{
  "title": "Properties of Operations on Integers - Grade 7 CBSE",
  "total_questions": 150,
  "questions": [

    {"id": 1, "difficulty": "easy", "question": "Which property does a + b = b + a represent?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Identity"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Which property is shown: (a + b) + c = a + (b + c)?", "options": {"A": "Commutative", "B": "Associative", "C": "Identity", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "Which property: a × 1 = a?", "options": {"A": "Zero property", "B": "Identity property", "C": "Inverse property", "D": "Commutative"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "What is a + 0 equal to?", "options": {"A": "0", "B": "2a", "C": "a", "D": "-a"}, "correct_answer": "D"},
    {"id": 5, "difficulty": "easy", "question": "a × 0 equals:", "options": {"A": "a", "B": "1", "C": "0", "D": "-a"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Which property: a × b = b × a?", "options": {"A": "Associative", "B": "Commutative", "C": "Identity", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Which property is used: a(b + c) = ab + ac?", "options": {"A": "Identity", "B": "Zero", "C": "Distributive", "D": "Inverse"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Additive inverse of +7 is:", "options": {"A": "-7", "B": "0", "C": "1", "D": "+7"}, "correct_answer": "D"},
    {"id": 9, "difficulty": "easy", "question": "Additive inverse of -9 is:", "options": {"A": "9", "B": "0", "C": "-9", "D": "1"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Which property does 5 + (-5) = 0 show?", "options": {"A": "Zero property", "B": "Inverse property", "C": "Identity property", "D": "Associative property"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "(a × b) × c = a × (b × c) is:", "options": {"A": "Commutative", "B": "Associative", "C": "Identity", "D": "Inverse"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "Zero is identity element for addition?", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Never"}, "correct_answer": "D"},
    {"id": 13, "difficulty": "easy", "question": "One is identity for multiplication?", "options": {"A": "Always", "B": "Never", "C": "Sometimes", "D": "Only for integers"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Which property allows rearranging terms in addition?", "options": {"A": "Commutative", "B": "Zero", "C": "Identity", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "Which property allows regrouping numbers?", "options": {"A": "Inverse", "B": "Associative", "C": "Distributive", "D": "Zero"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "Which property: (3 + 2) + 5 = 3 + (2 + 5)?", "options": {"A": "Commutative", "B": "Associative", "C": "Identity", "D": "Inverse"}, "correct_answer": "D"},
    {"id": 17, "difficulty": "easy", "question": "–a + a equals:", "options": {"A": "a", "B": "–a", "C": "1", "D": "0"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "a × (b × c) is same as (a × b) × c due to:", "options": {"A": "Identity", "B": "Zero", "C": "Associative", "D": "Distributive"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "a × (b + c) expands to:", "options": {"A": "ab + ac", "B": "a + b + c", "C": "abc", "D": "a + bc"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Additive identity for integers is:", "options": {"A": "1", "B": "0", "C": "-1", "D": "None"}, "correct_answer": "D"},

    {"id": 21, "difficulty": "medium", "question": "Which property: –3 + 7 = 7 + –3?", "options": {"A": "Associative", "B": "Identity", "C": "Commutative", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "(–2 + 5) + 8 = –2 + (5 + 8) uses:", "options": {"A": "Identity", "B": "Associative", "C": "Commutative", "D": "Distributive"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "Which property: 4(3 + 2) = 4×3 + 4×2?", "options": {"A": "Associative", "B": "Inverse", "C": "Distributive", "D": "Identity"}, "correct_answer": "D"},
