Tag: operations on rational numbers

Questions Related to operations on rational numbers

Arrange in ascending order $\sqrt [ 6 ]{ 7 } ,\sqrt [ 4 ]{ 3 } ,\sqrt [ 12 ]{ 48 } $

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\sqrt [ 4 ]{ 3 } ,\sqrt [ 12 ]{ 48 } ,\sqrt [ 6 ]{ 7 } $

  2. $\sqrt [ 12 ]{ 48 } ,\sqrt [ 4 ]{ 3 } ,\sqrt [ 6 ]{ 7 } $

  3. $\sqrt [ 6]{ 7 } ,\sqrt [ 12 ]{ 48 } ,\sqrt [ 4 ]{ 3 } $

  4. $None\ of\ these$

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Correct Option: A

The ascending order of minimum values of the function  $P:\sin ^{ -1 }{ x } -\cos ^{ -1 }{ x } $, $Q=\tan ^{ -1 }{ x } -\cot ^{ -1 }{ x } $, $R=\sec ^{ -1 }{ x } -\csc ^{ -1 }{ x } $

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. P, Q, R

  2. P, R, Q

  3. Q, P, R

  4. Q, R, P

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Correct Option: A

The value of $1+\dfrac{1}{4\times 3}+\dfrac{1}{4\times 3^2}+\dfrac{1}{4\times 3^3}+\dfrac{1}{4\times 3^4}$ is?

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\dfrac{121}{108}$

  2. $\dfrac{3}{2}$

  3. $\dfrac{31}{2}$

  4. $\dfrac{91}{81}$

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Correct Option: D
Explanation:

$1+\dfrac{1}{4\times 3}+\dfrac{1}{4\times 3^2}+\dfrac{1}{4\times 3^3}+\dfrac{1}{4\times 3^4}$


$=1+\dfrac{1}{12}+\dfrac{1}{36}+\dfrac{1}{108}+\dfrac{1}{324}$


$=\dfrac{324+27+9+3+1}{324}$

$=\dfrac{364}{324}$

$=\dfrac{91}{81}$

Hence, the answer is $\dfrac{91}{81}.$

The ascending order of $\sqrt { 2 } ,\sqrt [ 3 ]{ 4 } ,\sqrt [ 4 ]{ 6 } $ is

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\sqrt { 2 } ,\sqrt [ 3 ]{ 4 } ,\sqrt [ 4 ]{ 6 } $

  2. $\sqrt { 2 } ,\sqrt [ 4 ]{ 6 } ,\sqrt [ 3 ]{ 4 } $

  3. $\sqrt [ 3 ]{ 4 }, \sqrt {2},\sqrt [ 4 ]{ 6 } $

  4. $\sqrt [ 4 ]{ 6 },\sqrt [ 3 ]{ 4 } ,\sqrt {2}$

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Correct Option: A

Find the rational numbers between the following numbers. 

$-0.2$ and $-0.22$.

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $-0.210 > -0.211 > -0.312 > -0.213 > -0.314 > 0.220$

  2. $-0.210 > -0.211 > -0.212 > -0.213 > -0.314 > 0.220$

  3. $-0.210 > -0.211 > -0.312 > -0.213 > -0.214 > 0.220$

  4. $-0.210 > -0.211 > -0.212 > -0.213 > -0.214 > 0.220$

Show answer
Correct Option: D
Explanation:

Rational number between two numbers $ a $ and $ b = \dfrac {(a +

b)}{2} $

So, a rational number between $ -0.2 $ and $ - 0.22 = \dfrac {(-0.2 - 0.22)}{2} = -0.21 $

Now, another rational number between $ -0.21 $ and $ - 0.22 = \dfrac {(-0.21 - 0.22)}{2} = -0.215 $

rational number between $ -0.215 $ and $ - 0.21 = \dfrac {(-0.215 - 0.21)}{2} = -0.212 $ 

rational number between $ -0.215 $ and $ - 0.212 = \dfrac {(-0.215 - 0.212)}{2} = -0.213 $ 

rational number between $ -0.215 $ and $ - 0.213 = \dfrac {(-0.215 - 0.213)}{2} = -0.214 $ 

Similarly,
rational numbers between $ -0.2 $ and $ - 0.22 $ are $-0.210, -0.211 , -0.212, -0.213 , -0.214$ etc

Find the five rational numbers between $-5$ and $-6$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $-5.1 ,-5.2 , -3.3 , -5.4 , -5.5  $

  2. $-5.1 ,-5.2 , -5.3 , -5.4 , -5.5 $

  3. $-5.1 , -6.2 , -5.3 , -5.4 , -5.5 $

  4. $-6.1 , -5.2 , -5.3 , -5.4 , -5.5 $

Show answer
Correct Option: B
Explanation:
$−5>(−5−0.1)=−5.1>−5.2=(−5.1−0.1)>−5.3=(−5.2−0.1)>−5.4\\=(−5.3−0.1)>−5.5=(−5.4−0.1)>...>−6$

$-5>−5.1>−5.2>−5.3>−5.4>−5.5...>−6$

The five rational numbers between $−5$ and $−6$
$-5.1 ,-5.2 , -5.3 , -5.4 , -5.5 $

Which one is in the descending order in the following?

