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.
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Here are the solutions to your questions: 3. INTEGERS 3.1 Calculate the following and show all the steps: -23 - (-18) Step 1: Simplify the double negative. -23 - (-18) = -23 + 18 Step 2: Perform the addition. = -5 The result is -5. 3.2 2(8-3+4) Step 1: Perform the operations inside the parenthesis. 2(8-3+4) = 2(5+4) = 2(9) Step 2: Perform the multiplication. = 18 The result is 18. 3.3 3^3 + 4^2 - 5^2 Step 1: Calculate the powers. 3^3 = 27 4^2 = 16 5^2 = 25 Step 2: Substitute the values back into the expression. 27 + 16 - 25 Step 3: Perform addition and subtraction from left to right. 43 - 25 = 18 The result is 18. 3.4 sqrt(9) + 16 + 7 Step 1: Calculate the square root. sqrt(9) = 3 Step 2: Perform the additions from left to right. 3 + 16 + 7 = 19 + 7 = 26 The result is 26. 3.5 (-6+3(-4)-3(4))/((2+3)(-3)) Step 1: Calculate the numerator. -6 + 3(-4) - 3(4) = -6 - 12 - 12 = -30 Step 2: Calculate the denominator. (2+3)(-3) = (5)(-3) = -15 Step 3: Divide the numerator by the denominator. (-30)/(-15) = 2 The result is 2. 4. COMMON FRACTIONS 4.1 Calculate: 10 ÷ (5)/(8) Step 1: Convert division to multiplication by the reciprocal of the fraction. 10 ÷ (5)/(8) = 10 × (8)/(5) Step 2: Multiply the numbers. = (10 × 8)/(5) = (80)/(5) Step 3: Simplify the fraction. = 16 The result is 16. 4.2 Simplify: sqrt((25)/(49)) Step 1: Take the square root of the numerator and the denominator separately. sqrt((25)/(49)) = sqrt(25)sqrt(49) Step 2: Calculate the square roots. = (5)/(7) The simplified expression is (5)/(7). 4.3 Simplify: 3/(27) + ((1)/(2))^2 Step 1: Calculate the cube root of the first term. 3/(27) = [3]8[3]27 = (2)/(3) Step 2: Calculate the square of the second term. ((1)/(2))^2 = (1^2)/(2^2) = (1)/(4) Step 3: Add the two fractions. Find a common denominator, which is 12. (2)/(3) + (1)/(4) = (2 × 4)/(3 × 4) + (1 × 3)/(4 × 3) = (8)/(12) + (3)/(12) = (8+3)/(12) = (11)/(12) The simplified expression is (11)/(12). 4.4 Determine the percentage decrease if a chocolate that cost R10 is marked down to R7. Step 1: Calculate the amount of decrease. Decrease = Original Price - New Price Decrease = R10 - R7 = R3 Step 2: Calculate the percentage decrease using the formula: DecreaseOriginal Price × 100\%. Percentage Decrease = R3R10 × 100\% = 0.3 × 100\% = 30\% The percentage decrease is 30\%.