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Vidaara.orgClass 8 · Mathematics
CodeVID-M08-03-PRP-01
Properties of Integers - Assignment
Chapter: Integers & Absolute Value
Topic: Properties of Integers
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Integers are NOT closed under:
  • A.addition
  • B.subtraction
  • C.multiplication
  • D.division
2.
$3\times4=4\times3$ shows the ___ property.
  • A.associative
  • B.commutative
  • C.distributive
  • D.closure
3.
Is subtraction commutative?
  • A.Yes
  • B.No
  • C.Sometimes
  • D.Only positives
4.
The additive identity is:
  • A.$1$
  • B.$0$
  • C.$-1$
  • D.$10$
5.
The multiplicative identity is:
  • A.$0$
  • B.$1$
  • C.$-1$
  • D.$2$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Is $5-3=3-5$?
7.
Name the property: $3\times4=4\times3$.
8.
Are integers closed under division?
9.
The additive inverse of $-7$ is:
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Verify the associativity of addition for $-2,\ 3,\ -5$.
11.
Name the property: $(2\times3)\times4=2\times(3\times4)$.
12.
Show $4\times(-5+2)=4\times(-5)+4\times2$.
13.
Is subtraction associative? Test with $10,\ 5,\ 2$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Verify the distributive property $(-3)\times(4+(-6))=(-3)\times4+(-3)\times(-6)$.
15.
State and illustrate the closure, commutative and associative properties of integers under multiplication.

Answer Key

Section A — Multiple Choice Questions
  1. (D) division
  2. (B) commutative
  3. (B) No
  4. (B) $0$
  5. (B) $1$
Section B — Short Answer (2 marks)
  1. No.
  2. Commutative property.
  3. No.
  4. $7$.
Section C — Short Answer (3 marks)
  1. Both groupings give $-4$.
  2. Associative property.
  3. Both sides $=-12$.
  4. No ($3\ne7$).
Section D — Long Answer (5 marks)
  1. Both sides $=6$.
  2. Closure: $(-2)(3)=-6$; Commutative: $(-2)(3)=(3)(-2)$; Associative: $((-2)(3))(4)=(-2)((3)(4))=-24$.
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