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\displaystyle 6/7, 4/5, 3/4, 7/9$

  2. $\displaystyle 6/7, 4/5, 7/9, 3/4$

  3. $\displaystyle 3/4, 7/9, 4/5, 6/7$

  4. $\displaystyle 7/9, 3/4, 6/7, 4/5$

Show answer
Correct Option: B
Explanation:
Here we have four factors $\dfrac{3}{4},  \dfrac{4}{5},   \dfrac{6}{7},   \dfrac{7}{9}$
LCM of 4, 5, 7 and 9 is 1260
So, 
$\dfrac{3}{4} \times\dfrac{315}{315}$ = $\dfrac{945}{1260}$

$\dfrac{4}{5} \times\dfrac{252}{252}$ = $\dfrac{1008}{1260}$

$\dfrac{6}{7} \times\dfrac{180}{180}$ = $\dfrac{1080}{1260}$

$\dfrac{7}{9} \times\dfrac{140}{140}$ = $\dfrac{980}{1260}$
As, 
1080 > 1008 > 980 > 945
So, $\dfrac{6}{7} > \dfrac{4}{5} >  \dfrac{7}{9} >  \dfrac{3}{4}$

Arrange in descending order:
$1,00,000; 99,999; 9,90,000; 1,10,000$

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $1,00,000; 99,999; 9,90,000; 1,10,000$

  2. $ 1,10,000; 9,90,000; 99,999; 1,00,000$

  3. $ 9,90,000; 99,999; 1,10,000; 1,00,000$

  4. $ 9,90,000; 1,10,000; 1,00,000; 99,999$

Show answer
Correct Option: D
Explanation:

Comparing digits at lakh's place followed by ten thousand's, thousand's, hundred's, ten's and one's place,


We can arrange the given numbers in descending order as 
$9,90,000;\ 1,10,000;\ 1,00,000;\ 99,999$

Arrange the following in descending order.
$\dfrac{5}{2}$, $\dfrac{3}{2}$, $\dfrac{7}{2}$, $\dfrac{9}{5}$, $\dfrac{9}{8}$ 

maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

  1. $\dfrac{7}{2}$, $\dfrac{9}{8}$, $\dfrac{3}{2}$, $\dfrac{9}{5}$, $\dfrac{5}{2}$

  2. $\dfrac{7}{2}$, $\dfrac{5}{2}$, $\dfrac{9}{5}$, $\dfrac{3}{2}$, $\dfrac{9}{8}$

  3. $\dfrac{5}{2}$, $\dfrac{9}{5}$, $\dfrac{3}{2}$, $\dfrac{9}{8}$, $\dfrac{7}{2}$

  4. $\dfrac{9}{8}$, $\dfrac{5}{2}$, $\dfrac{3}{2}$, $\dfrac{7}{2}$, $\dfrac{9}{5}$

Show answer
Correct Option: B
Explanation:

$\cfrac{5}{2},\cfrac{3}{2},\cfrac{7}{2},\cfrac{9}{5},\cfrac{9}{8}$

We know that the number with largest denominator is the smallest one.
And among $\cfrac{5}{2},\cfrac{3}{2},\cfrac{7}{2}$ the one with largest numerator is the largest one.
Among $\cfrac{9}{5}$ and $\cfrac{3}{2},$ $\cfrac{9}{5}$ is larger.
Hence descending order is $\cfrac { 7 }{ 2 } ,\cfrac { 5 }{ 2 } ,\cfrac { 9 }{ 5 } ,\cfrac { 3 }{ 2 } ,\cfrac { 9 }{ 8 }.$

Milk is sold at $Rs\ 10\dfrac {3}{4}$ per liter, Find the cost of $6\dfrac {2}{5}$ liters of milk.

maths operations on rational numbers rational numbers on number line rational numbers and their decimal expansions rational numbers between two rational numbers

  1. $Rs \,107 \dfrac {1}{5}$

  2. $Rs \, 65 \dfrac {2}{5}$

  3. $Rs \, 103 \dfrac {1}{5}$

  4. $Rs \, 68 \dfrac {4}{5}$

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Correct Option: D
Explanation:

Price$=Rs\ 10\dfrac {3}{4}=Rs.\cfrac{43}{4}$ per liter


Price of $6\dfrac {2}{5} l=\cfrac{32}{5}l=Rs.\cfrac{43}{4}\times \cfrac{32}{5}=Rs.\cfrac{344}{5}=Rs.68\cfrac{4}{5}$