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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Section A: Multiple Choice Questions 1. What is LCM of 8 and 12? Multiples of 8: 8, 16, 24*, 32, ... Multiples of 12: 12, 24*, 36, ... The least common multiple (LCM) is 24. The correct option is (b) 24. 2. What is the difference between 15,124 and 4,167? Step 1: Subtract the smaller number from the larger number. 15,124 - 4,167 Step 2: Perform the subtraction. 15,124 - 4,167 = 10,957 The options provided are (a) 5123, (b) 11312, (c) 11690. None of these match the calculated difference. There might be a typo in the question or options. Assuming the question meant to ask for the difference between 15,124 and 4,167, the answer is 10,957. If the question was "What is the difference between 15,124 and 4,167?", and the options are for a different calculation, I cannot select from the given options. However, if one of the options was intended to be the correct answer for a slightly different problem, I cannot assume that. I will provide the correct calculation for the given numbers. The calculated difference is 10,957. 3. What is the place value of 5 in 4,320,500? (Assuming the number is 4,320,500, as the original image is unclear and this allows for one of the options to be correct.) In the number 4,320,500: The first 0 is in the ones place. The second 0 is in the tens place. The 5 is in the hundreds* place. The correct option is (a) hundred. 4. Convert 25% percentage to decimal. Step 1: To convert a percentage to a decimal, divide by 100. 25\% = (25)/(100) Step 2: Perform the division. (25)/(100) = 0.25 The correct option is (a) 0.25. 5. A 50kg bag of rice is shared between Ayo and Mrs. Uzor in the ratio of 2:3, find the share of each? Step 1: Find the total number of ratio parts. 2 + 3 = 5 parts Step 2: Calculate the value of one ratio part. 50 kg5 parts = 10 kg/part Step 3: Calculate Ayo's share. Ayo's share = 2 parts × 10 kg/part = 20 kg Step 4: Calculate Mrs. Uzor's share. Mrs. Uzor's share = 3 parts × 10 kg/part = 30 kg The correct option is (a) 20kg and 30kg. 6. Change this improper fraction to a mixed number (15)/(4)? Step 1: Divide the numerator by the denominator. 15 ÷ 4 = 3 with a remainder of 3 Step 2: Write the result as a mixed number (quotient and remainder over the original denominator). 3(3)/(4) The correct option is (c) 3(3)/(4). 7. What is the HCF of 20 and 30? Step 1: List the factors of 20. Factors of 20: 1, 2, 4, 5, 10, 20 Step 2: List the factors of 30. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Step 3: Identify the highest common factor (HCF). HCF(20, 30) = 10 The correct option is (a) 10. 8. What is product of 5 and 7? Step 1: Multiply the two numbers. 5 × 7 = 35 The correct option is (c) 35. 9. Write this as decimal 9/100? Step 1: Divide the numerator by the denominator. (9)/(100) = 0.09 The correct option is (b) 0.09. 10. How many days are there in the month of November? November has 30 days. The correct option is (a) 30 days. THEORY 1. Find the LCM of these numbers: a. 12 and 15 Step 1: List multiples of 12: 12, 24, 36, 48, 60*, 72, ... Step 2: List multiples of 15: 15, 30, 45, 60*, 75, ... The LCM of 12 and 15 is 60. b. 2 and 16 Step 1: List multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16*, 18, ... Step 2: List multiples of 16: 16*, 32, ... The LCM of 2 and 16 is 16. c. 35 and 40 Step 1: Find the prime factorization of each number. 35 = 5 × 7 40 = 2 × 2 × 2 × 5 = 2^3 × 5 Step 2: Take the highest power of each prime factor present. LCM(35, 40) = 2^3 × 5 × 7 Step 3: Calculate the product. 8 × 5 × 7 = 40 × 7 = 280 The LCM of 35 and 40 is 280. d. 7 and 21 Step 1: List multiples of 7: 7, 14, 21*, 28, ... Step 2: List multiples of 21: 21*, 42, ... The LCM of 7 and 21 is 21. 2. Convert these following to decimal: a. 50% Step 1: Divide the percentage by 100. 50\% = (50)/(100) Step 2: Perform the division. (50)/(100) = 0.50 The decimal form of 50% is 0.50. 3. Multiply these fractions: a. (1)/(2) × (3)/(4) Step 1: Multiply the numerators. 1 × 3 = 3 Step 2: Multiply the denominators. 2 × 4 = 8 Step 3: Write the new fraction. (3)/(8) The product is (3)/(8). b. (3)/(4) × (5)/(6) Step 1: Multiply the numerators. 3 × 5 = 15 Step 2: Multiply the denominators. 4 × 6 = 24 Step 3: Write the new fraction. (15)/(24) Step 4: Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3. \