 20. Step 2: Solve the second bracket: 3 × 2 = 6, then 15 - 6 = 9. Step 3: Solve the third bracket: 5 × 3 = 15, then 20 - 15 = 5. Step 4: Now compute: 20 × 9 ÷ 5. Step 5: 20 × 9 = 180. Step 6: 180 ÷ 5 = 36.

Question 20

If (2⁵ × 3⁴ × 5²) ÷ (2³ × 3² × 5) = 2^a × 3^b × 5^c, then find the value of (a + b + c).

Accepted Answer

Step 1: Apply exponent division rule: when dividing powers with same base, subtract exponents. Step 2: For base 2: 2⁵ ÷ 2³ = 2^(5-3) = 2². So a = 2. Step 3: For base 3: 3⁴ ÷ 3² = 3^(4-2) = 3². So b = 2. Step 4: For base 5: 5² ÷ 5¹ = 5^(2-1) = 5¹. So c = 1. Step 5: a + b + c = 2 + 2 + 1 = 5.

Question 21

If 40% of a number is 240, and 60% of another number is 360, then what is the ratio of the first number to the second number?

Accepted Answer

Step 1: Find the first number. If 40% of x = 240, then x = 240 ÷ 0.40 = 600. Step 2: Find the second number. If 60% of y = 360, then y = 360 ÷ 0.60 = 600. Step 3: Ratio of first to second = 600 : 600 = 1 : 1.

Question 22

Simplify: (√625 × ∛216) ÷ (√144 + √169) + 5²

Accepted Answer

Step 1: Calculate √625 = 25, ∛216 = 6, √144 = 12, √169 = 13. Step 2: Numerator = 25 × 6 = 150. Step 3: Denominator = 12 + 13 = 25. Step 4: 150 ÷ 25 = 6. Step 5: 6 + 5² = 6 + 25 = 31.

Question 23

Simplify: (144 ÷ 12) × 5 + 18 ÷ 3 − 8

Accepted Answer

Step 1: Solve division and multiplication from left to right: 144 ÷ 12 = 12. Step 2: 12 × 5 = 60. Step 3: 18 ÷ 3 = 6. Step 4: Now we have 60 + 6 − 8. Step 5: 60 + 6 = 66. Step 6: 66 − 8 = 58. Therefore, the answer is 58.

Question 24

Simplify: 1296 ÷ 36 × 4 + 125 − 78

Accepted Answer

Step 1: Follow BODMAS — Division first: 1296 ÷ 36 = 36. Step 2: Multiplication: 36 × 4 = 144. Step 3: Addition: 144 + 125 = 269. Step 4: Subtraction: 269 − 78 = 191. Therefore, the answer is 191.

Question 25

Simplify: (144 ÷ 12) × 5 + 18 − 6 ÷ 2

Accepted Answer

Step 1: Solve division first: 144 ÷ 12 = 12 and 6 ÷ 2 = 3. Step 2: Expression becomes 12 × 5 + 18 − 3. Step 3: Multiply: 12 × 5 = 60. Step 4: Add and subtract left to right: 60 + 18 − 3 = 75. Therefore, the answer is 75.

Question 26

Simplify: (25 × 4) ÷ (100 ÷ 10) + 6

Accepted Answer

Step 1: Solve the first bracket: 25 × 4 = 100. Step 2: Solve the second bracket: 100 ÷ 10 = 10. Step 3: Divide: 100 ÷ 10 = 10. Step 4: Add: 10 + 6 = 16. Therefore, the answer is 16.

Question 27

Simplify: (144 ÷ 12) × 5 + 18 ÷ 3 − 4

Accepted Answer

Step 1: Solve division and multiplication from left to right: 144 ÷ 12 = 12. Step 2: 12 × 5 = 60. Step 3: 18 ÷ 3 = 6. Step 4: Now we have 60 + 6 − 4. Step 5: 60 + 6 = 66. Step 6: 66 − 4 = 62. Therefore, the answer is 62.

Question 28

What is the value of √256 + √144 − √100?

Accepted Answer

Step 1: Calculate √256 = 16. Step 2: Calculate √144 = 12. Step 3: Calculate √100 = 10. Step 4: Now compute 16 + 12 − 10. Step 5: 16 + 12 = 28. Step 6: 28 − 10 = 18. Therefore, the answer is 18.

Question 29

What is 40% of 250?

Accepted Answer

Step 1: Convert 40% to decimal form: 40% = 40/100 = 0.4. Step 2: Multiply 0.4 by 250: 0.4 × 250 = 100. Therefore, 40% of 250 is 100.

Question 30

If 15 × 8 ÷ 4 + 12 = ?, what is the answer?

Accepted Answer

Step 1: Perform multiplication and division from left to right: 15 × 8 = 120. Step 2: 120 ÷ 4 = 30. Step 3: Add: 30 + 12 = 42. Therefore, the answer is 42.

Question 31

Simplify: 3² + 4² − 5

Accepted Answer

Step 1: Calculate 3² = 9. Step 2: Calculate 4² = 16. Step 3: Add: 9 + 16 = 25. Step 4: Subtract: 25 − 5 = 20. Therefore, the answer is 20.

