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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Question 6: Step 1: Convert mixed numbers to improper fractions. 5(1)/(8) = ((5 × 8) + 1)/(8) = (41)/(8) 2(1)/(4) = ((2 × 4) + 1)/(4) = (9)/(4) Step 2: Rewrite the expression with a common denominator of 8. (41)/(8) - (9)/(4) + (1)/(2) = (41)/(8) - (9 × 2)/(4 × 2) + (1 × 4)/(2 × 4) = (41)/(8) - (18)/(8) + (4)/(8) Step 3: Perform the operations. = (41 - 18 + 4)/(8) = (23 + 4)/(8) = (27)/(8) Step 4: Convert the improper fraction to a mixed number. (27)/(8) = 3(3)/(8) The correct option is B. B. 3(3)/(8) Question 7: Step 1: Set up the percentage equation. Let x be the percentage. x\% of 0.75 = 0.45 (x)/(100) × 0.75 = 0.45 Step 2: Solve for x. x = (0.45)/(0.75) × 100 x = (45)/(75) × 100 x = (3 × 15)/(5 × 15) × 100 x = (3)/(5) × 100 x = 3 × 20 x = 60 The correct option is A. A. 60\% Question 8: Step 1: Identify the hundreds digit and the digit to its right. The number is 87751. The hundreds digit is 7. The digit to its right (tens digit) is 5. Step 2: Apply rounding rules. Since the digit to the right of the hundreds place (5) is 5 or greater, round up the hundreds digit. The 7 becomes 8. All digits to the right of the hundreds place become zero. Step 3: Write the rounded number. 87751 rounded to the nearest hundred is 87800. The correct option is B. B. 87800 Question 9: Step 1: Interpret the phrase "increase of N240 by ratio 3:5". This phrase can be ambiguous. Given the options, we assume it means that the original amount (N240) and the increase itself are in the ratio 3:5. Let the increase be I. Original AmountIncrease = (3)/(5) (240)/(I) = (3)/(5) Step 2: Solve for I. 3I = 240 × 5 3I = 1200 I = (1200)/(3) I = 400 The increase is N400. The correct option is B. B. N400 Question 10: Step 1: Identify the principal, time, and rate. Principal (P) = N280 Time (T) = 2(1)/(2) years = 2.5 years Rate (R) = 3% per annum = (3)/(100) Step 2: Use the simple interest formula. Simple Interest (SI) = (P × R × T)/(100) (Here, R is the percentage value, so we divide by 100. Alternatively, use R as a decimal/fraction and omit the /100 in the formula). SI = (280 × 3 × 2.5)/(100) Step 3: Calculate the simple interest. SI = (280 × 3 × 5)/(2)100 SI = (280 × 15)/(200) SI = (4200)/(200) SI = 21 The simple interest is N21. The correct option is C. C. N21 Question 11: Step 1: Convert the percentage to a fraction. A percentage means "per hundred". So, 3% means 3 out of 100. 3\% = (3)/(100) Step 2: Simplify the fraction to its lowest terms. The numbers 3 and 100 have no common factors other than 1. Therefore, the fraction (3)/(100) is already in its lowest terms. The correct option is C. C. (3)/(100) That's 2 down. 3 left today — send the next one.