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: 1. Calculate: a) 16 ÷ 4 + 2 16 ÷ 4 + 2 = 4 + 2 = 6 b) 17 - 2 × (5 - 3) 17 - 2 × (5 - 3) = 17 - 2 × 2 = 17 - 4 = 13 c) 10 + 3 - 2 10 + 3 - 2 = 13 - 2 = 11 d) 9 - 4 + 6 9 - 4 + 6 = 5 + 6 = 11 2. Find the value of: a) 12 - 4 × 2 12 - 4 × 2 = 12 - 8 = 4 b) 15 + 8 - 4 × 2 15 + 8 - 4 × 2 = 15 + 8 - 8 = 23 - 8 = 15 c) 7 × (5 + 3) - 12 ÷ 4 7 × (5 + 3) - 12 ÷ 4 = 7 × 8 - 12 ÷ 4 = 56 - 3 = 53 d) 9 + 6 × (8 - 4) ÷ 2 9 + 6 × (8 - 4) ÷ 2 = 9 + 6 × 4 ÷ 2 = 9 + 24 ÷ 2 = 9 + 12 = 21 e) 50 ÷ 5 + 4 × 7 - 3 50 ÷ 5 + 4 × 7 - 3 = 10 + 28 - 3 = 38 - 3 = 35 3. Convert EACH of the following to an improper fraction: a) 8 (3)/(20) 8 (3)/(20) = (8 × 20 + 3)/(20) = (160 + 3)/(20) = (163)/(20) b) 10 (5)/(90) 10 (5)/(90) = (10 × 90 + 5)/(90) = (900 + 5)/(90) = (905)/(90) Simplify by dividing numerator and denominator by 5: (905 ÷ 5)/(90 ÷ 5) = (181)/(18) c) 1 (4)/(5) 1 (4)/(5) = (1 × 5 + 4)/(5) = (5 + 4)/(5) = (9)/(5) 4. Convert EACH of the following to a mixed number: a) (38)/(7) Divide 38 by 7: 38 ÷ 7 = 5 with a remainder of 3. (38)/(7) = 5 (3)/(7) b) (15)/(4) Divide 15 by 4: 15 ÷ 4 = 3 with a remainder of 3. (15)/(4) = 3 (3)/(4) c) (96)/(10) Divide 96 by 10: 96 ÷ 10 = 9 with a remainder of 6. (96)/(10) = 9 (6)/(10) Simplify the fraction part: 9 (6 ÷ 2)/(10 ÷ 2) = 9 (3)/(5) 5. Simplify EACH of the following: a) (5)/(6) + (3)/(4) Find a common denominator (LCM of 6 and 4 is 12): (5)/(6) + (3)/(4) = (5 × 2)/(6 × 2) + (3 × 3)/(4 × 3) = (10)/(12) + (9)/(12) = (10 + 9)/(12) = (19)/(12) Convert to a mixed number: (19)/(12) = 1 (7)/(12) b) 2 (1)/(2) - 1 (1)/(4) Convert mixed numbers to improper fractions: 2 (1)/(2) = (2 × 2 + 1)/(2) = (5)/(2) 1 (1)/(4) = (1 × 4 + 1)/(4) = (5)/(4) Subtract the improper fractions (common denominator is 4): (5)/(2) - (5)/(4) = (5 × 2)/(2 × 2) - (5)/(4) = (10)/(4) - (5)/(4) = (10 - 5)/(4) = (5)/(4) Convert to a mixed number: (5)/(4) = 1 (1)/(4) c) (4)/(5) × (3)/(8) Multiply the numerators and the denominators: (4)/(5) × (3)/(8) = (4 × 3)/(5 × 8) = (12)/(40) Simplify by dividing numerator and denominator by 4: (12 ÷ 4)/(40 ÷ 4) = (3)/(10) d) (5)/(7) ÷ (1)/(2) Multiply the first fraction by the reciprocal of the second fraction: (5)/(7) ÷ (1)/(2) = (5)/(7) × (2)/(1) = (5 × 2)/(7 × 1) = (10)/(7) Convert to a mixed number: (10)/(7) = 1 (3)/(7)