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Properties Quiz - CBSE Class 7 Mathematics

Free practice quiz: Properties (CBSE Class 7 Mathematics). 16 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 16 multiple-choice questions on Properties, and 16 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Closure, Commutative and Associative Properties

  • Adding, subtracting or multiplying two integers always gives an integer. This is the closure property.
  • Commutative: changing the order of two integers does not change their sum or product.
  • Associative: changing the grouping of three integers does not change their sum or product.
Closure
\[p, q \in \mathbb{Z} \Rightarrow p + q,\ p - q,\ p \times q \in \mathbb{Z}\]
Commutative
\[p + q = q + p,\quad p \times q = q \times p\]
Associative
\[(p + q) + r = p + (q + r),\quad (p \times q) \times r = p \times (q \times r)\]

Common mistake: Thinking subtraction is commutative. In general p - q is not equal to q - p for integers.

Identities and Additive Inverse

  • Zero is the additive identity because adding zero leaves an integer unchanged. One is the multiplicative identity.
  • Every integer x has an additive inverse -x. Their sum is zero.
  • Any integer multiplied by zero gives zero.
Additive identity
\[x + 0 = 0 + x = x\]
Multiplicative identity
\[x \times 1 = 1 \times x = x\]
Additive inverse
\[x + (-x) = (-x) + x = 0\]
Multiplication by zero
\[x \times 0 = 0 \times x = 0\]

Common mistake: Mixing up the identities: zero is the identity for addition and one is the identity for multiplication.

Subtraction Means Adding the Inverse

  • To subtract an integer, add its additive inverse instead.
  • Subtracting a negative integer is the same as adding the positive integer.
  • "Subtract p from q" means start with q and take away p, so write q - p.
Subtraction rule
\[p - q = p + (-q)\]
Subtracting a negative
\[p - (-q) = p + q\]
Subtract p from q
\[q - p\]

Common mistake: Writing "subtract p from q" as p - q. The number after "from" comes first.

Sign Rules for Multiplication

  • Two integers with the same sign give a positive product. Two integers with different signs give a negative product.
  • Multiplying any integer by -1 gives its additive inverse.
  • A nonzero integer times itself is always positive, because both factors have the same sign.
Negative times negative
\[(-p) \times (-q) = p \times q\]
Negative times positive
\[(-p) \times q = p \times (-q) = -(p \times q)\]
Multiplying by -1
\[(-1) \times n = -n\]
Square of a negative
\[(-n) \times (-n) = n \times n = n^2\]

Common mistake: Thinking a negative times a negative is negative. The product of two negative integers is always positive.

Distributive Property and Operation Order

  • Multiplication distributes over addition and subtraction. Multiply the outside integer with each term inside the bracket.
  • When there are no brackets, do multiplication before addition or subtraction.
Distributive over addition
\[x \times (y + z) = x \times y + x \times z\]
Distributive over subtraction
\[x \times (y - z) = x \times y - x \times z\]

Common mistake: Working left to right and adding before multiplying. In p + q × r, multiply q × r first, then add p.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is the result when you add an integer to its additive inverse?

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    Answer: B. Zero

    The sum of an integer and its additive inverse is always zero because they are opposite numbers.

  2. What is the value of (-7) - (-3)?

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    Answer: A. -4

    Subtracting a negative integer is the same as adding its positive, thus: (-7) + 3 = -4.

  3. Subtract: (5) from (-5).

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    Answer: A. -10

    (5) from (-5) results in: (-5) - 5 = -10.

  4. Solve: (-9) + [6 + (-4)].

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    Answer: A. -7

    First compute inside the brackets: 6 + (-4) = 2; then, (-9) + 2 = -7.

  5. Simplify the expression: 5 + (-3) * 2.

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    Answer: C. -1

    Apply order of operations: 5 + (-3) * 2 = 5 - 6 = -1.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. What property is shown by the equation a + (-a) = 0?
  2. When two integers are added, the result is an integer. This is known as which property?
  3. Which property explains the equation: (-2) + (7) = 7 + (-2)?
  4. Determine the result: (-3) * (-4).
  5. Use the distributive property to simplify: 3 * (5 + (-2)).
  6. What is the additive identity for integers?
  7. What is the result when multiplying any integer by zero?
  8. Determine: (-2) * [3 + (-1)] using the distributive property.
  9. Choose the property shown: -1 * a = -a.
  10. Find the identity element for multiplication with integers.
  11. Explain why (-a)^2 is always positive for any integer a.

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