{
  "title": "Properties of Rational Numbers - Grade 7 ICSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "Which property is shown? 2/3 + 5/7 = 5/7 + 2/3 🔄",
      "options": {
        "A": "Associative",
        "B": "Commutative",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "B"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "What is the additive inverse of 3/4? ➖",
      "options": { "A": "4/3", "B": "-3/4", "C": "-4/3", "D": "3/4" },
      "correct_answer": "B"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "What is the multiplicative identity for rational numbers? 🆔",
      "options": { "A": "0", "B": "1", "C": "-1", "D": "The number itself" },
      "correct_answer": "B"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "Fill in the blank: 5/6 × _ = 5/6",
      "options": { "A": "0", "B": "1", "C": "6/5", "D": "5/6" },
      "correct_answer": "B"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "Which property is used? (1/2 × 2/3) × 3/4 = 1/2 × (2/3 × 3/4) 🔗",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Identity"
      },
      "correct_answer": "B"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "What is 7/8 + (-7/8)?",
      "options": { "A": "14/8", "B": "0", "C": "1", "D": "-1" },
      "correct_answer": "B"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "The reciprocal of -5/9 is: 🔁",
      "options": { "A": "9/5", "B": "-9/5", "C": "5/9", "D": "-5/9" },
      "correct_answer": "B"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "What is the additive identity for rational numbers? 0️⃣",
      "options": { "A": "0", "B": "1", "C": "-1", "D": "Does not exist" },
      "correct_answer": "A"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "Which is true? Rational numbers are closed under: 🔒",
      "options": {
        "A": "Addition only",
        "B": "Subtraction only",
        "C": "Multiplication only",
        "D": "Addition, subtraction, multiplication"
      },
      "correct_answer": "D"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "If a/b is a rational number, its additive inverse is: 🌀",
      "options": { "A": "b/a", "B": "-a/b", "C": "-b/a", "D": "a/-b" },
      "correct_answer": "B"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "What is (2/5) × (5/2)?",
      "options": { "A": "0", "B": "1", "C": "2/5", "D": "5/2" },
      "correct_answer": "B"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "Which property? 3/4 × (5/6 + 7/8) = (3/4 × 5/6) + (3/4 × 7/8) 📐",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "C"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "The reciprocal of 1 is: ✔️",
      "options": { "A": "0", "B": "1", "C": "-1", "D": "Does not exist" },
      "correct_answer": "B"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "For any rational a, a + 0 = ?",
      "options": { "A": "0", "B": "1", "C": "a", "D": "-a" },
      "correct_answer": "C"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "Rational numbers are not closed under: 🚫",
      "options": {
        "A": "Addition",
        "B": "Subtraction",
        "C": "Division",
        "D": "Multiplication"
      },
      "correct_answer": "C"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "The product of a rational and its reciprocal is always: ✖️",
      "options": { "A": "0", "B": "1", "C": "-1", "D": "The number itself" },
      "correct_answer": "B"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "What is -(-3/7)? 🔄",
      "options": { "A": "-3/7", "B": "3/7", "C": "7/3", "D": "-7/3" },
      "correct_answer": "B"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "Which number has no reciprocal? ❌",
      "options": { "A": "1", "B": "-1", "C": "0", "D": "2" },
      "correct_answer": "C"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "If p/q is a rational, then p/q × 0 = ?",
      "options": { "A": "p/q", "B": "0", "C": "1", "D": "q/p" },
      "correct_answer": "B"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "The sum of a rational and its additive inverse is: ➕",
      "options": {
        "A": "0",
        "B": "1",
        "C": "The number itself",
        "D": "Reciprocal"
      },
      "correct_answer": "A"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "Which property is illustrated? (a/b + c/d) + e/f = a/b + (c/d + e/f) for rationals. 🧮",
      "options": {
        "A": "Commutative of addition",
        "B": "Associative of addition",
        "C": "Distributive",
        "D": "Closure"
      },
      "correct_answer": "B"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "If the additive inverse of x is -5/8, what is x? 🔍",
      "options": { "A": "5/8", "B": "-5/8", "C": "8/5", "D": "-8/5" },
      "correct_answer": "A"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "For rationals a, b, c, a × (b + c) = a×b + a×c. This is: 📐",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Distributive",
