Solve the following mental maths problems: 1. $sqrt(169) - sqrt(36)$ 2. $2 x 3 x 5$ 3. $10\% of 8000$ 4. $(15 - sqrt(25))2$ 5. $3 x (18 + 27)$ 6. $-19 x 0$ 7. $(60 + 132) / 12$ 8. \(6 x

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Asked on May 4, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-05-04T03:22:07.338Z

Hey Christina, good to see you again. Here are the solutions to the problems: Mental Maths 1. Step 1: Calculate the square roots. sqrt(169) = 13 sqrt(36) = 6 Step 2: Subtract the results. 13 - 6 = 7 2. Step 1: Multiply the numbers. 2 × 3 × 5 = 6 × 5 = 30 3. Step 1: Convert the percentage to a decimal and multiply. 10\% of 8000 = 0.10 × 8000 = 800 4. Step 1: Calculate the square root inside the parentheses. sqrt(25) = 5 Step 2: Perform the subtraction inside the parentheses. (15 - 5)^2 = (10)^2 Step 3: Square the result. (10)^2 = 100 5. Step 1: Perform the addition inside the parentheses. (18 + 27) = 45 Step 2: Multiply the result by 3. 45 × 3 = 135 6. Step 1: Any number multiplied by zero is zero. -19 × 0 = 0 7. Step 1: Perform the addition inside the parentheses. (60 + 132) = 192 Step 2: Divide the result by 12. 192 ÷ 12 = 16 8. Step 1: Perform the multiplication first (order of operations). 6 × 10 = 60 Step 2: Add 1 to the result. 60 + 1 = 61 9. Step 1: Perform the multiplication first (order of operations). 0 × 5 = 0 Step 2: Perform the subtractions from left to right. 84 - 0 - 13 = 84 - 13 = 71 10. Step 1: Perform the addition inside the parentheses. (20 + 25) = 45 Step 2: Divide the result by 5. 45 ÷ 5 = 9 Classwork 1. Use commutative property to prove the following: The commutative property of addition states that for any two numbers a and b, a + b = b + a. a) 3 + (-7) = (-7) + 3 Step 1: Evaluate the Left Hand Side (LHS). 3 + (-7) = 3 - 7 = -4 Step 2: Evaluate the Right Hand Side (RHS). (-7) + 3 = -4 Step 3: Compare LHS and RHS. Since -4 = -4, the statement is proven. b) (-9) + (-6) + 12 = 12 + (-6) + (-9) Step 1: Evaluate the LHS. (-9) + (-6) + 12 = -9 - 6 + 12 = -15 + 12 = -3 Step 2: Evaluate the RHS. 12 + (-6) + (-9) = 12 - 6 - 9 = 6 - 9 = -3 Step 3: Compare LHS and RHS. Since -3 = -3, the statement is proven. c) 21 - (+5) + (-8) = 21 - (-8) + (+5) The commutative property applies to addition. Let's rewrite the terms as additions: LHS: 21 + (-5) + (-8) RHS: 21 + 8 + 5 Step 1: Evaluate the LHS. 21 - (+5) + (-8) = 21 - 5 - 8 = 16 - 8 = 8 Step 2: Evaluate the RHS. 21 - (-8) + (+5) = 21 + 8 + 5 = 29 + 5 = 34 Step 3: Compare LHS and RHS. Since 8 ≠ 34, the given statement is incorrect as written. However, if the intention was to show the commutative property for addition, it would be: 21 + (-5) + (-8) = 21 + (-8) + (-5) Let's verify this correct application of the commutative property: LHS: 21 + (-5) + (-8) = 21 - 5 - 8 = 8 RHS: $21 + (-8) + (-5) = 21 - 8 - 5

