Tag: comparing fractions

Questions Related to comparing fractions

Compare and identify appropriate symbol.

 $+42\, \square \, +23$ 

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

  1. <

  2. >

  3. =

  4. $\neq $

Show answer
Correct Option: B
Explanation:

While comparing positive numbers greater is greater, smaller is smaller.

$42$ is greater than $23\implies 42>23$

Out of the rational numbers $\displaystyle\frac{-5} {11},\,\frac{-5}{12},\,\frac{-5}{17}$ which is greatest ?

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

  1. $\displaystyle\frac{-2}{11}$

  2. $\displaystyle\frac{5}{-12}$

  3. $\displaystyle\frac{-5}{17}$

  4. None

Show answer
Correct Option: C
Explanation:

$\displaystyle\frac{-5}{11},\,\frac{-5}{12},\,\frac{-5}{17}$

$\because$ All have same numerator. So the rational number having the least denominator is the greatest. But here all have negative sign. So the number having greatest denominator is greater.

Hence, $\displaystyle\frac{-5}{17}$ is greater.

Alter : Take any two given numbers. $\displaystyle\frac{-5}{11},\, \frac{-5}{12}$

$-5\,\times\,12, -5\,\times\, 11$

- 60, - 55 

$\because\, - 55\, >\, - 60$

So, $\displaystyle\frac{-5}{12}$ is greater.

Now compare this with $\displaystyle\frac{-5}{17}$ 

$\displaystyle\frac{-5}{12},\, \frac{-5}{17}$

$-5\,\times\,17, \, -5\,\times\, 12$

- 85, - 60

$\because\,- 60\, >\,- 85$

So, $\displaystyle\frac{-5}{17}$ is greater. 

The average of the middle two rational numbers when  $\displaystyle {\frac{4}{7},\, \frac{1}{3},\, \frac{2}{5},\, \frac{5}{9}}$ are arranged in ascending order is

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

  1. $\displaystyle \frac{86}{90}$

  2. $\displaystyle \frac{86}{45}$

  3. $\displaystyle \frac{43}{45}$

  4. $\displaystyle \frac{43}{90}$

Show answer
Correct Option: D
Explanation:

The numbers are

$\displaystyle \frac { 4 }{ 7 } ,\quad \frac { 1 }{ 3 } ,\quad \frac { 2 }{ 5 } \quad &amp; \quad \frac { 5 }{ 9 } $.
To  arrange them in ascending order, we make their denominators equal
to the L.C.M. of the denominators.
The L.C.M. of 7, 3, 5 & 9=315.
So $\displaystyle \frac { 4 }{ 7 } =\frac { 4\times 45 }{ 7\times 45 } =\frac { 180 }{ 315 } ,\ \displaystyle \frac { 1 }{ 3 } =\frac { 1\times 105 }{ 3\times 105 } =\frac { 105 }{ 315 } ,\ \displaystyle \frac { 2 }{ 5 } =\frac { 2\times 63 }{ 5\times 63 } =\frac { 126 }{ 315 } \quad &amp; \quad \ \displaystyle \frac { 5 }{ 9 } =\frac { 5\times 35 }{ 9\times 35 } =\frac { 175 }{ 315 } .\ \therefore \quad \displaystyle \frac { 105 }{ 315 } <\frac { 126 }{ 315 } <\frac { 175 }{ 315 } <\frac { 180 }{ 315 } \i.e \displaystyle \frac { 1 }{ 3 } <\frac { 2 }{ 5 } <\frac { 5 }{ 9 } <\frac { 4 }{ 7 } $.
Then, the average of the middle numbers
=$\displaystyle \frac { 1 }{ 2 } \left( \frac { 1 }{ 3 } +\frac { 2 }{ 5 }  \right) =\frac { 43 }{ 90 } $.
Ans- Option D.

Out of the rational numbers $\displaystyle {\frac{-5}{11},\, \frac{-5}{12},\, \frac{-5}{17}}$, which is greater ?

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

  1. $\displaystyle \frac{-5}{11}$

  2. $\displaystyle \frac{5}{-12}$

  3. $\displaystyle \frac{-5}{17}$

  4. None of these

Show answer
Correct Option: C
Explanation:

$\displaystyle {\frac{-5}{11},\, \frac{-5}{12},\, \frac{-5}{17}}$
$\because$ All have same numerator. Sothe rational number having theleast denominator is the greatest.But here all have negative sign.So, the number having greatestdenominator is greater. Hence, $\displaystyle \frac{-5}{17}$ is greater

What is the least number if $\displaystyle {\frac{3}{5},\, \frac{9}{5},\, \frac{1}{5},\, \frac{7}{5}}$ are arranged in ascending or descending order?

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

  1. $\dfrac39$

  2. $\dfrac15$

  3. $\dfrac75$

  4. $\dfrac35$

Show answer
Correct Option: B
Explanation:

The given numbers can be arranged in the ascending order as:
$ {\cfrac{1}{5}\, >\, \cfrac{3}{5}\, >\, \cfrac{7}{5}\, >\, \cfrac{9}{5}}$
Greatest number $= \cfrac{9}{5}$ and Least number $= \cfrac{1}{5}$

The given rational numbers are $\displaystyle \frac{1}{2},\, \displaystyle \frac{4}{-5},\, \displaystyle \frac{- 7}{8}$. If these numbers are arranged in the ascending order or descending order, then the middle number is

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

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

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

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

  4. None

Show answer
Correct Option: C
Explanation:

Let given numbers arranged in the descending order.
$\displaystyle \frac{1}{2},\, \displaystyle \frac{-4}{5},\, \displaystyle \frac{- 7}{8}$
$- 4\, \times\, 8,\, 5\, \times\, - 7$
$- 32,\, - 35$
$\displaystyle \frac{-4}{5}\, >\, \displaystyle \frac{-7}{8}$
The descending order is $\displaystyle \frac{1}{2}\, >\, \displaystyle \frac{-4}{5}\, >\, \displaystyle \frac{- 7}{8}$
So middle number is $\displaystyle \frac{- 4}{5}$.

If $p, q$ and $r$ are positive real numbers then the quantity $(p + r)/(q + r)$ is

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

  1. $>(p/q)$ if $p > q$

  2. $=(p/q)$ if $p > q$

  3. $>(p/q)$ if $p < q$

  4. $<(p/q)$ if $p < q$

Show answer
Correct Option: C

Which one is in the descending order in the following? 

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

  1. 6/7,4/5,3/4,7/9

  2. 6/7,4/5,7/9,3/4

  3. 3/4,7/9,4/5,617

  4. 7/9,3/4,617,4/5

Show answer
Correct Option: B
Explanation:

$\displaystyle \dfrac { 6 }{ 7 } ,\dfrac { 4 }{ 5 } ,\dfrac { 7 }{ 9 } ,\dfrac { 3 }{ 4 } \Rightarrow 0.85<0.8<0.78<0.75$

Compare  $\displaystyle \frac { 8 }{ 16 } \Box \frac { 8 }{ 4 } $

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:

$ \dfrac{8}{16}=\dfrac{1}{2}\ and\ \dfrac{8}{4}=2$


obviously $\dfrac{1}{2} < 2$

Compare $\frac {9}{16}\square \frac {13}{5}$

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: C
Explanation:

The denominator is the total number of parts in the whole. The lesser the number of parts the greater the value of each part.

The numerator is the number of parts out of the denominator to be selected. The greater the number of parts more the value.
So in the given fractions, the first is smaller than the second.
9/16<13/5
So, option C is the correct answer.