Question 32

Simplify: (8 + 2) × 3 ÷ 2 + 5

Accepted Answer

Step 1: Solve the bracket first: 8 + 2 = 10. Step 2: Multiply: 10 × 3 = 30. Step 3: Divide: 30 ÷ 2 = 15. Step 4: Add: 15 + 5 = 20. Therefore, the answer is 20.

Question 33

If the ratio of two numbers is 7:5 and their difference is 18, what is the larger number?

Accepted Answer

Step 1: Let the two numbers be 7x and 5x (maintaining the ratio 7:5). Step 2: Their difference is 7x - 5x = 2x. Step 3: Given that the difference is 18: 2x = 18, so x = 9. Step 4: The larger number is 7x = 7 × 9 = 63. Therefore, the answer is 63.

Question 34

Simplify: (√625 + √441) × (√256 - √169) ÷ (√144 + √121)

Accepted Answer

Step 1: Evaluate each square root: √625 = 25, √441 = 21, √256 = 16, √169 = 13, √144 = 12, √121 = 11. Step 2: Substitute into the expression: (25 + 21) × (16 - 13) ÷ (12 + 11). Step 3: Simplify the brackets: 46 × 3 ÷ 23. Step 4: Calculate: 138 ÷ 23 = 6. Therefore, the answer is 6.

Question 35

Simplify: (2⁵ × 3⁴) ÷ (2³ × 3²) + 12 = ?

Accepted Answer

Step 1: Apply exponent division rules: 2⁵⁻³ × 3⁴⁻² = 2² × 3² = 4 × 9 = 36. Step 2: Add 12: 36 + 12 = 48.

Question 36

If 40% of a number is 96, what is 65% of that number?

Accepted Answer

Step 1: Let the number be x. Given: 40% of x = 96, so 0.40x = 96. Step 2: Solve for x: x = 96 ÷ 0.40 = 240. Step 3: Find 65% of 240: 0.65 × 240 = 156. Therefore, the answer is 156.

Question 37

Simplify: (√625 × ∛216 + 144 ÷ 12) / (5² - 3²)

Accepted Answer

Step 1: √625 = 25, ∛216 = 6, so √625 × ∛216 = 25 × 6 = 150. Step 2: 144 ÷ 12 = 12. Step 3: Numerator = 150 + 12 = 162. Step 4: 5² - 3² = 25 - 9 = 16. Step 5: 162 ÷ 16 = 10.125 = 81/8.

Question 38

Approximate: (√1024 + ∜256) × (7³ - 6³) / (2⁵ + 2⁴)

Accepted Answer

Step 1: √1024 = 32, ∜256 = 4, so √1024 + ∜256 = 36. Step 2: 7³ = 343, 6³ = 216, so 7³ - 6³ = 127. Step 3: 2⁵ = 32, 2⁴ = 16, so 2⁵ + 2⁴ = 48. Step 4: (36 × 127) / 48 = 4572 / 48 = 95.25.

Question 39

Simplify: (5⁴ - 5³) × (3³ + 3²) ÷ (4² × 5) = ?

Accepted Answer

Step 1: 5⁴ - 5³ = 625 - 125 = 500. Step 2: 3³ + 3² = 27 + 9 = 36. Step 3: 500 × 36 = 18,000. Step 4: 4² × 5 = 16 × 5 = 80. Step 5: 18,000 ÷ 80 = 225.

Question 40

Simplify: [√(144 + 25) × √(100 - 36)] ÷ √(49 + 15) = ?

Accepted Answer

Step 1: 144 + 25 = 169, so √169 = 13. Step 2: 100 - 36 = 64, so √64 = 8. Step 3: 13 × 8 = 104. Step 4: 49 + 15 = 64, so √64 = 8. Step 5: 104 ÷ 8 = 13.

Question 41

If (3⁵ - 3⁴) × (2⁶ ÷ 2⁴) = k, then what is the value of k ÷ 12?

Accepted Answer

Step 1: 3⁵ - 3⁴ = 243 - 81 = 162. Step 2: 2⁶ ÷ 2⁴ = 64 ÷ 16 = 4. Step 3: k = 162 × 4 = 648. Step 4: k ÷ 12 = 648 ÷ 12 = 54.

Question 42

Simplify: (√625 × ∛216 − 24) ÷ (√144 − 2) + 15% of 80

Accepted Answer

Step 1: Evaluate √625 = 25. Step 2: Evaluate ∛216 = 6. Step 3: Calculate 25 × 6 = 150. Step 4: Subtract: 150 − 24 = 126. Step 5: Evaluate √144 = 12. Step 6: Subtract: 12 − 2 = 10. Step 7: Divide: 126 ÷ 10 = 12.6. Step 8: Calculate 15% of 80 = 0.15 × 80 = 12. Step 9: Add: 12.6 + 12 = 24.6. Therefore, the answer is 24.6.

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Simplification & Approximation — Practice Questions

60-Second Revision — Simplification & Approximation