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 the problems you sent, Ozoemena! 9. Simplify (2)/(5) + (1)/(6)(3)/(5) Step 1: Simplify the numerator (2)/(5) + (1)/(6). The least common multiple (LCM) of 5 and 6 is 30. (2)/(5) + (1)/(6) = (2 × 6)/(5 × 6) + (1 × 5)/(6 × 5) = (12)/(30) + (5)/(30) = (12+5)/(30) = (17)/(30) Step 2: Divide the simplified numerator by the denominator (3)/(5). (17)/(30)(3)/(5) = (17)/(30) ÷ (3)/(5) To divide by a fraction, multiply by its reciprocal. (17)/(30) × (5)/(3) = (17 × 5)/(30 × 3) = (85)/(90) Step 3: Simplify the resulting fraction. Divide both the numerator and the denominator by their greatest common divisor, which is 5. (85 ÷ 5)/(90 ÷ 5) = (17)/(18) The correct option is not listed among A, B, C, D, E. Let me recheck my calculation. Recheck Step 2: (17)/(30) × (5)/(3) = 17 × 5^130^6 × 3 = (17 × 1)/(6 × 3) = (17)/(18) The calculation is correct. The answer is (17)/(18). None of the options match this result. 10. Which of the fraction (5)/(36), (1)/(3), (5)/(12), (2)/(9) and (7)/(18) is the largest? Step 1: Find a common denominator for all fractions. The denominators are 36, 3, 12, 9, and 18. The least common multiple (LCM) of these numbers is 36. Step 2: Convert each fraction to an equivalent fraction with a denominator of 36. (5)/(36) (1)/(3) = (1 × 12)/(3 × 12) = (12)/(36) (5)/(12) = (5 × 3)/(12 × 3) = (15)/(36) (2)/(9) = (2 × 4)/(9 × 4) = (8)/(36) (7)/(18) = (7 × 2)/(18 × 2) = (14)/(36) Step 3: Compare the numerators to find the largest fraction. The numerators are 5, 12, 15, 8, 14. The largest numerator is 15. Therefore, the largest fraction is (15)/(36), which is equivalent to (5)/(12). The correct option is C. 11. Simplify 1(1)/(3) of (3)/(8) ÷ (1)/(2) Step 1: Convert the mixed number to an improper fraction. 1(1)/(3) = ((1 × 3) + 1)/(3) = (4)/(3) The expression becomes (4)/(3) of (3)/(8) ÷ (1)/(2). Step 2: Perform the division operation first (following order of operations, "of" is multiplication, which has the same precedence as division, but typically evaluated left-to-right or division before multiplication if "of" is interpreted as a grouping). Let's treat "of" as multiplication and follow standard order of operations (PEMDAS/BODMAS), so division before multiplication. (3)/(8) ÷ (1)/(2) = (3)/(8) × (2)/(1) = (3 × 2)/(8 × 1) = (6)/(8) = (3)/(4) Step 3: Perform the "of" operation (multiplication). (4)/(3) × (3)/(4) = (4 × 3)/(3 × 4) = (12)/(12) = 1 The correct option is D. 12. Olu spent (1)/(2) of his pocket money on food, (1)/(4) of the remainder on transport. If he was left with N30, how much was Olu's pocket money? Step 1: Let Olu's total pocket money be P. Money spent on food = (1)/(2)P. Step 2: Calculate the remainder after spending on food. Remainder = P - (1)/(2)P = (1)/(2)P. Step 3: Calculate money spent on transport. Money spent on transport = (1)/(4) of the remainder = (1)/(4) × (1)/(2)P = (1)/(8)P. Step 4: Calculate the total money spent. Total spent = Money on food + Money on transport = (1)/(2)P + (1)/(8)P. To add these, find a common denominator (8): (4)/(8)P + (1)/(8)P = (5)/(8)P Step 5: Calculate the money left and set it equal to N30. Money left = Total pocket money - Total spent P - (5)/(8)P = (3)/(8)P We are given that he was left with N30. (3)/(8)P = 30 Step 6: Solve for P. P = 30 × (8)/(3) P = (30 × 8)/(3) = (240)/(3) = 80 Olu's pocket money was N80.00. The correct option is B. 13. Simplify (0.024 × 2.8)/(0.12 × 0.28) Step 1: Rewrite the decimals as fractions to simplify. 0.024 = (24)/(1000) 2.8 = (28)/(10) 0.12 = (12)/(100) 0.28 = (28)/(100) Step 2: Substitute these into the expression. (24)/(1000) × (28)/(10)(12)/(100) × (28)/(100) = (24 × 28)/(10000)(12 × 28)/(10000) Step 3: Simplify the expression. (24 × 28)/(10000) ÷ (12 × 28)/(10000) = (24 × 28)/(10000) × (10000)/(12 × 28) Cancel out common terms: 28 and 10000. (24)/(12) = 2 The correct option is E. (The options provided in the image are A. 0.0002, B. 0.002, C. 0.02, D. 0.2. There is no E option visible, but the answer is 2. Assuming there's an option E=2 or similar, I will provide the calculated answer.) The calculated answer is 2. 14. From 19.35 subtract 8.972. Step 1: Align the decimal points and add trailing zeros to ensure equal decimal places. c 019.350 \\ -008.972 \\ Step 2: Perform the subtraction. c 019.350 \\ -008.972 \\ 10.378 \\ The result is 10.378. The correct option is D. 15. Reduce 0.075 to a fraction in its lowest term. Step 1: Convert the decimal to a fraction. 0.075 means 75 thousandths. 0.075 = (75)/(1000) Step 2: Simplify the fraction to its lowest terms by dividing the numerator and denominator by their greatest common divisor. Both 75 and 1000 are divisible by 25. (75 ÷ 25)/(1000 ÷ 25) = (3)/(40) The fraction in its lowest term is (3)/(40). The correct option is A. That's 2 down. 3 left today — send the next one.