Accepted Answer · 2026-05-04T03:22:07.338Z

Hey Christina, good to see you again. Here are the solutions to the problems: Mental Maths 1. Step 1: Calculate the square roots. sqrt(169) = 13 sqrt(36) = 6 Step 2: Subtract the results. 13 - 6 = 7 2. Step 1: Multiply the numbers. 2 × 3 × 5 = 6 × 5 = 30 3. Step 1: Convert the percentage to a decimal and multiply. 10\% of 8000 = 0.10 × 8000 = 800 4. Step 1: Calculate the square root inside the parentheses. sqrt(25) = 5 Step 2: Perform the subtraction inside the parentheses. (15 - 5)^2 = (10)^2 Step 3: Square the result. (10)^2 = 100 5. Step 1: Perform the addition inside the parentheses. (18 + 27) = 45 Step 2: Multiply the result by 3. 45 × 3 = 135 6. Step 1: Any number multiplied by zero is zero. -19 × 0 = 0 7. Step 1: Perform the addition inside the parentheses. (60 + 132) = 192 Step 2: Divide the result by 12. 192 ÷ 12 = 16 8. Step 1: Perform the multiplication first (order of operations). 6 × 10 = 60 Step 2: Add 1 to the result. 60 + 1 = 61 9. Step 1: Perform the multiplication first (order of operations). 0 × 5 = 0 Step 2: Perform the subtractions from left to right. 84 - 0 - 13 = 84 - 13 = 71 10. Step 1: Perform the addition inside the parentheses. (20 + 25) = 45 Step 2: Divide the result by 5. 45 ÷ 5 = 9 Classwork 1. Use commutative property to prove the following: The commutative property of addition states that for any two numbers a and b, a + b = b + a. a) 3 + (-7) = (-7) + 3 Step 1: Evaluate the Left Hand Side (LHS). 3 + (-7) = 3 - 7 = -4 Step 2: Evaluate the Right Hand Side (RHS). (-7) + 3 = -4 Step 3: Compare LHS and RHS. Since -4 = -4, the statement is proven. b) (-9) + (-6) + 12 = 12 + (-6) + (-9) Step 1: Evaluate the LHS. (-9) + (-6) + 12 = -9 - 6 + 12 = -15 + 12 = -3 Step 2: Evaluate the RHS. 12 + (-6) + (-9) = 12 - 6 - 9 = 6 - 9 = -3 Step 3: Compare LHS and RHS. Since -3 = -3, the statement is proven. c) 21 - (+5) + (-8) = 21 - (-8) + (+5) The commutative property applies to addition. Let's rewrite the terms as additions: LHS: 21 + (-5) + (-8) RHS: 21 + 8 + 5 Step 1: Evaluate the LHS. 21 - (+5) + (-8) = 21 - 5 - 8 = 16 - 8 = 8 Step 2: Evaluate the RHS. 21 - (-8) + (+5) = 21 + 8 + 5 = 29 + 5 = 34 Step 3: Compare LHS and RHS. Since 8 ≠ 34, the given statement is incorrect as written. However, if the intention was to show the commutative property for addition, it would be: 21 + (-5) + (-8) = 21 + (-8) + (-5) Let's verify this correct application of the commutative property: LHS: 21 + (-5) + (-8) = 21 - 5 - 8 = 8 RHS: $21 + (-8) + (-5) = 21 - 8 - 5

Solve the following mental maths problems: 1. \(sqrt(169) - sqrt(36)\) 2. \(2 x 3 x 5\) 3. \(10\% of 8000\) 4. \((15 - sqrt(25))2\) 5. \(3 x (18 + 27)\) 6. \(-19 x 0\) 7. \((60 + 132) / 12\) 8. \(6 x

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Solve the following mental maths problems: 1. \(sqrt(169) - sqrt(36)\) 2. \(2 x 3 x 5\) 3. \(10\% of 8000\) 4. \((15 - sqrt(25))2\) 5. \(3 x (18 + 27)\) 6. \(-19 x 0\) 7. \((60 + 132) / 12\) 8. \(6 x

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