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.
ScanSolve AI Answer
Here are the solutions to the problems: A. Calculate the following a) Multiples of 7: 7, 14, 21, 28, 35, ... Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ... LCM: 28 b) Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, ... Multiples of 8: 8, 16, 24, 32, 40, 48, ... LCM: 40 B. Calculate the following a) (2)/(3) + (1)/(2) Step 1: Find the least common multiple (LCM) of the denominators 3 and 2. The LCM of 3 and 2 is 6. Step 2: Convert the fractions to have a common denominator of 6. (2)/(3) = (2 × 2)/(3 × 2) = (4)/(6) (1)/(2) = (1 × 3)/(2 × 3) = (3)/(6) Step 3: Add the fractions. (4)/(6) + (3)/(6) = (4+3)/(6) = (7)/(6) The answer is (7)/(6) b) (7)/(8) - (1)/(2) Step 1: Find the LCM of the denominators 8 and 2. The LCM of 8 and 2 is 8. Step 2: Convert the fractions to have a common denominator of 8. (7)/(8) (1)/(2) = (1 × 4)/(2 × 4) = (4)/(8) Step 3: Subtract the fractions. (7)/(8) - (4)/(8) = (7-4)/(8) = (3)/(8) The answer is (3)/(8) C. Calculate the following a) (1)/(2) + (1)/(3) Step 1: Find the LCM of the denominators 2 and 3. The LCM of 2 and 3 is 6. Step 2: Convert the fractions to have a common denominator of 6. (1)/(2) = (1 × 3)/(2 × 3) = (3)/(6) (1)/(3) = (1 × 2)/(3 × 2) = (2)/(6) Step 3: Add the fractions. (3)/(6) + (2)/(6) = (3+2)/(6) = (5)/(6) The answer is (5)/(6) b) (4)/(5) - (1)/(2) Step 1: Find the LCM of the denominators 5 and 2. The LCM of 5 and 2 is 10. Step 2: Convert the fractions to have a common denominator of 10. (4)/(5) = (4 × 2)/(5 × 2) = (8)/(10) (1)/(2) = (1 × 5)/(2 × 5) = (5)/(10) Step 3: Subtract the fractions. (8)/(10) - (5)/(10) = (8-5)/(10) = (3)/(10) The answer is (3)/(10)