Tag: operations on rational numbers

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Questions Related to operations on 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

A rational number between $\dfrac {-2}{3}$ and $\dfrac {1}{2}$ is

  1. $-\dfrac {3}{6}$
  2. $\dfrac {-1}{12}$
  3. $\dfrac {-5}{6}$
  4. $\dfrac {5}{6}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find a rational number between -2/3 and 1/2, we need a value satisfying -2/3 < x < 1/2. Option A: -3/6 = -1/2, which satisfies -2/3 < -1/2 < 1/2. Option B: -1/12 ≈ -0.083 also satisfies the condition, making both A and B technically correct.

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 three rational number between $5$ and $6$ are $ [\displaystyle\frac{21}{4},\frac{22}{4},\frac{23}{4}]$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$5=\frac { 20 }{ 4 } \quad and\quad 6=\frac { 24 }{ 4 } ,\ \frac { 21 }{ 4 } ,\frac { 22 }{ 4 } and\frac { 23 }{ 4 } \quad are\quad three\quad rational\quad numbers\quad lying\quad between\quad 5\quad and\quad 6.\quad \quad \ $

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 lying between $\displaystyle \frac{5}{6}$ and $\displaystyle \frac{6}{7}$ is :

  1. $\displaystyle \frac{1}{2}$
  2. $\displaystyle \frac{15}{21}$
  3. $\displaystyle \frac{35}{42}$
  4. $\displaystyle \frac{71}{84}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The rational number lying between $\displaystyle \frac{5}{6}$ and $\displaystyle \frac{6}{7}$ is
 $\displaystyle \frac{1}{2}\left ( \frac{5}{6}+\frac{6}{7} \right )=\frac{1}{2}\left ( \frac{35+36}{42} \right )=\frac{71}{84}$

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 pair of rational numbers lying between $\displaystyle \frac{1}{4}$ and $\displaystyle -\frac{3}{4}$ is ?

  1. $\displaystyle \frac{262}{1000}$, $\displaystyle \frac{752}{1000}$
  2. $\displaystyle \frac{63}{250}$, $\displaystyle \frac{187}{250}$
  3. $\displaystyle \frac{13}{50}$, $\displaystyle \frac{264}{350}$
  4. $\displaystyle \frac{9}{50}$, $\displaystyle \frac{31}{40}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The rational numbers $\displaystyle \frac{1}{4}$ and $\displaystyle \frac{3}{4}$ can be written
as $\displaystyle \frac{250}{1000}$ and $\displaystyle \frac{750}{1000}$ Therefore $\displaystyle \frac{63}{250}=\frac{252}{1000}$

and $\displaystyle \frac{187}{250}=\frac{748}{1000}$ satisfy this condition

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 $9$ rational numbers between $-\displaystyle\frac{1}{9}\;and\;\displaystyle\frac{1}{5}$.

  1. $\displaystyle\frac{-7}{45},\,\displaystyle\frac{-3}{45},\,\displaystyle\frac{-2}{45},\,\displaystyle\frac{-1}{45},\,\displaystyle\frac{2}{45},\,\displaystyle\frac{3}{45},\,\displaystyle\frac{4}{45},\,\displaystyle\frac{5}{45},\,\displaystyle\frac{8}{45}$
  2. $\displaystyle\frac{-4}{45},\,\displaystyle\frac{-3}{45},\,\displaystyle\frac{-2}{45},\,\displaystyle\frac{-1}{45},\,\displaystyle\frac{16}{45},\,\displaystyle\frac{3}{45},\,\displaystyle\frac{4}{45},\,\displaystyle\frac{5}{45},\,\displaystyle\frac{8}{45}$
  3. $\displaystyle\frac{-4}{45},\,\displaystyle\frac{-3}{45},\,\displaystyle\frac{-2}{45},\,\displaystyle\frac{-1}{45},\,\displaystyle\frac{2}{45},\,\displaystyle\frac{83}{45},\,\displaystyle\frac{4}{45},\,\displaystyle\frac{5}{45},\,\displaystyle\frac{8}{45}$
  4. $\displaystyle\frac{-4}{45},\,\displaystyle\frac{-3}{45},\,\displaystyle\frac{-2}{45},\,\displaystyle\frac{-1}{45},\,\displaystyle\frac{2}{45},\,\displaystyle\frac{3}{45},\,\displaystyle\frac{4}{45},\,\displaystyle\frac{5}{45},\,\displaystyle\frac{8}{45}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Convert the rational numbers into equivalent rational numbers with the same denominator.


LCM of $9\;and\;5$ is $45$.

$-\displaystyle\frac{1}{9}=\displaystyle\frac{-1\times5}{9\times5}=\displaystyle\frac{-5}{45}\;and\;\displaystyle\frac{1}{5}=\displaystyle\frac{1\times9}{5\times9}=\displaystyle\frac{9}{45}$

The integers between $-5\;and\;9$ are
$-4,\,-3,\,-2,\,-1,\,0,\,1,\,2,\,3,\,4,\,5,\,6,\,7,\,8$.

The corresponding rational numbers are $\displaystyle\frac{-4}{45},\,\displaystyle\frac{-3}{45},\,\displaystyle\frac{-2}{45},\,\displaystyle\frac{-1}{45},\,\displaystyle\frac{0}{45},\,\displaystyle\frac{1}{45},\,\displaystyle\frac{2}{45},\,\displaystyle\frac{3}{45},\,\displaystyle\frac{4}{45},\,\displaystyle\frac{5}{45},\,\displaystyle\frac{6}{45},\,\displaystyle\frac{7}{45},\,\displaystyle\frac{8}{45}$

On selecting any $9$ of them, we get $9$ rational numbers between $-\displaystyle\frac{1}{9}\;and\;\displaystyle\frac{1}{5}$

$\displaystyle\frac{-4}{45},\,\displaystyle\frac{-3}{45},\,\displaystyle\frac{-2}{45},\,\displaystyle\frac{-1}{45},\,\displaystyle\frac{2}{45},\,\displaystyle\frac{3}{45},\,\displaystyle\frac{4}{45},\,\displaystyle\frac{5}{45},\,\displaystyle\frac{8}{45}$

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

State TRUE or FALSE
The three rational number between $\dfrac{1}{3}$ and $\dfrac{1}{2}$ are $\displaystyle\frac{9}{24},\frac{10}{24},\frac{11}{24}$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$x=\frac { 1 }{ 3 } =\frac { 8 }{ 24 } \quad and\quad y=\frac { 1 }{ 2 } =\frac { 12 }{ 24 } ,\ $

$ \frac { 9 }{ 24 } ,\frac { 10 }{ 24 } \ and\ \frac { 11 }{ 24 } are\quad three\quad rational\quad numbers\quad lying\quad between\quad x\quad and\quad y.\quad \quad \ $

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

A rational number between $\displaystyle \frac{1}{4}$ and $\displaystyle \frac{1}{3}$ is

  1. $\displaystyle \frac{7}{24}$
  2. $0.29$
  3. $\displaystyle \frac{13}{48}$

  4. All the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\dfrac{1}{4} = \dfrac{6}{24} = \dfrac{12}{48} = 0.25$


$\dfrac{1}{3} = \dfrac{8}{24} = \dfrac{16}{48} = 0.33$

From this, we can see $\dfrac{7}{24} , \dfrac{13}{48}, 0.29$ all lie between $\dfrac{1}{4}$ and $\dfrac{1}{3}$

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}$.