Tag: rational numbers between two rational numbers

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Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers
Among the following 
$-\frac{3}{2},-1,3,0,\frac{1}{2}$
find the rational numbers less than $2.$
  1. $0$
  2. $-\frac{3}{2}$
  3. $-1$
  4. $\frac{1}{2}$
Reveal answer Fill a bubble to check yourself
A,B,C,D Correct answer
Explanation

$\dfrac{-3}{2},-1,3,0,\dfrac{1}{2}$


$-1.5,-1,3,0,0.5$


$\implies $ Among five rational numbers $-1.5,-1,0,0.5$ are lesser than $2$ expect $3$.


All options are correct.

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

Choose the rational number which does not lie between rational numbers $-\dfrac{2}{5}$ and $-\dfrac{1}{5}$.

  1. $-\dfrac{1}{4}$
  2. $-\dfrac{3}{10}$
  3. $\dfrac{3}{10}$
  4. $-\dfrac{7}{20}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a rational number to lie between $\dfrac{-2}{5}$ and $\dfrac{-1}{5}$,it should be less than $\dfrac{-1}{5}$ and greater than $\dfrac{-2}{5}$.
Now,$\dfrac{3}{10}$ is not less than $\dfrac{-1}{5}$.
So,$\dfrac{3}{10}$ does not lie between $\dfrac{-1}{5}$ and $\dfrac{-2}{5}$.

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

Choose the rational number which does not lie between rational numbers $\dfrac{3}{5}$ and $\dfrac{2}{3}$.

  1. $\dfrac{46}{75}$
  2. $\dfrac{47}{75}$
  3. $\dfrac{49}{75}$
  4. $\dfrac{50}{75}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

All the options have denominator $75$. Hence, let us convert into equivalent fractions having denominator $75$. 
$\dfrac{3}{5} $ $=\dfrac{3\times 15}{5\times 15} $ $=\dfrac{45}{75}$

$\dfrac{2}{3}$ $=\dfrac{2\times 25}{3\times 25}$ $=\dfrac{50}{75}$

Hence, $\dfrac{50}{75}$ does not lie between the given numbers.

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

Rationalising the denominator of $\dfrac {5}{\sqrt 3-\sqrt 5}$ is -

  1. $(\frac {5}{2}(\sqrt 3+\sqrt 5)$
  2. $(-\frac {5}{2}(\sqrt 3+\sqrt 5)$
  3. $(\frac {5}{2}(\sqrt 3-\sqrt 5)$
  4. $(-\frac {5}{2}(\sqrt 3-\sqrt 5)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

here, $\dfrac {5}{\sqrt 3-\sqrt 5}$

$=\dfrac {5}{\sqrt 3-\sqrt 5}\times \dfrac {\sqrt 3+\sqrt 5}{\sqrt 3+\sqrt 5}$

$=\dfrac {5(\sqrt 3+\sqrt 5)}{3-5}$


$=-\dfrac {5}{2}(\sqrt 3+\sqrt 5)$

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

A train of length 180 m crosses a man standing on a platform in 12 seconds and cross another train coming from opposite direction in 12 sec. If the second train running at 2/3 rd speed of the firstthen find the length of the second train?

  1. 56

  2. 120

  3. 20

  4. 44
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Length of the first train$=180m$


 Time taken by  the train to cross the man standing on the platform$=12s$


Speed of the first train$=\dfrac{180}{12}$

                                      $=15m/s$

Speed of the second train$=\dfrac{2}{3}\times15$

                                            $=10m/s$

Relative speed$=15+10$

                          $=25m/s$
 
Let the length of the train be $y$ metres.

$Distance =Speed\times time$

$y+180=25\times12$

$y+180=300$

$y=300-180$
$y=120$
So, the length of the second train$=120m$

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

 Rational numbers between $\displaystyle \frac{3}{8}$ and $\displaystyle \frac{7}{12}$ are

  1. $\displaystyle \frac{3}{8}, \frac{41}{96}, \frac{23}{48}, \frac{7}{12}$
  2. $\displaystyle \frac{3}{8}, \frac{41}{196}, \frac{23}{48}, \frac{7}{12}$
  3. $\displaystyle \frac{3}{8}, \frac{41}{96}, \frac{23}{148}, \frac{7}{12}$

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

b)}{2} $
So, a rational number between $\dfrac {3}{8} $ and $ \dfrac {7}{12}$

$ = \dfrac {\dfrac {3}{8} + \dfrac {7}{12}}{2} = \dfrac {23}{48} $

Now, another rational number between $ \dfrac {3}{8} $ and $ \dfrac {23}{48} $

$= \dfrac {\dfrac {3}{8} + \dfrac {23}{48}}{2} = \dfrac {41}{96} $ 

Hence, required two rational numbers between $\dfrac {3}{8} $ and $ \dfrac {7}{12} $ are $\dfrac {3}{8} ,\dfrac {41}{96}, \dfrac {23}{48}, \dfrac {7}{12}$

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

__________ are rational numbers between between 5 and -2.

  1. $\displaystyle 5, \frac{33}{4},\ \frac{3}{2}, -\frac{1}{4}, -2$
  2. $\displaystyle \frac{13}{4},\ \frac{3}{2}, -\frac{1}{4} $
  3. $\displaystyle 5, \frac{13}{4},\ \frac{13}{2}, -\frac{1}{4}, -2$

  4. none of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A rational number between two numbers $ a $ and $ b = \dfrac {(a + b)}{2} $

So, a rational number between $ 5 $ and $ - 2 = \dfrac

{( 5 - 2 )}{2} = \dfrac {3}{2} $


Now, another rational number between $ 5 $ and $ \dfrac {3}{2} =

\dfrac {( 5 + \dfrac {3}{2})}{2} = \dfrac {13}{4} $

Another rational number between $ \dfrac {3}{2} $ and $ -2 =

\dfrac {( \dfrac {3}{2}) - 2}{2} = -\dfrac {1}{4} $

 $ \therefore \dfrac {13}{4},  \dfrac {3}{2}, - \dfrac {1}{4} $  are the rational numbers between $ 5 $ and $ -2 $

Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

________ are rational numbers between $\displaystyle \frac{1}{3}$ and $\displaystyle \frac{1}{4}$

  1. $\displaystyle \frac{1}{3}, \frac{7}{64}, \frac{13}{48}, \frac{1}{4}$
  2. $\displaystyle \frac{1}{3}, \frac{7}{24}, \frac{13}{48}, \frac{1}{4}$
  3. $\displaystyle \frac{1}{3}, \frac{7}{24}, \frac{13}{68}, \frac{1}{4}$

  4. none of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A

rational number between two numbers $ a $ and $ b = \frac {(a +

b)}{2} $

So, a

rational number between $\frac {1}{3} $ and $ \frac {1}{4} = \frac {(\frac {1}{3} + \frac {1}{4})}{2} = \frac {7}{24} $

Now, another rational number between $ \frac {7}{24} $ and $ \frac {1}{4} = \frac {(\frac {7}{24} + \frac {1}{4})}{2} = \frac {13}{48} $



Hence, required two rational numbers between $\frac {1}{3} $ and $ \frac {1}{4} $ are $\frac {1}{3} ,\frac {7}{24}, \frac {13}{48}, \frac {1}{4}$