        "D": "Identity"
      },
      "correct_answer": "C"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "The multiplicative inverse of -1/3 is: 🔁",
      "options": { "A": "3", "B": "-3", "C": "1/3", "D": "-1/3" },
      "correct_answer": "B"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "Which is not always true for rationals p and q? 🤔",
      "options": {
        "A": "p + q = q + p",
        "B": "p - q = q - p",
        "C": "p × q = q × p",
        "D": "p × 1 = p"
      },
      "correct_answer": "B"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "If a/b and c/d are rationals, then a/b - c/d = ? ➖",
      "options": {
        "A": "c/d - a/b",
        "B": "(ad - bc)/bd",
        "C": "(bc - ad)/bd",
        "D": "a/d - b/c"
      },
      "correct_answer": "B"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "The rational number that is equal to its additive inverse is: ⚖️",
      "options": { "A": "0", "B": "1", "C": "-1", "D": "No such number" },
      "correct_answer": "A"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "If the product of two rationals is 1, they are _ of each other.",
      "options": {
        "A": "additive inverses",
        "B": "multiplicative inverses",
        "C": "equal",
        "D": "reciprocals"
      },
      "correct_answer": "D"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "Simplify using properties: 2/5 × (-3/7) - 1/6 × 3/7 + 1/14 × 2/5 🧩",
      "options": {
        "A": "-3/14",
        "B": "-1/7",
        "C": "1/14",
        "D": "2/7"
      },
      "correct_answer": "A"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "Which statement is false? ❌",
      "options": {
        "A": "Subtraction is commutative for rationals.",
        "B": "Addition is associative for rationals.",
        "C": "Multiplication is distributive over addition.",
        "D": "Every rational has an additive inverse."
      },
      "correct_answer": "A"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "The multiplicative inverse of a negative rational is: 📉",
      "options": {
        "A": "Positive",
        "B": "Negative",
        "C": "Zero",
        "D": "Depends"
      },
      "correct_answer": "B"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "If (3/4) × (x) = 1, then x is the _ of 3/4.",
      "options": {
        "A": "additive inverse",
        "B": "reciprocal",
        "C": "negative",
        "D": "double"
      },
      "correct_answer": "B"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "Find x if (5/9) + x = 0",
      "options": { "A": "9/5", "B": "-5/9", "C": "5/9", "D": "-9/5" },
      "correct_answer": "B"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "For rational numbers, division is _ over addition.",
      "options": {
        "A": "distributive",
        "B": "associative",
        "C": "commutative",
        "D": "not distributive"
      },
      "correct_answer": "D"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "The rational number which is its own reciprocal is/are: 🔄",
      "options": { "A": "1", "B": "-1", "C": "Both 1 and -1", "D": "0" },
      "correct_answer": "C"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "If p, q, r are rationals and p × (q - r) = 0, then: 🤨",
      "options": {
        "A": "p=0",
        "B": "q=r",
        "C": "p=0 or q=r",
        "D": "Always false"
      },
      "correct_answer": "C"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "Which property justifies: (-7/8) × 1 = -7/8? ✅",
      "options": {
        "A": "Commutative",
        "B": "Multiplicative identity",
        "C": "Associative",
        "D": "Distributive"
      },
      "correct_answer": "B"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "The sum of a rational and its reciprocal is 2. The number could be: 🎯",
      "options": { "A": "1", "B": "-1", "C": "2", "D": "1/2" },
      "correct_answer": "A"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "If a/b and c/d are multiplicative inverses, then a/b × c/d = ? ✖️",
      "options": { "A": "0", "B": "1", "C": "-1", "D": "a/d" },
      "correct_answer": "B"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "For any non-zero rational x, (1/x) is called its: 📛",
      "options": {
        "A": "Additive inverse",
        "B": "Multiplicative inverse",
        "C": "Negative",
        "D": "Opposite"
      },
      "correct_answer": "B"
    },
    {
      "id": 41,
      "difficulty": "hard",
      "question": "If a, b, c are rationals and a × b = a × c, then what can we conclude? 🤯",
      "options": {
        "A": "b = c always",
        "B": "a = 0 or b = c",
        "C": "a = 1",
        "D": "Nothing"
      },
      "correct_answer": "B"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "The property used in: (2/3 + -5/7) + 1/4 = 2/3 + (-5/7 + 1/4) is? 🔗",
