Simplify the following expressions: a) (1/2 2/3) + (1/2 of 3/4) + 1/2 b) (2.4 1.6 3.4) / (0.8 3.2 * 5.1)

1. a) Step 1: Simplify the terms in the brackets. The expression is ((1)/(2) · (2)/(3)) + ((1)/(2) of (3)/(4)) + (1)/(2). "of" means multiplication. (1)/(2) × (2)/(3) = (1 × 2)/(2 × 3) = (2)/(6) = (1)/(3) (1)/(2) × (3)/(4) = (1 × 3)/(2 × 4) = (3)/(8) Step 2: Substitute the simplified terms back into the expression. (1)/(3) + (3)/(8) + (1)/(2) Step 3: Find a common denominator for 3, 8, and 2, which is 24. Convert each fraction. (1)/(3) = (1 × 8)/(3 × 8) = (8)/(24) (3)/(8) = (3 × 3)/(8 × 3) = (9)/(24) (1)/(2) = (1 × 12)/(2 × 12) = (12)/(24) Step 4: Add the fractions. (8)/(24) + (9)/(24) + (12)/(24) = (8 + 9 + 12)/(24) = (29)/(24) The simplified expression is (29)/(24). 1. b) Step 1: Rewrite the expression to simplify common factors. (2.4 × 1.6 × 3.4)/(0.8 × 3.2 × 5.1) = (2.4)/(0.8) × (1.6)/(3.2) × (3.4)/(5.1) Step 2: Simplify each fraction. (2.4)/(0.8) = (24)/(8) = 3 (1.6)/(3.2) = (16)/(32) = (1)/(2) (3.4)/(5.1) = (34)/(51) = (2 × 17)/(3 × 17) = (2)/(3) Step 3: Multiply the simplified fractions. 3 × (1)/(2) × (2)/(3) = (3 × 1 × 2)/(2 × 3) = (6)/(6) = 1 The simplified expression is 1. 2. Given = \1, 2, 3, 4, 5, 6, 7, 8, 9, ..., 20\. a) Set A = Multiples of 3 Step 1: Identify multiples of 3 within the set . Multiples of 3 are numbers that can be divided by 3 without a remainder. 3 × 1 = 3 3 × 2 = 6 3 × 3 = 9 3 × 4 = 12 3 × 5 = 15 3 × 6 = 18 The next multiple, 3 × 7 = 21, is outside . Set A is \3, 6, 9, 12, 15, 18\. b) Set B = Odd numbers greater than 6 Step 1: Identify numbers in that are greater than 6. These are \7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\. Step 2: From this list, identify the odd numbers (numbers not divisible by 2). The odd numbers are 7, 9, 11, 13, 15, 17, 19. Set B is \7, 9, 11, 13, 15, 17, 19\. Send me the next one 📸