    {"id": 24, "difficulty": "medium", "question": "Solve using properties: (10 + –10) + 5", "options": {"A": "0", "B": "-5", "C": "5", "D": "10"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Which property proves a + (–a) = 0?", "options": {"A": "Zero", "B": "Identity", "C": "Inverse", "D": "Associative"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Which is true by commutative property?", "options": {"A": "8 – 3 = 3 – 8", "B": "8 × 3 = 3 × 8", "C": "8 ÷ 2 = 2 ÷ 8", "D": "8 – 0 = 8"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "Which property helps simplify (–7 × 5) × 2 = –7 × (5 × 2)?", "options": {"A": "Commutative", "B": "Associative", "C": "Distributive", "D": "Identity"}, "correct_answer": "D"},
    {"id": 28, "difficulty": "medium", "question": "a + b + 0 = a + b shows:", "options": {"A": "Zero property", "B": "Identity property", "C": "Inverse property", "D": "Associative property"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Which property: 6 × (4 + –4) = 6×4 + 6×(–4)?", "options": {"A": "Zero", "B": "Distributive", "C": "Associative", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Evaluate using identity: 0 × –9", "options": {"A": "9", "B": "0", "C": "-9", "D": "1"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "(–3 × 4) × 2 = –3 × (4 × 2) is:", "options": {"A": "Associative property", "B": "Commutative property", "C": "Zero property", "D": "Identity property"}, "correct_answer": "D"},
    {"id": 32, "difficulty": "medium", "question": "(–9 + 4) + 6 = –9 + (4 + 6) due to:", "options": {"A": "Identity", "B": "Associative", "C": "Inverse", "D": "Zero"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Which property is used: 5 × –7 = –7 × 5?", "options": {"A": "Commutative", "B": "Associative", "C": "Identity", "D": "Distributive"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Which property: 3 + (–3 + 9) = (3 + –3) + 9?", "options": {"A": "Zero", "B": "Associative", "C": "Inverse", "D": "Distributive"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "Simplify using inverse: –6 + 6 + 3", "options": {"A": "0", "B": "3", "C": "6", "D": "9"}, "correct_answer": "D"},
    {"id": 36, "difficulty": "medium", "question": "Which property allows 4×(–5 + 2) = 4×–5 + 4×2?", "options": {"A": "Distributive", "B": "Associative", "C": "Commutative", "D": "Identity"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Zero multiplied by any integer equals:", "options": {"A": "1", "B": "0", "C": "-1", "D": "Same integer"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Which is identity element for multiplication?", "options": {"A": "0", "B": "1", "C": "-1", "D": "2"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "Which property allows switching numbers in multiplication?", "options": {"A": "Associative", "B": "Commutative", "C": "Zero", "D": "Distributive"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Which property justifies: 8 + (–8) = 0?", "options": {"A": "Identity", "B": "Inverse", "C": "Zero", "D": "Associative"}, "correct_answer": "C"},

    {"id": 41, "difficulty": "hard", "question": "Simplify using distributive: –4(7 – 2)", "options": {"A": "-16", "B": "-20", "C": "-24", "D": "-28"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "Evaluate: 6(–3 + 5) using properties", "options": {"A": "6", "B": "12", "C": "18", "D": "24"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "Which property helps simplify 3×(–8) + 3×(5)?", "options": {"A": "Associative", "B": "Inverse", "C": "Distributive", "D": "Commutative"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "hard", "question": "Simplify: –5(–6 – 4)", "options": {"A": "40", "B": "45", "C": "50", "D": "55"}, "correct_answer": "D"},
