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Vidaara.orgClass 8 · Mathematics
CodeVID-M08-01-INT-01
Introduction to Rational Numbers - Assignment
Chapter: Rational Numbers
Topic: Introduction to Rational Numbers
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.
A rational number is of the form $\tfrac{p}{q}$ where:
  • A.$q=0$
  • B.$q\ne0$
  • C.$p=0$
  • D.$p\ne0$
2.
The additive identity is:
  • A.$1$
  • B.$0$
  • C.$-1$
  • D.$\tfrac12$
3.
The multiplicative identity is:
  • A.$0$
  • B.$1$
  • C.$-1$
  • D.$2$
4.
The additive inverse of $\tfrac35$ is:
  • A.$\tfrac53$
  • B.$-\tfrac35$
  • C.$-\tfrac53$
  • D.$\tfrac35$
5.
The reciprocal of $\tfrac27$ is:
  • A.$-\tfrac27$
  • B.$\tfrac72$
  • C.$\tfrac27$
  • D.$-\tfrac72$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Write the additive inverse of $-\tfrac49$.
7.
Write the reciprocal of $-\tfrac53$.
8.
Is $7$ a rational number?
9.
Name the property: $a+b=b+a$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Verify the commutativity of addition for $\tfrac12$ and $\tfrac13$.
11.
Find the additive inverse and the reciprocal of $-\tfrac{8}{11}$.
12.
Which rational number (other than $1$) is its own reciprocal?
13.
Name the property shown by $\tfrac23\times1=\tfrac23$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Verify the distributive property $a\times(b+c)=a\times b+a\times c$ for $a=\tfrac12,\ b=\tfrac23,\ c=\tfrac16$.
15.
State the closure, commutative, associative and distributive properties of rational numbers, with one example each.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $q\ne0$
  2. (B) $0$
  3. (B) $1$
  4. (B) $-\tfrac35$
  5. (B) $\tfrac72$
Section B — Short Answer (2 marks)
  1. $\tfrac49$.
  2. $-\tfrac35$.
  3. Yes ($\tfrac71$).
  4. Commutative property.
Section C — Short Answer (3 marks)
  1. Both give $\tfrac56$.
  2. Additive inverse $\tfrac{8}{11}$; reciprocal $-\tfrac{11}{8}$.
  3. $-1$.
  4. Multiplicative identity.
Section D — Long Answer (5 marks)
  1. Both sides $=\tfrac{5}{12}$.
  2. Closure: $\tfrac12+\tfrac13=\tfrac56$; Commutative: $\tfrac14+\tfrac34=\tfrac34+\tfrac14$; Associative: $(\tfrac12+\tfrac13)+\tfrac16=\tfrac12+(\tfrac13+\tfrac16)$; Distributive: $\tfrac12(\tfrac23+\tfrac16)=\tfrac12\cdot\tfrac23+\tfrac12\cdot\tfrac16$.
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