Tag: comparing and ordering fractions

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

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

  1. $\displaystyle\frac{-2}{11}$
  2. $\displaystyle\frac{5}{-12}$
  3. $\displaystyle\frac{-5}{17}$

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
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. 

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

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

  1. $\displaystyle \frac{86}{90}$
  2. $\displaystyle \frac{86}{45}$
  3. $\displaystyle \frac{43}{45}$
  4. $\displaystyle \frac{43}{90}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The numbers are

$\displaystyle \frac { 4 }{ 7 } ,\quad \frac { 1 }{ 3 } ,\quad \frac { 2 }{ 5 } \quad & \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.

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

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

  1. $\displaystyle \frac{-5}{11}$
  2. $\displaystyle \frac{5}{-12}$
  3. $\displaystyle \frac{-5}{17}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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

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

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?

  1. $\dfrac39$
  2. $\dfrac15$
  3. $\dfrac75$
  4. $\dfrac35$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $= \cfrac{1}{5}$

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

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

  1. $\displaystyle \frac{1}{2}$
  2. $\displaystyle \frac{- 7}{8}$
  3. $\displaystyle \frac{4}{- 5}$

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $\displaystyle \frac{- 4}{5}$.

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

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

  1. $>(p/q)$ if $p > q$
  2. $=(p/q)$ if $p > q$
  3. $>(p/q)$ if $p < q$
  4. $<(p/q)$ if $p < q$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If p < q, then adding the same positive number r to both numerator and denominator makes the fraction closer to 1. For example, if p=1, q=2, r=1, then (1+1)/(2+1) = 2/3, which is greater than 1/2.

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

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

  1. =

  2. >

  3. <

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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.