    {"id": 45, "difficulty": "hard", "question": "Compute using associative: (–9 × 4) × 2", "options": {"A": "-60", "B": "-70", "C": "-72", "D": "-80"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Which property used: (–3 + 6) + 9 = –3 + (6 + 9)?", "options": {"A": "Identity", "B": "Associative", "C": "Commutative", "D": "Inverse"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "hard", "question": "Simplify: –2(–7 + 3)", "options": {"A": "6", "B": "8", "C": "10", "D": "14"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "hard", "question": "What is (–3 × –5) × 2 using associative?", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "D"},
    {"id": 49, "difficulty": "hard", "question": "Simplify: 12 + –(12)", "options": {"A": "0", "B": "12", "C": "-12", "D": "-24"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "Simplify: –4(–3 – 5)", "options": {"A": "24", "B": "28", "C": "32", "D": "36"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "hard", "question": "Which property helps evaluate –7 + 7 + –4?", "options": {"A": "Zero", "B": "Inverse", "C": "Associative", "D": "Identity"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "hard", "question": "Compute using distributive: 3(–4 + 9)", "options": {"A": "9", "B": "12", "C": "15", "D": "18"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "hard", "question": "Simplify: –8 × (6 – 10)", "options": {"A": "16", "B": "24", "C": "32", "D": "40"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "Simplify: –6(3 – 7)", "options": {"A": "-18", "B": "18", "C": "24", "D": "-24"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "Which property shows a + (b – b) = a?", "options": {"A": "Distributive", "B": "Inverse", "C": "Zero", "D": "Associative"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "hard", "question": "Simplify using distributive: –3(–8 + 2)", "options": {"A": "12", "B": "15", "C": "18", "D": "21"}, "correct_answer": "D"},
    {"id": 57, "difficulty": "hard", "question": "Compute: (–4 × 5) × –2 using associative", "options": {"A": "20", "B": "30", "C": "40", "D": "50"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "Simplify: 7 + –3 + –4 + 0", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "hard", "question": "Find: –9(2 – 5)", "options": {"A": "18", "B": "21", "C": "24", "D": "27"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "hard", "question": "Simplify fully: –2(–6 + 1)", "options": {"A": "8", "B": "10", "C": "12", "D": "14"}, "correct_answer": "D"}
 ,
  {"id":61,"difficulty":"easy","question":"Which property does a + b = b + a show?","options":{"A":"Associative","B":"Commutative","C":"Distributive","D":"Identity"},"correct_answer":"B"},
  {"id":62,"difficulty":"easy","question":"Which property does a × b = b × a show?","options":{"A":"Commutative","B":"Associative","C":"Identity","D":"Zero"},"correct_answer":"A"},
  {"id":63,"difficulty":"easy","question":"Which property does (a + b) + c = a + (b + c) show?","options":{"A":"Commutative","B":"Associative","C":"Inverse","D":"Identity"},"correct_answer":"B"},
  {"id":64,"difficulty":"easy","question":"Which property does (a × b) × c = a × (b × c) show?","options":{"A":"Distributive","B":"Commutative","C":"Associative","D":"Zero"},"correct_answer":"C"},
  {"id":65,"difficulty":"easy","question":"What is the additive identity for integers?","options":{"A":"1","B":"-1","C":"0","D":"None"},"correct_answer":"C"},
