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Rational Numbers MATHS - Rational Numbers

Gujarat Board (GSEB) - STD 8 - MATHS (GSEB - English Medium). 78 questions in this chapter.

Question types

Rational Numbers question types

78 questions across 9 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

78
Questions
9
Question groups
5
Question types
Sample Questions

Rational Numbers questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q. [1 Marks Each]1 Mark
One (1) is
  • A
    the identity for addition of rational numbers.
  • B
    the identity for subtraction of rational numbers.
  • ✓
    the identity for multiplication of rational numbers.
  • D
    the identity for division of rational numbers.

Answer: C.

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Q 2M.C.Q. [1 Marks Each]1 Mark
Zero (0) is
  • ✓
    the identity for addition of rational numbers.
  • B
    the identity for subtraction of rational numbers.
  • C
    the identity for multiplication of rational numbers.
  • D
    the identity for division of rational numbers.

Answer: A.

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Q 3M.C.Q. [1 Marks Each]1 Mark
Which of the following is not true?
  • A
    Rational numbers are closed under addition.
  • B
    Rational numbers are closed under subtraction.
  • C
    Rational numbers are closed under multiplication.
  • ✓
    Rational numbers are closed under division.

Answer: D.

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Q 4M.C.Q. [1 Marks Each]1 Mark
Which of the following is an example of distributive property over addition for rational number?
  • A
    $\frac{-5}{4} \times\left(\frac{6}{17}+\frac{15}{9}\right)=\left(\frac{6}{17}+\frac{15}{9}\right) \times\left(\frac{-5}{4}\right)$
  • ✓
    $\frac{2}{3} \times\left(\frac{-7}{18}-\frac{19}{2}\right)=\frac{2}{3} \times\left(\frac{-7}{18}\right)-\frac{2}{3} \times \frac{19}{2}$
  • C
    $\frac{2}{3} \times\left(\frac{-7}{15}+\frac{19}{2}\right)=\frac{2}{3} \times\left(\frac{-7}{18}\right)+\frac{2}{3}+\frac{19}{2}$
  • D
    $\frac{15}{8} \times\left[\frac{6}{17}+\left(\frac{-5}{4}\right)\right]=\frac{15}{8} \times \frac{6}{17}+\left(\frac{-5}{4}\right)$

Answer: B.

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Q 11Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A) If $x+0=0+x=x, x$ is a rational number, then 0 is called the additive inverse of $x$.
Reason (R) Multiplicative inverse of $x$ is $\frac{1}{x}.$
  • A
    Both (A) and (R) are true and (R) is the correct explanation of (A)
  • B
    Both (A) and (R) are true but (R) is not the correct explanation of (A)
  • C
    (A) is true but (R) is false
  • ✓
    (A) is false but (R) is true

Answer: D.

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Q 12Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A) For any three rational numbers $x, y$ and $z,$
$ x+(y \times z)=(x+y) \times(x+z).$
Reason (R) For any three rational numbers $a, b$ and $c$,
$ a(b+c)=a b+a c$
  • A
    Both (A) and (R) are true and (R) is the correct explanation of (A)
  • B
    Both (A) and (R) are true but (R) is not the correct explanation of (A)
  • C
    (A) is true but (R) is false
  • ✓
    (A) is false but (R) is true

Answer: D.

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Q 13Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A) The multiplicative Inverse of $1.6$ is $\frac{5}{8}.$
Reason (R) The multiplicative inverse of any rational number $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q} \neq 0$ is $\frac{\text{-p}}{\text{q}}.$
  • A
    Both (A) and (R) are true and (R) is the correct explanation of (A)
  • B
    Both (A) and (R) are true but (R) is not the correct explanation of (A)
  • ✓
    (A) is true but (R) is false
  • D
    (A) is false but (R) is true

Answer: C.

