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

State True or False.

The five rational numbers between $\dfrac{3}{5}$ and $\dfrac{4}{5}$ are $ \displaystyle \frac{19}{30},\frac{20}{30},\frac{21}{30},\frac{22}{30},\frac{23}{30}$.

  1. True

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

Since we want five  numbers we write $\frac{3}{5}$ and $\frac{4}{5}$
So multiply in numerator and denominator by 5+1 = 6 we get
$\Rightarrow \frac{3}{5}=\frac{3\times 6}{5\times 6}=\frac{18}{30}$
$\Rightarrow \frac{4}{5}=\frac{4\times 6}{5\times 6}=\frac{24}{30}$
We know that $18<19<20<21<22<23<24$
$\Rightarrow \frac{18}{30}<\frac{19}{30}<\frac{20}{30}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{24}{30}$
Hence 5 rational number between $\frac{3}{5} and  \frac{4}{5}$are
$\frac{19}{30},\frac{20}{30},\frac{21}{30},\frac{22}{30},\frac{23}{30},$

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 50 numbers Each numbers is subtracted from 53 and the mean of the numbers so obtained is found to be -3.5 The mean of the given numbers is 

  1. $48.9$
  2. $49.5$
  3. $52.5$
  4. $56.5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$   Total observation is $50$

$\Rightarrow$  Let sum of $50$ number be $x$
$\therefore$    $\dfrac{x-(50\times 53)}{50}=-3.5$
$\therefore$    $x-2650=-3.5\times 50$
$\therefore$    $x-2650=-175$
$\therefore$    $x=-175+2650$
$\therefore$    $x=2475$
$\Rightarrow$   Original mean = $\dfrac{2475}{50}=49.5$

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

Write any $10$ rational numbers between $0\;and\;2$.

  1. $\displaystyle\frac{1}{10},\,\displaystyle\frac{2}{10},\,\displaystyle\frac{3}{10},\,\displaystyle\frac{4}{10},\,\displaystyle\frac{5}{10},\,\displaystyle\frac{6}{10},\,\displaystyle\frac{7}{10},\,\displaystyle\frac{88}{10},\,\displaystyle\frac{9}{10},\,\displaystyle\frac{10}{10}$
  2. $\displaystyle\frac{1}{10},\,\displaystyle\frac{2}{10},\,\displaystyle\frac{3}{10},\,\displaystyle\frac{4}{10},\,\displaystyle\frac{21}{10},\,\displaystyle\frac{6}{10},\,\displaystyle\frac{7}{10},\,\displaystyle\frac{8}{10},\,\displaystyle\frac{9}{10},\,\displaystyle\frac{10}{10}$
  3. $\displaystyle\frac{1}{10},\,\displaystyle\frac{2}{10},\,\displaystyle\frac{3}{10},\,\displaystyle\frac{4}{10},\,\displaystyle\frac{35}{10},\,\displaystyle\frac{6}{10},\,\displaystyle\frac{7}{10},\,\displaystyle\frac{8}{10},\,\displaystyle\frac{9}{10},\,\displaystyle\frac{10}{10}$
  4. $\displaystyle\frac{1}{10},\,\displaystyle\frac{2}{10},\,\displaystyle\frac{3}{10},\,\displaystyle\frac{4}{10},\,\displaystyle\frac{5}{10},\,\displaystyle\frac{6}{10},\,\displaystyle\frac{7}{10},\,\displaystyle\frac{8}{10},\,\displaystyle\frac{9}{10},\,\displaystyle\frac{10}{10}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let us write $0$ as $\displaystyle\frac{0}{10}\;and\;2$ as $\displaystyle\frac{20}{10}$.

The rational numbers between these are


$\displaystyle\frac{1}{10},\,\displaystyle\frac{2}{10},\,\displaystyle\frac{3}{10},\,\displaystyle\frac{4}{10},\,\displaystyle\frac{5}{10},\,\displaystyle\frac{6}{10},\,\displaystyle\frac{7}{10},\,\displaystyle\frac{8}{10},\,\displaystyle\frac{9}{10},\,\displaystyle\frac{10}{10},\,\displaystyle\frac{11}{10},\,\displaystyle\frac{12}{10},\,\displaystyle\frac{13}{10},\,\displaystyle\frac{14}{10},\,\displaystyle\frac{15}{10},\,\displaystyle\frac{16}{10},\,\displaystyle\frac{17}{10},\,\displaystyle\frac{18}{10},\,\displaystyle\frac{19}{10}$

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 rational numbers $ \displaystyle \frac{3}{5} $ and $ \displaystyle \frac{2}{3} $ :

  1. $ \displaystyle \frac{46}{75} $
  2. $ \displaystyle \frac{47}{75} $
  3. $ \displaystyle \frac{49}{75} $
  4. $ \displaystyle \frac{50}{75} $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For $\dfrac{3}{5}$ multiply numerator and denominator by $15$ to make denominator $75$ that comes into $\dfrac{45}{75}.$
Similarly doing for second then we have $\dfrac{50}{75}.$
Now question is asking about rational lying between them.