  {"id":66,"difficulty":"easy","question":"What is the multiplicative identity for integers?","options":{"A":"0","B":"1","C":"-1","D":"2"},"correct_answer":"B"},
  {"id":67,"difficulty":"easy","question":"Which property is shown: a + 0 = a?","options":{"A":"Inverse","B":"Commutative","C":"Identity","D":"Associative"},"correct_answer":"C"},
  {"id":68,"difficulty":"easy","question":"Which property is shown: a × 1 = a?","options":{"A":"Zero","B":"Identity","C":"Inverse","D":"Commutative"},"correct_answer":"B"},
  {"id":69,"difficulty":"easy","question":"Additive inverse of 9 is","options":{"A":"1","B":"-9","C":"0","D":"9"},"correct_answer":"B"},
  {"id":70,"difficulty":"easy","question":"Additive inverse of -11 is","options":{"A":"11","B":"-11","C":"0","D":"1"},"correct_answer":"A"},
  {"id":71,"difficulty":"easy","question":"What is a × 0 equal to?","options":{"A":"a","B":"1","C":"0","D":"-a"},"correct_answer":"C"},
  {"id":72,"difficulty":"easy","question":"Which property shows a + (-a) = 0?","options":{"A":"Identity","B":"Inverse","C":"Associative","D":"Commutative"},"correct_answer":"B"},
  {"id":73,"difficulty":"easy","question":"Which property allows changing order in addition?","options":{"A":"Associative","B":"Commutative","C":"Inverse","D":"Distributive"},"correct_answer":"B"},
  {"id":74,"difficulty":"easy","question":"Which property allows regrouping numbers?","options":{"A":"Identity","B":"Inverse","C":"Associative","D":"Zero"},"correct_answer":"C"},
  {"id":75,"difficulty":"easy","question":"Which property does a(b + c) = ab + ac represent?","options":{"A":"Commutative","B":"Associative","C":"Distributive","D":"Identity"},"correct_answer":"C"},
  {"id":76,"difficulty":"easy","question":"What is -a + a equal to?","options":{"A":"a","B":"-a","C":"1","D":"0"},"correct_answer":"D"},
  {"id":77,"difficulty":"easy","question":"Zero is identity element for which operation?","options":{"A":"Multiplication","B":"Division","C":"Addition","D":"Subtraction"},"correct_answer":"C"},
  {"id":78,"difficulty":"easy","question":"One is identity element for which operation?","options":{"A":"Addition","B":"Multiplication","C":"Subtraction","D":"Division"},"correct_answer":"B"},
  {"id":79,"difficulty":"easy","question":"Which property shows 5 + (-5) = 0?","options":{"A":"Identity","B":"Inverse","C":"Zero","D":"Associative"},"correct_answer":"B"},
  {"id":80,"difficulty":"easy","question":"Which property shows 4 × (5 + 1) = 4×5 + 4×1?","options":{"A":"Associative","B":"Distributive","C":"Commutative","D":"Identity"},"correct_answer":"B"},
  {"id":81,"difficulty":"easy","question":"Which property allows switching numbers in multiplication?","options":{"A":"Associative","B":"Commutative","C":"Inverse","D":"Zero"},"correct_answer":"B"},
  {"id":82,"difficulty":"easy","question":"Which property shows a + b + 0 = a + b?","options":{"A":"Inverse","B":"Associative","C":"Identity","D":"Distributive"},"correct_answer":"C"},
  {"id":83,"difficulty":"easy","question":"Which property applies to a × (b × c)?","options":{"A":"Commutative","B":"Associative","C":"Inverse","D":"Zero"},"correct_answer":"B"},
  {"id":84,"difficulty":"easy","question":"Which property makes calculation easier by grouping?","options":{"A":"Identity","B":"Distributive","C":"Associative","D":"Zero"},"correct_answer":"C"},
  {"id":85,"difficulty":"easy","question":"Which property is NOT applicable to subtraction?","options":{"A":"Associative","B":"Commutative","C":"Both A and B","D":"Identity"},"correct_answer":"C"},
  {"id":86,"difficulty":"easy","question":"Which property is NOT applicable to division?","options":{"A":"Commutative","B":"Associative","C":"Both A and B","D":"Identity"},"correct_answer":"C"},