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Q 162 Marks Questions2 Marks
Tell, what property allows you to compute
$ \frac{1}{3} \times\left(6 \times \frac{4}{3}\right) \text { as }\left(\frac{1}{3} \times 6\right) \times \frac{4}{3} ? $
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Q 182 Marks Questions2 Marks
Name the property used in each of the following
(i) $\left(-\frac{7}{11}\right) \times\left(\frac{-3}{5}\right)=\left(\frac{-3}{5}\right) \times\left(\frac{-7}{11}\right)$
(ii) $\frac{2}{3} \times[\frac{3}{4}+(\frac{-1}{2})]=[(\frac{-2}{3})\times\frac{3}{4}] +[(\frac{-2}{3})\times (\frac{-1}{2})]$
(iii) $\frac{1}{3} +[\frac{4}{9}+(\frac{4}{3})]-[\frac{1}{3}+\frac{4}{9}]+(\frac{-4}{3})$
(iv) $\frac{-2}{7}+0=0+(\frac{-2}{7})=\frac{2}{7}$
(v) $\frac{3}{8} \times1=1\times\frac{3}{8}=\frac{3}{8}$
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Q 203 Marks Question3 Marks
Name the property under multiplication used in each of the following
(i) $\frac{-4}{5} \times 1=1 \times\left(\frac{-4}{5}\right)=-\frac{4}{5}$
(ii) $\frac{-13}{17} \times\left(\frac{-2}{7}\right)=\frac{-2}{7} \times\left(\frac{-13}{17}\right)$
(iii) $\frac{-19}{29} \times\left(\frac{29}{-19}\right)=1$
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Q 213 Marks Question3 Marks
Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.
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Q 223 Marks Question3 Marks
Simplify each of the following by using suitable property. Also, name the properties.
(i) $\left[\frac{1}{2} \times \frac{1}{4}\right]+\left[\frac{1}{2} \times 6\right]$
(ii) $\left[\frac{1}{5} \times \frac{2}{15}\right]-\left[\frac{1}{5} \times \frac{2}{5}\right]$
(iii) $\frac{-3}{5} \times\left[\frac{3}{7}+\left(\frac{-5}{6}\right)\right]$
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Q 233 Marks Question3 Marks
Robin writes the properties of rational numbers as
Property 1 For any two rational number$x$ and $y$,
$ x+y=y+x $
Property 2 For any two rational number $x$ and $y,$
$x-y=y-x$
Property 3 For any two rational number $x$ and $y,$
$x / y=y / x$
Property 4 For any two rational number $x$ and $y,$
$x \times y=y \times x$
Which properties written by Robin are incorrect? Why are they incorrect?
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Q 24MATCH THE FOLLOWING.4 Marks
Match the Column A with Column B
Column AColumn B
(a) Additive inverse of 0 is(i) Division
(b) Rational numbers are not associative for(ii) $\frac{-8}{3}$
(c) The reciprocal of 0 is(iii) 0
(d) Sum of additive inverse and multiplicative inverse of 3(iv) not defined
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Q 25MATCH THE FOLLOWING.4 Marks
Match the Column A with Column B
Column AColumn B
(a) Additive identity of $\frac{4}{5}$ is(i) 1
(b) Additive inverse of $\left(\frac{-3}{-9}\right)$ is(ii) 0
(c) Multiplicative identity of $\left(\frac{3}{8}\right)$ is(iii) $\frac{-5}{6}$
(d) Multiplicative inverse of $-1 \frac{1}{5}$ is(iv) $\frac{-3}{9}$
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Q 364 Mark Question4 Marks
Complete the following table
NumbersAssociative for
AdditionSubstractionMultiplicationDivision
Rational numbers---No
Integers--Yes-
Whole numbersYes---
Natural numbers-No--
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Q 374 Mark Question4 Marks
Complete the following table
NumbersCommutative for
AdditionSubstractionMultiplicationDivision
Rational numbersYes
IntegersNo
Whole numbersYes
Natural numbersNo
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Q 384 Mark Question4 Marks
Fill in the blanks in the following table
Numbers Closed under 
 AdditionSubstractionMultiplicationDivision
Rational numbersYesYes No
Integers Yes No
Whole numbers  Yes 
Natural numbers No  
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