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: 1. State true or false. a) |-10| > 0 The absolute value of -10 is 10. Since 10 > 0, the statement is true. Answer: True b) Subtraction of integers is associative. For example, (5 - 3) - 1 = 2 - 1 = 1, but 5 - (3 - 1) = 5 - 2 = 3. Since 1 ≠ 3, subtraction is not associative. Answer: False c) The result of -2 × -1 × -5 - 3 is a positive integer. Step 1: Perform multiplication. -2 × -1 × -5 = 2 × -5 = -10 Step 2: Perform subtraction. -10 - 3 = -13 Since -13 is a negative integer, the statement is false. Answer: False d) Division of an integer by zero gives 0 as the quotient. Division by zero is undefined. Answer: False e) 6 + 2 + 1 = 2 Step 1: Perform addition. 6 + 2 + 1 = 9 Since 9 ≠ 2, the statement is false. Answer: False 2. Choose the correct answer. a) ____ is the identity of multiplication of integers. The identity for multiplication is 1, because any integer multiplied by 1 remains unchanged. Answer: iii) 1 b) -100 - 60 = Step 1: Perform subtraction. -100 - 60 = -160 Answer: iv) -160 c) 200 - (-50) = Step 1: Simplify the double negative. 200 - (-50) = 200 + 50 Step 2: Perform addition. 200 + 50 = 250 Answer: i) 250 d) 24 ÷ 3 × (2 + 2) = Step 1: Perform the operation inside the parentheses. 2 + 2 = 4 Step 2: Perform division from left to right. 24 ÷ 3 = 8 Step 3: Perform multiplication. 8 × 4 = 32 Answer: i) 32 e) 10 × (3 + 4) = 10 × 3 + 10 × 4. This is the ____ property. This equation demonstrates the distributive property of multiplication over addition. Answer: iv) distributive f) The division of integers does not have closure property because ____ The closure property means that the result of an operation on two integers is always an integer. For division, this is not always true (e.g., 5 ÷ 2 = 2.5, which is not an integer). Answer: iii) quotient can be a fraction 3. Add. a) -15 + 28 -15 + 28 = 13 The sum is 13. b) -10 + (-18) -10 + (-18) = -10 - 18 = -28 The sum is -28. c) 24 + (-14) + (-65) 24 - 14 - 65 = 10 - 65 = -55 The sum is -55. d) -100 + 110 + (-90) + 40 -100 + 110 - 90 + 40 = 10 - 90 + 40 = -80 + 40 = -40 The sum is -40. 4. Subtract. a) 75 - 120 75 - 120 = -45 The difference is -45. *