  {"id":87,"difficulty":"easy","question":"Which property shows a × 0 = 0?","options":{"A":"Zero","B":"Identity","C":"Inverse","D":"Associative"},"correct_answer":"A"},
  {"id":88,"difficulty":"easy","question":"Which property shows a + (-a) + b = b?","options":{"A":"Associative","B":"Inverse","C":"Identity","D":"Commutative"},"correct_answer":"B"},
  {"id":89,"difficulty":"easy","question":"Which property is used first while regrouping numbers?","options":{"A":"Commutative","B":"Associative","C":"Distributive","D":"Inverse"},"correct_answer":"B"},
  {"id":90,"difficulty":"easy","question":"Which property combines multiplication and addition?","options":{"A":"Associative","B":"Commutative","C":"Distributive","D":"Identity"},"correct_answer":"C"},

  {"id":91,"difficulty":"medium","question":"Which property justifies -3 + 7 = 7 + (-3)?","options":{"A":"Associative","B":"Inverse","C":"Commutative","D":"Identity"},"correct_answer":"C"},
  {"id":92,"difficulty":"medium","question":"Which property justifies (-2 + 5) + 8 = -2 + (5 + 8)?","options":{"A":"Commutative","B":"Associative","C":"Inverse","D":"Zero"},"correct_answer":"B"},
  {"id":93,"difficulty":"medium","question":"Which property is used in 6(3 + 4) = 6×3 + 6×4?","options":{"A":"Associative","B":"Distributive","C":"Commutative","D":"Identity"},"correct_answer":"B"},
  {"id":94,"difficulty":"medium","question":"Evaluate using properties: (10 + -10) + 6","options":{"A":"0","B":"6","C":"-6","D":"10"},"correct_answer":"B"},
  {"id":95,"difficulty":"medium","question":"Which property proves a + 0 + b = a + b?","options":{"A":"Associative","B":"Inverse","C":"Identity","D":"Distributive"},"correct_answer":"C"},
  {"id":96,"difficulty":"medium","question":"Which is true by commutative property?","options":{"A":"8 - 3 = 3 - 8","B":"8 × 3 = 3 × 8","C":"8 ÷ 2 = 2 ÷ 8","D":"8 - 0 = 8"},"correct_answer":"B"},
  {"id":97,"difficulty":"medium","question":"Which property simplifies (−4 × 5) × 2 = −4 × (5 × 2)?","options":{"A":"Distributive","B":"Commutative","C":"Associative","D":"Identity"},"correct_answer":"C"},
  {"id":98,"difficulty":"medium","question":"Which property helps simplify 7 + (-7) + 3?","options":{"A":"Associative","B":"Inverse","C":"Commutative","D":"Identity"},"correct_answer":"B"},
  {"id":99,"difficulty":"medium","question":"Which property is used in 9 × (4 + 0) = 9 × 4?","options":{"A":"Inverse","B":"Identity","C":"Distributive","D":"Associative"},"correct_answer":"B"},
  {"id":100,"difficulty":"medium","question":"Evaluate using distributive: 5(2 + -2)","options":{"A":"0","B":"5","C":"10","D":"-10"},"correct_answer":"A"},
  {"id":101,"difficulty":"medium","question":"Which property shows a + (b + c) = (a + b) + c?","options":{"A":"Commutative","B":"Associative","C":"Inverse","D":"Identity"},"correct_answer":"B"},
  {"id":102,"difficulty":"medium","question":"Which property shows 4 × (-1) = -4?","options":{"A":"Identity","B":"Inverse","C":"Zero","D":"Commutative"},"correct_answer":"B"},
  {"id":103,"difficulty":"medium","question":"Which property is used to simplify 6 + (0 + 4)?","options":{"A":"Associative","B":"Identity","C":"Inverse","D":"Commutative"},"correct_answer":"B"},
  {"id":104,"difficulty":"medium","question":"Which property applies: (a + b)c = ac + bc?","options":{"A":"Associative","B":"Commutative","C":"Distributive","D":"Identity"},"correct_answer":"C"},
  {"id":105,"difficulty":"medium","question":"Which property is violated in subtraction?","options":{"A":"Associative","B":"Commutative","C":"Both","D":"None"},"correct_answer":"C"},
  {"id":106,"difficulty":"medium","question":"Which property is violated in division?","options":{"A":"Associative","B":"Commutative","C":"Both","D":"None"},"correct_answer":"C"},
