Tag: fractions, decimals and rational numbers

Questions Related to fractions, decimals and rational numbers

Which of the following represents a rational number between $-6$ and $-7$?

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

  1. $\dfrac {-6 - 7}{2}$

  2. $\dfrac {-6 + 7}{2}$

  3. $\dfrac {6 + 7}{2}$

  4. $-6 - 7$

Show answer
Correct Option: A
Explanation:

Mean $= \dfrac {(-6) + (-7)}{2} = \dfrac {-6 -7}{2}$.

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

A rational number between $\dfrac {-9}{10}$ and $\dfrac {4}{5}$ is:

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

  1. $\left (\dfrac {-9}{10} + \dfrac {4}{5}\right ) \times \dfrac {1}{2}$

  2. $\left (\dfrac {-9}{10} - \dfrac {4}{5}\right ) + \dfrac {1}{2}$

  3. $\left (\dfrac {-9}{10} + \dfrac {4}{5}\right ) \times 2$

  4. All above are correct

Show answer
Correct Option: A
Explanation:
Mean of two numbers always lies between the two numbers.

Mean 

$= \dfrac{\left (\dfrac {-9}{10} + \dfrac {4}{5}\right )}{2}$

$= \left (\dfrac {-9}{10} + \dfrac {4}{5}\right )\times \dfrac {1}{2}$.

So, answer is option $A.$

Which of the following rational numbers lies between $\dfrac {3}{4}$ and $\dfrac {13}{8}$?

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

  1. $\dfrac {11}{16}$

  2. $\dfrac {12}{16}$

  3. $\dfrac {19}{16}$

  4. $\dfrac {26}{16}$

Show answer
Correct Option: C
Explanation:

$Mean = \dfrac{\left (\dfrac {3}{4} + \dfrac {13}{8}\right )}{2} = \dfrac {6 + 13}{8} \times \dfrac {1}{2} = \dfrac {19}{16}$.

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

Which of the following rational number lies between $\dfrac {4}{9}$ and $\dfrac {4}{5}$?

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

  1. $-1$

  2. $\dfrac {28}{45}$

  3. $0$

  4. $1$

Show answer
Correct Option: B
Explanation:

$Mean = \dfrac{\left (\dfrac {4}{9} + \dfrac {4}{5}\right )}{2} = \left (\dfrac {20 + 36}{45}\right ) \times \dfrac {1}{2} = \dfrac {56}{45}\times \dfrac {1}{2}$
$= \dfrac {28}{45}$

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

What fraction lies exactly halfway between $\dfrac{2}{3}$ and $\dfrac{3}{4}$?

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

  1. $\dfrac{3}{5}$

  2. $\dfrac{5}{6}$

  3. $\dfrac{7}{12}$

  4. $\dfrac{9}{16}$

  5. $\dfrac{17}{24}$

Show answer
Correct Option: E
Explanation:

Consider $3 \times 4 = 12$, so 
$\dfrac 23 = \dfrac{8}{12}$


$\dfrac 34 = \dfrac{9}{12}$

Multiplying the numerator and denominator by $2$:
$\dfrac{16}{24}$ and $\dfrac{18}{24}$.

The mid point is $\dfrac{17}{24}$

Hence option $E$ is correct.

Choose the rational number, which does not lie, between the rational numbers, $\dfrac{-2}{3}$ and $\dfrac{-1}{5}$

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

  1. $\dfrac{-3}{10}$

  2. $\dfrac{3}{10}$

  3. $\dfrac{-1}{4}$

  4. $\dfrac{-7}{20}$

Show answer
Correct Option: B
Explanation:

The given rational numbers $-\dfrac { 2 }{ 3 }$ and $-\dfrac { 1 }{ 5 }$ are negative rational numbers because the numerator and denominator of both the rational numbers are of opposite signs that is the numerator of both the integers is negative while the denominators are positive.


Therefore, none of the positive rational number can lie between the given negative rational numbers $-\dfrac { 2 }{ 3 }$ and $-\dfrac { 1 }{ 5 }$.


Hence, $\dfrac { 3 }{ 10 }$ does not lie between the rational numbers $-\dfrac { 2 }{ 3 }$ and $-\dfrac { 1 }{ 5 }$.