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Rational Numbers - Important Questions Model Paper In 8th Maths

Published on: 27/07/2018

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Questions:

Multiple Choice Question

5 x 1 = 5

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

(d)

rational numbers are closed under division

Zero (0) is

(a)

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.

Which of the following statements is always true?

(a)

\(\frac{x-y}{2}\) is a rational number between x and y

(b)

\(\frac{x+y}{2}\) is a rational number between x and y

(c)

\(\frac{x\times y}{2}\) is a rational number between x and y

(d)

\(\frac{x\div y}{2}\) is a rational number between x and y

\(\frac{x+y}{2}\) is a rational number

(a)

between x and y

(b)

less than x and y both

(c)

greater than x and y both

(d)

less than x but greater than y

Three rational numbers lying between\(\frac{-5}{4}\) and \(\frac{1}{2}\)are

(a)

-1, 0 ,\(\frac{4}{3}\)

(b)

\(\frac{-3}{4},\frac{-1}{2},\frac{1}{4}\)

(c)

\(\frac{-3}{4},\frac{4}{3},\frac{1}{4}\)

(d)

\(\frac{-7}{4},-1,0\)

Fill up / 1 Marks

3 x 1 = 3

Numbers	Associative for
Numbers	Addition	Subtraction	Multiplication	Division
Whole numbers	yes	________	_________	________

Numbers	Closed under
Numbers	Addition	Subtraction	Multiplication	Division
Natural numbers	___________	no	___________	__________

Numbers	Closed under
Numbers	Addition	Subtraction	Multiplication	Division
Whole numbers	___________	___________	Yes	__________

Generic 3

8 x 3 = 24

Write five rational numbers between the multiplicative inverse of \(5{1\over5}\) and additive inverse of 1.

10.

Write five rational numbers which are greater than -7

11.

Find five rational numbers between \({1\over4}and\ {1\over2}\)

12.

Find ten rational numbers between \({-2\over5} and {1\over2}\)

13.

Multiply the multiplicative inverse of -2 with its reciprocal.

14.

Solve \(-5+{7\over10}+{3\over7}+(-3)+{5\over14}+{-4\over5}\)

15.

Find using distributivity. \(\{ {9\over16}\times {4\over12} \} +\{ {9\over 16}\times {-3\over 9} \}\)

16.

Find using distributivity. \( \{{7\over5}\times ({-3\over12}) \}+ \{{7\over16}\times {5\over12} \}\)

Generic 2

4 x 2 = 8

17.

Verify that -(-x) = x,for x = \(-13\over17\)

18.

Write the additive inverse of the following \(19\over-6\)

19.

Write the additive inverse of the following \(-5\over9\)

20.

Write the additive inverse of the following \(2\over8\)

Generic 5

2 x 5 = 10

21.

Rearrange suitably and find the sum in each of the following:
\({-5\over7}+{5\over6}+{1\over7}+3+{-13\over6}\)

22.

Find the value of \({x\over y }+xy\) , using appropriate property and name it \(x={1\over3},y={2\over 5}\)

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Answers Key:

Multiple Choice Question

5 x 1 = 5

(d)
rational numbers are closed under division

(a)
the identity for addition of rational numbers

(b)
\(\frac{x+y}{2}\) is a rational number between x and y

(a)
between x and y

(b)
\(\frac{-3}{4},\frac{-1}{2},\frac{1}{4}\)

Fill up / 1 Marks

3 x 1 = 3

()

Numbers	Associative for
Numbers	Addition	Subtraction	Multiplication	Division
Whole numbers	Yes, e.g. 2 +(0+5) =(2 +0)+5 \(\Rightarrow\)7=7, which is true	\(No \ e.g \\ 2-(0-5)\\ \neq (2-0)-5\\ \Rightarrow 7 \neq -3\) which is not true	Yes, e.g.2 x[3 x (-5)] =(2 x3)x(-5) \(\Rightarrow\)2 x[-15]=(6)x(-5) \(\Rightarrow\)-30=- 30, which is true.	No eg \((2\div 3)\div 5\neq 2 \div (3\div5) \\ \Rightarrow ({2\over 3})\div 5\neq2 \div ({3\over 5}) \\ \Rightarrow {2\over 3}\times {1\over 5} \neq 2 \times {5\over 3}\\ \Rightarrow {2\over 15} \neq {10\over 3}\) which is not true