  {"id":107,"difficulty":"medium","question":"Which property shows a × (b + c) = ab + ac?","options":{"A":"Associative","B":"Distributive","C":"Commutative","D":"Inverse"},"correct_answer":"B"},
  {"id":108,"difficulty":"medium","question":"Which property allows (-5 + 5) + a = a?","options":{"A":"Inverse","B":"Identity","C":"Associative","D":"Zero"},"correct_answer":"A"},
  {"id":109,"difficulty":"medium","question":"Which property allows rearranging terms before grouping?","options":{"A":"Commutative","B":"Associative","C":"Inverse","D":"Identity"},"correct_answer":"A"},
  {"id":110,"difficulty":"medium","question":"Which property simplifies 0 × (a + b)?","options":{"A":"Distributive","B":"Identity","C":"Zero","D":"Associative"},"correct_answer":"C"},
  {"id":111,"difficulty":"medium","question":"Which property shows (a × b) × 1 = a × b?","options":{"A":"Zero","B":"Identity","C":"Associative","D":"Inverse"},"correct_answer":"B"},
  {"id":112,"difficulty":"medium","question":"Which property allows 3 × (4 + 5) to expand?","options":{"A":"Commutative","B":"Associative","C":"Distributive","D":"Identity"},"correct_answer":"C"},
  {"id":113,"difficulty":"medium","question":"Which property shows -a + a + b = b?","options":{"A":"Associative","B":"Identity","C":"Inverse","D":"Commutative"},"correct_answer":"C"},
  {"id":114,"difficulty":"medium","question":"Which property keeps value unchanged when adding zero?","options":{"A":"Inverse","B":"Identity","C":"Associative","D":"Commutative"},"correct_answer":"B"},
  {"id":115,"difficulty":"medium","question":"Which property combines numbers without changing order?","options":{"A":"Associative","B":"Commutative","C":"Inverse","D":"Distributive"},"correct_answer":"A"},
  {"id":116,"difficulty":"medium","question":"Which property is used in mental math to rearrange terms?","options":{"A":"Associative","B":"Inverse","C":"Commutative","D":"Identity"},"correct_answer":"C"},
  {"id":117,"difficulty":"medium","question":"Which property helps remove brackets in multiplication?","options":{"A":"Associative","B":"Commutative","C":"Distributive","D":"Identity"},"correct_answer":"C"},
  {"id":118,"difficulty":"medium","question":"Which property shows (-1) × a = -a?","options":{"A":"Zero","B":"Identity","C":"Inverse","D":"Associative"},"correct_answer":"C"},
  {"id":119,"difficulty":"medium","question":"Which property simplifies (a + b) + 0?","options":{"A":"Associative","B":"Identity","C":"Inverse","D":"Commutative"},"correct_answer":"B"},
  {"id":120,"difficulty":"medium","question":"Which property allows grouping before multiplying?","options":{"A":"Associative","B":"Commutative","C":"Distributive","D":"Inverse"},"correct_answer":"A"},

  {"id":121,"difficulty":"hard","question":"Simplify using distributive: -4(6 - 2)","options":{"A":"-8","B":"-16","C":"-24","D":"-32"},"correct_answer":"B"},
  {"id":122,"difficulty":"hard","question":"Evaluate using distributive: 5(-3 + 7)","options":{"A":"10","B":"15","C":"20","D":"25"},"correct_answer":"C"},
  {"id":123,"difficulty":"hard","question":"Which property helps factor: 3a + 3b?","options":{"A":"Associative","B":"Commutative","C":"Distributive","D":"Inverse"},"correct_answer":"C"},
  {"id":124,"difficulty":"hard","question":"Simplify: -6(4 - 7)","options":{"A":"-18","B":"18","C":"24","D":"-24"},"correct_answer":"B"},
  {"id":125,"difficulty":"hard","question":"Evaluate: (−8 × 3) × 2","options":{"A":"-32","B":"-40","C":"-48","D":"-56"},"correct_answer":"C"},
  {"id":126,"difficulty":"hard","question":"Which property is used: (a + b) + c = a + (b + c)?","options":{"A":"Commutative","B":"Associative","C":"Identity","D":"Inverse"},"correct_answer":"B"},
