Tag: operations on rational numbers

Questions Related to operations on rational numbers

Which of the following rational numbers lies between $0$ and $-1$?

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

  1. $0$

  2. $-1$

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

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

Show answer
Correct Option: C
Explanation:

Clearly, $0$ and $-1$ cannot lie between $0$ and $-1$. 

Also, 
$0=\dfrac{0}{4}$ and $-1=\dfrac{-4}{4}$
We can clearly see that $\dfrac {-1}{4}$ lies between $0$ and $-1$.

If we divide a positive integer by another positive integer, what is the resulting number?

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

  1. It is always a natural number

  2. It is always an integer

  3. It is a rational number

  4. It is an irrational number

Show answer
Correct Option: C
Explanation:

When a positive integer is divided by another positive integer will yield a rational number

The rational number lying exactly in between the numbers $\displaystyle \frac { 1 }{ 5 } $ and $\displaystyle \frac { 1 }{ 3 } $ is

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

  1. $\displaystyle \frac { 1 }{ 2 } $

  2. $\displaystyle \frac { 1 }{ 4 } $

  3. $\displaystyle \frac { 2 }{ 15 } $

  4. $\displaystyle \frac { 4 }{ 15 } $

  5. $\displaystyle \frac { 8 }{ 15 } $

Show answer
Correct Option: D
Explanation:

Required number $=$ $\dfrac{1}{2}\left(\dfrac{1}{5}+\dfrac{1}{3}\right)$

$\Rightarrow \dfrac{1}{2}\left(\dfrac{3+5}{15}\right)$
$\Rightarrow \dfrac{1}{2}\times \dfrac{8}{15}=\dfrac{4}{15}$
Hence, $\dfrac{4}{15}$ is a rational number lying between $\dfrac{1}{5}$ and $\dfrac{1}{3}$.

Identify a rational number between $\dfrac {1}{3}$ and $\dfrac {4}{5}$

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

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

  2. $\dfrac {9}{10}$

  3. $\dfrac {17}{30}$

  4. $\dfrac {7}{10}$

Show answer
Correct Option: C,D
Explanation:

Converting the given fraction in decimal format we get $\frac { 1 }{ 3 } =0.33\quad and\quad \frac { 4 }{ 5 } =0.8$

Now converting all option in decimal we get
A.  $\frac{1}{4}$=0.25
B. $\frac{9}{10}$=0.9
C. $\frac{17}{30}$=0.567
D.  $\frac{7}{10}$ =0.7
So it is clear that option C and D lies between 0.33 and 0.8 and both are rational numbers so correct answer will be option C and D

State true or false:

Five rational numbers between.
$\dfrac{2}{3}$ and $\dfrac{4}{5}$ are $\dfrac{41}{60},\dfrac{42}{60},\dfrac{43}{60},\dfrac{44}{60},\dfrac{45}{60}$
maths operations on rational numbers rational numbers on number line rational numbers and their decimal expansions rational numbers between two rational numbers

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

To get the rational numbers between $\displaystyle\frac{2}{3}$ and $\displaystyle\frac{4}{5}$

Take an LCM of these two numbers: $\displaystyle\frac{10}{15}$ and $\displaystyle\frac{12}{15}$

Multiply numerator and denominator by 4: $\displaystyle\frac{40}{60}$ and $\displaystyle\frac{48}{60}$

All the numbers between $\displaystyle\frac{40}{60}$ and $\displaystyle\frac{48}{60}$ form the answer

Some of these numbers are $\displaystyle\frac{41}{60}$, $\displaystyle\frac{42}{60}$, $\displaystyle\frac{43}{60}$, $\displaystyle\frac{44}{60}$, $\displaystyle\frac{45}{60}$


Hence the statement is true

Three rational numbers between $\frac{2}{5}$ and $\frac{3}{5}$ is  $\frac{9}{20},\frac{10}{20},\frac{11}{20}$
If true then enter $1$ and if false then enter $0$

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

  1. True

  2. False

Show answer
Correct Option: A

The rational number between $\displaystyle \frac{1}{3}$ and $\displaystyle \frac{1}{2}$ is _________.

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

  1. $\displaystyle \frac{2}{5}$

  2. $\displaystyle \frac{1}{5}$

  3. $\displaystyle \frac{3}{5}$

  4. $\displaystyle \frac{4}{5}$

Show answer
Correct Option: A
Explanation:

$\dfrac{1}{3} = 0.3333.....$


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

Option A :
$\dfrac{2}{5} = 0.4$

Option B :
$\dfrac{1}{5} = 0.2$

Option C :
$\dfrac{3}{5} = 0.6$

Option D :
$\dfrac{4}{5} = 0.8$

$\therefore$ Option A lies in between $\dfrac{1}{3}$ and $\dfrac{1}{2}$

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

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

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

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

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

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

Show answer
Correct Option: B
Explanation:

Both given rational numbers are negative rational number. So, a rational number between both these rational numbers will be negative. But option B is a positive. So, option B will not lie between the given rational numbers. So, correct answer is option B.

State true or false:

Five rational numbers between.
$\dfrac{1}{4}$ and $\dfrac{1}{2}$ are $\displaystyle\frac{9}{32},\frac{10}{32},\frac{11}{32},\frac{12}{32},\frac{13}{32}$
maths operations on rational numbers rational numbers on number line rational numbers and their decimal expansions rational numbers between two rational numbers

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

To get the rational numbers between $\displaystyle\frac{1}{4}$ and $\displaystyle\frac{1}{2}$

Take an LCM of these two numbers: $\displaystyle\frac{1}{4}$ and $\displaystyle\frac{2}{4}$

Multiply numerator and denominator by 8: $\displaystyle\frac{8}{32}$ and $\displaystyle\frac{16}{32}$

All the numbers between $\displaystyle\frac{8}{32}$ and $\displaystyle\frac{16}{32}$ form the answer

Some of these numbers are $\displaystyle\frac{9}{32}$, $\displaystyle\frac{10}{32}$, $\displaystyle\frac{11}{32}$, $\displaystyle\frac{12}{32}$, $\displaystyle\frac{13}{32}$

State true or false:

Five rational numbers between.
$\dfrac{-3}{2}$ and $\dfrac{5}{3}$ are $\dfrac{-8}{6},\dfrac{-7}{6},0,\dfrac{1}{6},\dfrac{2}{6}$
maths operations on rational numbers rational numbers on number line rational numbers and their decimal expansions rational numbers between two rational numbers

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

To get the rational numbers between $\displaystyle\frac{-3}{2}$ and $\displaystyle\frac{5}{3}$

Take an LCM of these two numbers: $\displaystyle\frac{-9}{6}$ and $\displaystyle\frac{10}{6}$

All the numbers between $\displaystyle\frac{-9}{6}$ and $\displaystyle\frac{10}{6}$ form the answer

Some of these numbers are $\displaystyle\frac{-8}{6}$, $\displaystyle\frac{-7}{6}$, $\displaystyle{0}$, $\displaystyle\frac{1}{6}$, $\displaystyle\frac{2}{6}$


Hence the statement is true