()

Numbers	Closed under
Numbers	Addition	Subtraction	Multiplication	Division
Natural numbers	yes e.g (2+3=5)Natural numbers	no e.g (2-3=-1)Not a Natural numbers	e.g (2x3=6)Natural numbers	no e.g (2\(\div\) 3)Not a Natural numbers

()

Numbers	Closed under
Numbers	Addition	Subtraction	Multiplication	Division
Whole numbers	yes e.g (0+5=5)Whole numbers	No e.g (5-7=-2)Not a Whole numbers	Yes e.g (3x7=21)Whole numbers	No e.g (5\(\div\)8) Not a Whole numbers

Generic 3

8 x 3 = 24

The multiplicative inverse of \(5{1\over5}\) \((={26\over5})\ is\ {5\over26}\)
And the additive inverse of 1 is-1.
Now, on making same denominator, we get
-1 = \({-1\times26\over 26}\)

10.

Five rational numbers greater than -7 are
\({-7\over2},{-7\over3},{-7\over4},{-7\over5},{-7\over6}\)

11.

Converting \(\frac { 1 }{ 4 } \) and \(\frac { 1 }{ 2 } \) rational numbers with the same denominations , we have
\(\frac { 1 }{ 4 } \times \frac { 8 }{ 8 } =\frac { 8 }{ 32 } \) and \(\frac { 1 }{ 2 } \times \frac { 16 }{ 16 } =\frac { 16 }{ 32 } \)
Five rational numbers between \({8\over32}=({1\over4})and{16\over32}=({1\over2})are{9\over32},{10\over32},{11\over32},{12\over32},{13\over32}\)

12.

We have, \({-2\over5}={-2\times4 \over 5\times4}={-8\over20}\)
[multiplying the numerator and denominator both by 4] and \({1\over2}={1\times10 \over 2\times10}={10\over20}\)
Here, difference between 10 and -8 = 10 - (-8) = 18
(i.e. more than 10)
Hence, rational numbers between \({-8\over20}and {10\over20}\) are \({-7\over20},{-6\over20},{-5\over20},{-4\over20},{-3\over20}.{-2\over20},{-1\over20},0,{1\over20},{2\over20}\)

13.

\(1\over4\)

14.

\(-256\over35\)

15.

We have,\(\{ {9\over16}\times {4\over12} \} +\{ {9\over 16}\times {-3\over 9} \} = {9\over16} \times [{4\over12}+({-3\over9})] \)
[by distributivity, taking \( {9\over16}\) as common factor]
\(={9\over16}\times[{4\over12}-{3\over9}]={9\over16}\times[{12-12\over36}]\)
\([\because LCM \ of\ 12\ and \ 9=36]\)
\(={9\over16}\times {0\over36}\)
\(= {9\over16}\times0=0\)

16.

We have, \( \{{7\over5}\times ({-3\over12}) \}+ \{{7\over16}\times {5\over12} \}={7\over5}\times[{-3\over12}+{5\over12}]\)
[by distributivity, taking \({7\over5}\) as common factor]
\(={7\over5}\times[{-3+5 \over 12}]= {7\over5}\times {2\over 12}={7\over30}\)

Generic 2

4 x 2 = 8

17.

We have, x = \(-13\over17\)
\(LHS =-(-x)=-\{-({-13\over17})\}=-\{{13\over17}\}\)
=-\({13\over17}\) = x = RHS
So, - (-x) = x is verified for x = \({13\over17}\).

18.

we have, \(19\over-6\) so, additive inverse of \(19\over-6\) is \(19\over6\)

19.

we have, \(-5\over9\) so, additive inverse of \(-5\over9\) is \(5\over9\)

20.

we have, \(2\over8\) so, additive inverse of \(2\over8\) is \(-2\over8\)

Generic 5

2 x 5 = 10

21.

\(23\over21\)

22.

\({29\over30}\)