  {"id":127,"difficulty":"hard","question":"Simplify: -3(-5 + 2)","options":{"A":"6","B":"9","C":"15","D":"21"},"correct_answer":"B"},
  {"id":128,"difficulty":"hard","question":"Evaluate: (-4 × -5) × 3","options":{"A":"40","B":"50","C":"60","D":"70"},"correct_answer":"C"},
  {"id":129,"difficulty":"hard","question":"Simplify using inverse: 9 + (-9) + 4","options":{"A":"0","B":"4","C":"9","D":"-4"},"correct_answer":"B"},
  {"id":130,"difficulty":"hard","question":"Simplify: -2(-6 - 4)","options":{"A":"16","B":"18","C":"20","D":"24"},"correct_answer":"C"},
  {"id":131,"difficulty":"hard","question":"Which property allows 7 + (-7) + a = a?","options":{"A":"Identity","B":"Inverse","C":"Associative","D":"Commutative"},"correct_answer":"B"},
  {"id":132,"difficulty":"hard","question":"Evaluate: 4(3 + -5)","options":{"A":"-4","B":"-8","C":"-12","D":"-16"},"correct_answer":"B"},
  {"id":133,"difficulty":"hard","question":"Simplify: -7(2 - 6)","options":{"A":"14","B":"21","C":"28","D":"-28"},"correct_answer":"C"},
  {"id":134,"difficulty":"hard","question":"Which property helps rewrite 2a + 2b?","options":{"A":"Associative","B":"Inverse","C":"Distributive","D":"Commutative"},"correct_answer":"C"},
  {"id":135,"difficulty":"hard","question":"Evaluate: (-3 × 4) × (-2)","options":{"A":"12","B":"18","C":"24","D":"30"},"correct_answer":"C"},
  {"id":136,"difficulty":"hard","question":"Simplify fully: -5(-2 + 7)","options":{"A":"-15","B":"15","C":"20","D":"25"},"correct_answer":"B"},
  {"id":137,"difficulty":"hard","question":"Which property is used to remove brackets in 6(a - b)?","options":{"A":"Associative","B":"Commutative","C":"Distributive","D":"Identity"},"correct_answer":"C"},
  {"id":138,"difficulty":"hard","question":"Simplify: -9(1 - 4)","options":{"A":"18","B":"21","C":"24","D":"27"},"correct_answer":"B"},
  {"id":139,"difficulty":"hard","question":"Evaluate: (-2 × -3) × (-4)","options":{"A":"-12","B":"-18","C":"-24","D":"-30"},"correct_answer":"C"},
  {"id":140,"difficulty":"hard","question":"Simplify using properties: 0 × (a - b)","options":{"A":"a","B":"b","C":"0","D":"a-b"},"correct_answer":"C"},
  {"id":141,"difficulty":"hard","question":"Which property allows regrouping before multiplying three numbers?","options":{"A":"Commutative","B":"Associative","C":"Distributive","D":"Inverse"},"correct_answer":"B"},
  {"id":142,"difficulty":"hard","question":"Simplify: -4(-3 - 2)","options":{"A":"16","B":"20","C":"24","D":"28"},"correct_answer":"B"},
  {"id":143,"difficulty":"hard","question":"Evaluate: 3(-2 + -4)","options":{"A":"-12","B":"-18","C":"-6","D":"6"},"correct_answer":"A"},
  {"id":144,"difficulty":"hard","question":"Which property combines like terms by factoring?","options":{"A":"Associative","B":"Inverse","C":"Distributive","D":"Commutative"},"correct_answer":"C"},
  {"id":145,"difficulty":"hard","question":"Simplify: -8(5 - 9)","options":{"A":"24","B":"32","C":"36","D":"40"},"correct_answer":"B"},
  {"id":146,"difficulty":"hard","question":"Evaluate: (-5 × 6) × (-2)","options":{"A":"40","B":"50","C":"60","D":"70"},"correct_answer":"C"},
  {"id":147,"difficulty":"hard","question":"Simplify using inverse: a + (-a) + (-3)","options":{"A":"-3","B":"3","C":"0","D":"a"},"correct_answer":"A"},
  {"id":148,"difficulty":"hard","question":"Evaluate: 7(-3 + 1)","options":{"A":"-7","B":"-14","C":"-21","D":"14"},"correct_answer":"B"},
  {"id":149,"difficulty":"hard","question":"Simplify: -6(-4 - 1)","options":{"A":"24","B":"30","C":"36","D":"40"},"correct_answer":"B"},
  {"id":150,"difficulty":"hard","question":"Which property is most used in algebraic simplification?","options":{"A":"Identity","B":"Inverse","C":"Distributive","D":"Zero"},"correct_answer":"C"}
 ]
}