      "options": {
        "A": "Commutative",
        "B": "Associative",
        "C": "Closure",
        "D": "Distributive"
      },
      "correct_answer": "B"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "Find the value of x if (x + 5/9) is the additive inverse of (2/3 - 1/6). 🧮",
      "options": { "A": "-19/18", "B": "-1/18", "C": "1/18", "D": "19/18" },
      "correct_answer": "A"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "If p/q and r/s are two rationals (q,s ≠ 0), then p/q ÷ r/s = ? ➗",
      "options": { "A": "pr/qs", "B": "ps/qr", "C": "qr/ps", "D": "qs/pr" },
      "correct_answer": "B"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "Which rational number satisfies: Its additive inverse equals its multiplicative inverse? ⚖️",
      "options": {
        "A": "1",
        "B": "-1",
        "C": "Both 1 and -1",
        "D": "No rational"
      },
      "correct_answer": "D"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "For a non-zero rational a, what is (1/a)⁻¹? 🔁",
      "options": { "A": "a", "B": "1/a", "C": "-a", "D": "-1/a" },
      "correct_answer": "A"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "If the sum of a rational and its reciprocal is 2.5, what is the number? 🤔",
      "options": {
        "A": "2 or 1/2",
        "B": "3 or 1/3",
        "C": "4 or 1/4",
        "D": "No such rational"
      },
      "correct_answer": "A"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "Simplify using distributive: 3/5 × (7/9 - 2/3) + 3/5 × 4/9",
      "options": { "A": "1/3", "B": "1/5", "C": "7/15", "D": "11/45" },
      "correct_answer": "A"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "If x and y are rationals such that x + y = x, then y must be: 🔍",
      "options": {
        "A": "0",
        "B": "1",
        "C": "Additive inverse of x",
        "D": "Reciprocal of x"
      },
      "correct_answer": "A"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "The rational number which when multiplied by -5/12 gives the product as 1 is: 🎁",
      "options": { "A": "12/5", "B": "-12/5", "C": "5/12", "D": "-5/12" },
      "correct_answer": "B"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "For rational numbers, if a × b = 0, then: ⚠️",
      "options": {
        "A": "a=0",
        "B": "b=0",
        "C": "a=0 or b=0",
        "D": "Both must be 0"
      },
      "correct_answer": "C"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "Which of the following is not a property of rational numbers? 🚫",
      "options": {
        "A": "Commutativity for subtraction",
        "B": "Associativity for multiplication",
        "C": "Distributivity of multiplication over addition",
        "D": "Existence of additive identity"
      },
      "correct_answer": "A"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Find a rational x such that its reciprocal is 2 less than itself. 🧩",
      "options": {
        "A": "2",
        "B": "1/2",
        "C": "-1",
        "D": "No real solution"
      },
      "correct_answer": "D"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "If (a/b)⁻¹ = (c/d)⁻¹, then: 🔄",
      "options": {
        "A": "a/b = c/d",
        "B": "a/b = -c/d",
        "C": "ad = bc",
        "D": "a=c and b=d"
      },
      "correct_answer": "A"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "The product of a non-zero rational and its multiplicative inverse is always positive. True or False? 🎯",
      "options": {
        "A": "True",
        "B": "False",
        "C": "Sometimes true",
        "D": "Cannot say"
      },
      "correct_answer": "A"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "If p, q are rationals and p × q = p, and p ≠ 0, then q must be: 🔎",
      "options": {
        "A": "0",
        "B": "1",
        "C": "Reciprocal of p",
        "D": "Additive inverse of p"
      },
      "correct_answer": "B"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "Simplify: [ (2/3) × ( (-4/5) + (7/10) ) ] using distributive property.",
      "options": { "A": "-1/15", "B": "1/15", "C": "-2/15", "D": "2/15" },
      "correct_answer": "A"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "For any rational a, a ÷ 1 = ?",
      "options": { "A": "1", "B": "0", "C": "a", "D": "1/a" },
      "correct_answer": "C"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "The rational number that is equal to its negative is: ➖",
      "options": { "A": "1", "B": "-1", "C": "0", "D": "No such number" },
      "correct_answer": "C"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "If x and y are two different rationals, which is always true? ✅",
      "options": {
        "A": "x + y = y + x",
        "B": "x - y = y - x",
        "C": "x ÷ y = y ÷ x",
        "D": "x + 0 = y + 0"
      },
      "correct_answer": "A"
    }
  ]
}