Tag: operations on rational numbers

Quizzes (9) Questions (77)

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

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

  1. $0$
  2. $-1$
  3. $\dfrac {-1}{4}$
  4. $\dfrac {1}{4}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $-1$.

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

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

  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 } $
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $\dfrac{1}{3}$.

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

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

  1. $\dfrac {1}{4}$
  2. $\dfrac {9}{10}$
  3. $\dfrac {17}{30}$
  4. $\dfrac {7}{10}$
Reveal answer Fill a bubble to check yourself
C,D Correct answer
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

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:

Five rational numbers between.
$\dfrac{2}{3}$ and $\dfrac{4}{5}$ are $\dfrac{41}{60},\dfrac{42}{60},\dfrac{43}{60},\dfrac{44}{60},\dfrac{45}{60}$

  1. True

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

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

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 $0$

  1. True

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

2/5 = 8/20 and 3/5 = 12/20. The numbers 9/20, 10/20, and 11/20 are all strictly between 8/20 and 12/20. Thus, the statement is true.

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 $\displaystyle \frac{1}{3}$ and $\displaystyle \frac{1}{2}$ is _________.

  1. $\displaystyle \frac{2}{5}$
  2. $\displaystyle \frac{1}{5}$
  3. $\displaystyle \frac{3}{5}$
  4. $\displaystyle \frac{4}{5}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $\dfrac{1}{2}$

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

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

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

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:

Five rational numbers between.
$\dfrac{1}{4}$ and $\dfrac{1}{2}$ are $\displaystyle\frac{9}{32},\frac{10}{32},\frac{11}{32},\frac{12}{32},\frac{13}{32}$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $\displaystyle\frac{9}{32}$, $\displaystyle\frac{10}{32}$, $\displaystyle\frac{11}{32}$, $\displaystyle\frac{12}{32}$, $\displaystyle\frac{13}{32}$

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:

Five rational numbers between.
$\dfrac{-3}{2}$ and $\dfrac{5}{3}$ are $\dfrac{-8}{6},\dfrac{-7}{6},0,\dfrac{1}{6},\dfrac{2}{6}$

  1. True

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