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: 6. Name the property used in each of the following. a) (3)/(8) + (5)/(12) = (5)/(12) + (3)/(8) This is the Commutative Property of Addition. b) (-5)/(8) + 0 = (-5)/(8) This is the Additive Identity Property. c) (-3)/(11) + (3)/(11) = 0 This is the Additive Inverse Property. d) (-5)/(4) × (4)/(-5) = 1 This is the Multiplicative Inverse Property. 7. Manish bought 2 (1)/(2) kg potatoes and 3 (1)/(4) kg onions. How many kg of vegetables did he buy? Step 1: Convert mixed numbers to improper fractions. Potatoes: 2 (1)/(2) = ((2 × 2) + 1)/(2) = (5)/(2) kg Onions: 3 (1)/(4) = ((3 × 4) + 1)/(4) = (13)/(4) kg Step 2: Add the quantities. Total vegetables = (5)/(2) + (13)/(4) Find a common denominator, which is 4. (5)/(2) = (5 × 2)/(2 × 2) = (10)/(4) Total vegetables = (10)/(4) + (13)/(4) = (10+13)/(4) = (23)/(4) kg Step 3: Convert the improper fraction back to a mixed number. (23)/(4) = 5 (3)/(4) kg Manish bought 5 (3)/(4) kg of vegetables. 8. The sides of a triangular field are 4 (1)/(2) cm, 4 (3)/(4) cm and 5 (1)/(8) cm. Find its perimeter. Step 1: Convert mixed numbers to improper fractions. Side 1: 4 (1)/(2) = ((4 × 2) + 1)/(2) = (9)/(2) cm Side 2: 4 (3)/(4) = ((4 × 4) + 3)/(4) = (19)/(4) cm Side 3: 5 (1)/(8) = ((5 × 8) + 1)/(8) = (41)/(8) cm Step 2: Add the lengths of the sides to find the perimeter. Perimeter = (9)/(2) + (19)/(4) + (41)/(8) Find a common denominator, which is the LCM of 2, 4, and 8, which is 8. (9)/(2) = (9 × 4)/(2 × 4) = (36)/(8) (19)/(4) = (19 × 2)/(4 × 2) = (38)/(8) Perimeter = (36)/(8) + (38)/(8) + (41)/(8) = (36+38+41)/(8) = (115)/(8) cm Step