So, we need to check the numerator only that lies in between $45$ and $50$ or not.
Clearly $D$ is 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

Find five rational numbers between $1$ and $2.$

  1. $\dfrac {1}{10}, \dfrac {2}{10}, \dfrac {3}{10}, \dfrac {4}{10}, \dfrac {5}{10}$
  2. $\dfrac {1}{5}, \dfrac {2}{5}, \dfrac {3}{5}, \dfrac {4}{5}, \dfrac {5}{5}$
  3. $\dfrac {1}{2}, \dfrac {1}{3}, \dfrac {1}{4}, \dfrac {1}{5}, \dfrac {1}{6}$
  4. $\dfrac {8}{7}, \dfrac {9}{7}, \dfrac {10}{7}, \dfrac {11}{7}, \dfrac {12}{7}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The given rational numbers are $1$ and $2$.

Let us multiply both the numbers by $\dfrac {7}{7}$.
$1\times \dfrac {7}{7} = \dfrac {7}{7}$ and $2\times \dfrac {7}{7} = \dfrac {14}{7}$.
Thus, five rational numbers between $\dfrac {7}{7} = 1$ and $\dfrac {14}{7} = 2$ are $\dfrac {8}{7}, \dfrac {9}{7}, \dfrac {10}{7}, \dfrac {11}{7}, \dfrac {12}{7}$.

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 rational numbers $-\cfrac {2}{5}$ and $-\cfrac {1}{5}$

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

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


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

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

Identity the rational number that does not lie between  $ \cfrac{3}{5}$ and $ \cfrac{2}{3}$.

  1. $ \cfrac{46}{75}$
  2. $ \cfrac{47}{75}$
  3. $ \cfrac{49}{75}$
  4. $ \cfrac{50}{75}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Changing the fractions to denominator $=75$


$\dfrac{3}{5} = \dfrac{45}{75}$

$\dfrac{2}{3} = \dfrac{50}{75}$

$\therefore \dfrac{50}{75}$ doesn't lie in between $\dfrac{3}{5}$ and $\dfrac{2}{3}$

Multiple choice 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

The rational number is not lying between $\dfrac {5}{16}$ and $\dfrac {1}{2}$ is _________.

  1. $\dfrac {3}{8}$
  2. $\dfrac {7}{16}$
  3. $\dfrac {1}{4}$
  4. $\dfrac {13}{32}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

5/16 = 0.3125 and 1/2 = 0.5. Comparing options: 3/8 = 0.375 (in range), 7/16 = 0.4375 (in range), 1/4 = 0.25 (not in range), 13/32 = 0.40625 (in range).

Multiple choice 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

Find 9 rational numbers between  $2$ and $3$

  1. $2 < 2.1 < 2.2 < 3.3 < 2.4 < ... < 2.9 < 3$
  2. $2 < 4.1 < 2.2 < 2.3 < 2.4 < ... < 2.9 < 3$
  3. $2 < 2.1 < 2.2 < 2.3 < 2.4 < ... < 2.9 < 3$
  4. $2 < 2.1 < 2.2 < 2.3 < 2.4 < ... < 0.9 < 3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$2 < 2.1=(2+0.1) < 2.2=(2.1+0.1) < 2.3=(2.2+0.1) < 2.4=(2.3+0.1) < ... < 2.9=(2.8+0.1) < 3=(2.9+0.1)$


$2 < 2.1 < 2.2 < 2.3 < 2.4 < ... < 2.9 < 3$

Multiple choice 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

Write two rational numbers between $\displaystyle \sqrt{2}$ and $\displaystyle \sqrt{3}.$

  1. $1.5,\ 1.6$
  2. $1.4,\ 1.6$
  3. $1.5,\ 1.8$

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

We know that, $ \sqrt {2} = 1.414

$ and $ \sqrt {3} = 1.732 $

Hence two rational numbers between $ 1.414 $ and $ 1.732

$  can be $ 1.5 (= \frac {3}{2}) $ and $ 1.6 (= \frac {16}{10}= \frac {8}{5}) $