Tag: comparing and ordering fractions

Questions Related to comparing and ordering fractions

Which is the greatest number in the following

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. $16\frac{2}{3}\% $

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

  3. $\frac{1}{{11}}$

  4. $0.17$

Show answer
Correct Option: D
Explanation:
$16 \dfrac 2 3 \% ; \dfrac{2}{15} ; \dfrac{1}{11} ; 0.17$

$\Rightarrow \dfrac{50}{3} \times \dfrac{1}{100} ; \dfrac{2}{15} ; 0.0909.... ; 0.17$

$\Rightarrow \dfrac{1}{3 \times 2} ; 0.1333 ; 0.0909 .... ; 0.17$

$\Rightarrow 0.1666...7 ; 0.1333 ; 0.0909 ; 0.17$

$\therefore 0.17$ is greater 

If the fractions $\cfrac{3}{5}$,$\cfrac{2}{11}$, $\cfrac{4}{7}$, $\cfrac{1}{3}$, $\cfrac{5}{6},$ and $\cfrac{3}{8}$are arranged in the ascending order which fraction will be at the 3rd place ?

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. $\cfrac{1}{3}$

  2. $\cfrac{3}{5}$

  3. $\cfrac{2}{11}$

  4. $\cfrac{3}{8}$

Show answer
Correct Option: D
Explanation:

LCM of the denominators of given rational numbers i.e. 5, 11, 7, 3, 6, and 8 = 9240

Now by equating the denominators we get, 
$\dfrac { 3 }{ 5 } =\dfrac { 5652 }{ 9240 }$

$\dfrac { 2 }{ 11 } =\dfrac { 1680 }{ 9240 }$

$\dfrac { 4 }{ 7 } =\dfrac { 5280 }{ 9240 }$

$\dfrac { 1 }{ 3 } =\dfrac { 3080 }{ 9240 }$

$\dfrac { 5 }{ 6 } =\dfrac { 7700 }{ 9240 }$

$\dfrac { 3 }{ 8 } =\dfrac { 3465 }{ 9240 }$
 On seeing the rational numbers it is clear that the rational number at third position in ascending order is $\dfrac { 3465 }{ 9240 } \  i.e.\dfrac { 3 }{ 8 }$
So, correct answer is option D. 

The fraction equivalent to $\displaystyle \frac{1}{2}$ is

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

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

  2. $\displaystyle \frac{3}{6}$

  3. $\displaystyle \frac{8}{16}$

  4. all the above

Show answer
Correct Option: D
Explanation:

$\displaystyle \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$
$\displaystyle \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$
$\displaystyle \frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16}$
So, $\displaystyle \frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{8}{16}$

Which of the following fractions is less than $\displaystyle \frac{7}{8}$ and greater than $\displaystyle \frac{1}{3}$?

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

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

  2. $\displaystyle \frac{23}{24}$

  3. $\displaystyle \frac{11}{12}$

  4. $\displaystyle \frac{17}{24}$

Show answer
Correct Option: D
Explanation:

$\displaystyle \frac{1}{3} = 0.333000,$ $\displaystyle \frac{7}{8} = 0.875$
$\displaystyle \frac{1}{4} = 0.25,$ $\displaystyle \frac{23}{24} = 0.9583000,$ $\displaystyle \frac{11}{12} = 0.9166000$
$\displaystyle \frac{17}{24} = 0.7083000$
Since $0.7083000 \displaystyle \left ( =\frac{17}{24} \right )$ is greater than 
$0.333000 \displaystyle \left ( =\frac{1}{3} \right )$ and less than $0.875 \displaystyle \left ( =\frac{17}{24} \right )$$\displaystyle \left ( =\frac{7}{8} \right )$
Therefore $\displaystyle \frac{17}{24}$ lies between $\displaystyle \frac{1}{3}$ and $\displaystyle \frac{7}{8}$

Which of the following fractions is the largest ?

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. $\displaystyle \frac{13}{16}$

  2. $\displaystyle \frac{7}{8}$

  3. $\displaystyle \frac{31}{40}$

  4. $\displaystyle \frac{63}{80}$

Show answer
Correct Option: B
Explanation:

$\displaystyle \frac{13}{16}=\frac{13\times 5}{16\times 5}=\frac{65}{80}, \frac{7\times 10}{8\times 10}=\frac{70}{80},\frac{31}{40}=\frac{31\times 2}{40\times 2}$
$\displaystyle =\frac{62}{80}$ and last fraction is $\displaystyle =\frac{63}{80}$
Out of these the largest fraction is $\displaystyle \frac{70}{80}$ $\displaystyle =\frac{7}{8}$

$\displaystyle \frac{4}{15}$of $\displaystyle \frac{5}{7}$ of a number is greater than $\displaystyle \frac{4}{9}$ of $\displaystyle \frac{2}{5}$ of the same number by $8$. What is half of that number?

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. $630$

  2. $315$

  3. $210$

  4. $105$

Show answer
Correct Option: B
Explanation:

Let the number be $x$

So from the question, we have
$\dfrac{4}{15}.\dfrac{5}{7}.x-\dfrac{4}{9}.\dfrac{2}{5}.x=8$
$\Rightarrow \dfrac {4x}{21}-\dfrac {8x}{45}=8$
$\Rightarrow x=\dfrac {24\times 7\times 15}{4}$
$\Rightarrow x=6\times 7\times 15$
$\Rightarrow x=630$
Half of that number is equal to $315$.

Compare $\displaystyle \frac {9}{16}$ .......... $\displaystyle \frac {13}{5}$

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. $=$

  2. $>$

  3. $<$

  4. None

Show answer
Correct Option: C
Explanation:

Given fractions are

$\displaystyle \frac{9}{16} = 0.5625$

$\displaystyle \frac{13}{5}=2.6$

Hence$ \displaystyle \frac{9}{16}<\frac{13}{5}$

OR
$9\times 5<13\times16$
 $ \displaystyle \frac{9}{16}<\frac{13}{5}$

Which of the following fraction is the largest?

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. $\displaystyle \frac {29}{30}$

  2. $\displaystyle \frac {29}{23}$

  3. $\displaystyle \frac {29}{27}$

  4. $\displaystyle \frac {29}{25}$

Show answer
Correct Option: B
Explanation:

$\because$ all fractions are having same numerator.
So the fraction having smallest denominator is the largest.
Hence $\displaystyle \frac {29}{23}$ is the largest.

By how much is $\displaystyle \frac {19}{20}$ greater than $\displaystyle \frac {2}{20}$ ?

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. $\displaystyle \frac {21}{10}$

  2. $\displaystyle \frac {21}{40}$

  3. $\displaystyle \frac {17}{20}$

  4. $\displaystyle \frac {17}{40}$

Show answer
Correct Option: C
Explanation:

$\displaystyle \frac {19}{20}\, -\, \displaystyle \frac {2}{20}\, =\, \displaystyle \frac {19-2}{20}\, =\, \displaystyle \frac {17}{20}$

Compare $12.1280\, \square \, 12.129$ (using >, <, =)

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. >

  2. <

  3. =

  4. None of these

Show answer
Correct Option: B
Explanation:

$12.1280 < 12.129$