Tag: rational numbers between two rational numbers

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

Find $3$ rational numbers between $0$ and $1$.

  1. $\displaystyle\frac{3}{2},\,\displaystyle\frac{1}{4}$ and $\displaystyle\frac{3}{4}$
  2. $\displaystyle\frac{1}{2},\,\displaystyle\frac{1}{4}$ and $\displaystyle\frac{3}{4}$
  3. $\displaystyle\frac{1}{2},\,\displaystyle\frac{5}{4}$ and $\displaystyle\frac{3}{4}$
  4. $\displaystyle\frac{1}{2},\,\displaystyle\frac{1}{4}$ and $\displaystyle\frac{7}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The mean of $0 $ and $ 1$ is $\cfrac{0+1}{2}=\cfrac{1}{2}$.

The mean of $0 $ and $ \cfrac{1}{2}$ is $\begin{pmatrix}0+\cfrac{1}{2}\end{pmatrix}\div2=\cfrac{1}{2}\div2=\cfrac{1}{2}\times\cfrac{1}{2}=\cfrac{1}{4}$

The mean of $\cfrac{1}{2} $ and $ 1$ is $\begin{pmatrix}\cfrac{1}{2}+1\end{pmatrix}\div2$

$=\begin{pmatrix}\cfrac{1+2}{2}\end{pmatrix}\div2=\cfrac{3}{2}\div2=\cfrac{3}{2}\times\cfrac{1}{2}=\cfrac{3}{4}$.

So, the $3$ rational numbers between $0 $ and $ 1$ are $\cfrac{1}{2},\,\cfrac{1}{4} $ and $ \cfrac{3}{4}$.
Multiple choice maths operations on rational numbers rational numbers on number line rational numbers and their decimal expansions rational numbers between two rational numbers

Write five rational numbers greater than $-2$.

  1. $-\displaystyle\frac{3}{2},\,\displaystyle\frac{-1}{2},\,-1,\,\sqrt5,\,\displaystyle\frac{1}{2}$
  2. $-\displaystyle\frac{3}{2},\,\displaystyle\frac{-1}{2},\,-1,\,0,\,\displaystyle\frac{1}{2}$
  3. $-\displaystyle\frac{3}{2},\,\displaystyle\frac{-1}{2},\,-\sqrt3,\,0,\,\displaystyle\frac{1}{2}$
  4. $-\displaystyle\frac{5}{2},\,\displaystyle\frac{-1}{2},\,-1,\,0,\,\displaystyle\frac{1}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Five rational numbers greater than $-2$ may be taken as: 
$-\displaystyle\frac{3}{2},\,-1,\,\displaystyle\frac{-1}{2},\,0,\,\displaystyle\frac{1}{2}$
There can be many more such rational numbers.

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

There are ..........  rational numbers between two rational numbers. 

  1. infinite

  2. two

  3. one

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

There are infinite rational numbers between two rational numbers.


For example take two fractions  $\dfrac{3}{5},\dfrac{4}{5}$


we can have infinite rationals like $\dfrac{3.1}{5},\dfrac{3.2}{5},\dfrac{3.3}{5}......$  betwen these two given rationals.

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

Which of the following rational numbers lies between $\dfrac {3}{2}$ and $4$ ?

  1. $\dfrac {1}{2}$
  2. $3$
  3. $\dfrac {8}{2}$
  4. $\dfrac {9}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We have to find a rational number between $\dfrac {3}{2}$ and $4$. The L.C.M. of the denominators of both numbers is $2$.
$\therefore \dfrac {3}{2} = \dfrac {3}{2}$ and $4\times \dfrac {2}{2} = \dfrac {8}{2}$.
$\therefore$ From the above given options, only $\dfrac {6}{2}$
i.e. $=3$ lies between $\dfrac {3}{2}$ and $4$.

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

The rational number between $\cfrac{1}{2}$ and $0.6$ is

  1. $\cfrac{1}{4}$
  2. $\cfrac{3}{4}$
  3. $\cfrac{21}{40}$
  4. $\cfrac{33}{100}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\dfrac{1}{2}=0.5$

$\therefore 0.5$ and $0.6$ can be written as 
$\dfrac{5}{10}$ and $\dfrac{6}{10}$
Multiplying the denominator and numerator by $4$ we get,
$\dfrac{5}{10}\times 4=\dfrac{20}{40}$ and
$\dfrac{6}{10}\times 4=\dfrac{24}{40}$
Number between $\dfrac{20}{40}$ and $\dfrac{24}{40}$ is $\dfrac{21}{40}$

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

If $\frac {4+3\sqrt 5}{\sqrt 5}=a+b\sqrt 5$ then, the value of b is

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

$\frac {4+3\sqrt 5}{\sqrt 5}=a+b\sqrt 5$
$\frac {(4+3\sqrt 5)\sqrt 5}{\sqrt 5\times \sqrt 5}=\frac {4\sqrt 5+15}{5}=\frac {4\sqrt 5}{5}+\frac {15}{5}$
$=3+\frac {4\sqrt 5}{5}$
Clearly, $a=3$
$b=\frac {4}{5}$.

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

There exists ....... number of rational numbers between $\dfrac {2}{5}$ and $\dfrac {4}{5}.$

  1. $0$
  2. $1$
  3. $5$

  4. infinite
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

There exists infinite number of rational numbers between any two rational numbers. i.e. in this case between $\dfrac {2}{5}$ and $\dfrac {4}{5}$.

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

Which of the following numbers lies between $2\dfrac {1}{7}$ and $3\dfrac {1}{7}$?

  1. $\dfrac {37}{7}$
  2. $\dfrac {14}{7}$
  3. $\dfrac {37}{14}$
  4. $2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$Mean = \dfrac{\left (\dfrac {15}{7} + \dfrac {22}{7}\right )}{2} = \left (\dfrac {15 + 22}{7}\right ) \times \dfrac {1}{2} = \dfrac {37}{7}\times \dfrac {1}{2}$
$= \dfrac {37}{14}$

Mean of two numbers always lies between the two numbers.
So, answer is option $C.$