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Questions Related to maths

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

The average of the middle two rational numbers if $\displaystyle \frac{4}{7},\, \displaystyle \frac{1}{3},\, \displaystyle \frac{2}{5},\, \displaystyle \frac{5}{9}$ 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

$\displaystyle \frac{4}{7},\, \displaystyle \frac{1}{3},\, \displaystyle \frac{2}{5},\, \displaystyle \frac{5}{9}$
The above numbers in ascending order are
$\displaystyle \frac{1}{3}\, <\, \displaystyle \frac{2}{5}\, <\, \displaystyle \frac{5}{9}\, <\, \displaystyle \frac{4}{7}$
Middle two numbers are $\displaystyle \frac{2}{5}$ & $\displaystyle \frac{5}{9}$.
$\therefore$ Average = $\displaystyle \frac{\displaystyle \frac{2}{5}\, +\, \displaystyle \frac{5}{9}}{2}\, =\, \displaystyle \frac{43}{90}$.

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

Out of the rational numbers $\displaystyle\frac{7}{-13},\,\frac{-5}{13},\,\frac{-11}{13}$ which is smaller ?

  1. $\displaystyle \frac{7}{13}$
  2. $\displaystyle \frac{- 5}{13}$
  3. $\displaystyle \frac{- 11}{13}$

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

Take any two given rational numbers
$\displaystyle \frac{-7}{13},\, \displaystyle \frac{-5}{13}$
$- 7\, \times\, 13,\, -5\, \times\, 13$
$- 91,\, -65$
$\because\, - 65\, >\, - 91$
So $\displaystyle \frac{-7}{13}$ is smaller.
Now compare this with $\displaystyle \frac{- 11}{13}$
$\displaystyle \frac{- 7}{13},\, \displaystyle \frac{- 11}{13}$
$-7\, \times\, 13,\, - 11\, \times\, 13$
$- 91\, ,\, - 143$
$\because\, - 91\, >\, - 143$
So $\displaystyle \frac{- 11}{13}$ is smaller.

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

Arrange the following numbers in descending order. $\displaystyle\, -2,\, \frac{4}{-5},\, \frac{-11}{20},\, \frac{3}{4}$ 

  1. $\displaystyle\frac{3}{4}\, >\, -2\, >\, \frac{-11}{20}\, >\, \frac{4}{-5}$
  2. $\displaystyle\frac{3}{4}\, >\, \frac{-11}{20}\, >\, \frac{-4}{5}\, >\,- 2$
  3. $\displaystyle\frac{3}{4}\, >\, \frac{4}{-5}\, >\, -2\,>\, \frac{-11}{20}$
  4. $\displaystyle\frac{3}{4}\, >\, \frac{4}{-5}\, >\, \frac{-11}{20}\, >\, - 2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By verification process, $A\,\rightarrow\, \displaystyle\frac{3}{4},\, \frac{-2}{1}, \, \frac{-11}{20},\, \frac{-4}{5}$

$3\,\times\, 1,\, -2\,\times\, 4$

3, - 8

Correct, $-2\,\times\, 20, \, -11\,\times\, 1$

- 40, - 11

Wrong.

$B\, \rightarrow\, \displaystyle \frac {3}{4},\, \frac{-11}{20}, \frac{-4}{5},\, \frac{-2}{1}$

$3\,\times\, 20, \, -11\,\times\, 4$

60, - 44

$\displaystyle\frac{3}{4}\, >\,\frac{-11}{20}$ $-11\,\times\, 5,\, -4\,\times\, 20$

- 55, - 80

$\because\, \displaystyle\frac{-11}{20}\, >\, \frac{-4}{5}$

$-4\,\times\, 1,\, -2\,\times\, 5$

- 4, - 10

$\because\, \displaystyle\frac{-4}{5}\, >\, -2$

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

27 > 18 and (-9) is negative.
(Where a = 27, b = 18 , c = -9)  

  1. $\displaystyle \frac { 27 }{ -9 } >\frac { 18 }{ -9 } $
  2. $\displaystyle \frac { -9 }{ 27 } >\frac { -9 }{ 18 } $
  3. $\displaystyle \frac { 27 }{ 9 } >\frac { 18 }{ 9 } $
  4. $\displaystyle \frac { 27 }{ -9 } <\frac { 18 }{ -9 } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When dividing an inequality by a negative number, the inequality sign must be reversed. Since 27 > 18, dividing both sides by -9 results in 27/-9 < 18/-9, which is -3 < -2.

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

Arrange the following in ascending order:
$\cfrac { 2 }{ 5 } ,\cfrac { 1 }{ 3 } ,\cfrac { 3 }{ 10 } $

  1. $\cfrac { 1 }{ 3 } ,\cfrac { 3 }{ 10 } ,\cfrac { 2 }{ 5 } $
  2. $\cfrac { 3 }{ 10 } ,\cfrac { 2 }{ 5 } ,\cfrac { 1 }{ 3 } $
  3. $\cfrac { 3 }{ 10 } ,\cfrac { 1 }{ 3 } ,\cfrac { 2 }{ 5 } $
  4. $\cfrac { 2 }{ 5 } ,\cfrac { 1 }{ 3 } ,\cfrac { 3 }{ 10 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, 

$\dfrac{2}{5}, \dfrac{1}{3}, \dfrac{3}{10}$

LCM $5, 3, 10$ is $30$
So, 
$\dfrac{2}{5} \times \dfrac{6}{6}$ = $\dfrac{12}{30}$

$\dfrac{1}{3} \times \dfrac{10}{10}$ = $\dfrac{10}{30}$

$\dfrac{3}{10} \times \dfrac{3}{3}$ = $\dfrac{9}{30}$

As we know, $9 < 10 < 12$
So, 
$\dfrac{3}{10} < \dfrac{1}{3} < \dfrac{2}{5}$

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

Arrange the following in ascending order:
$\cfrac { 5 }{ 8 } ,\cfrac { 5 }{ 6 } ,\cfrac { 1 }{ 2 } $

  1. $\cfrac { 1 }{2 } ,\cfrac { 5 }{ 8 } ,\cfrac { 5 }{ 6 } $
  2. $\cfrac { 5 }{6 } ,\cfrac { 5 }{ 8 } ,\cfrac { 1 }{ 2 } $
  3. $\cfrac { 5 }{8 } ,\cfrac { 1 }{ 2 } ,\cfrac { 5 }{ 6 } $
  4. $\cfrac { 1 }{2 } ,\cfrac { 5 }{ 6 } ,\cfrac { 5 }{ 8 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, 

$\dfrac{5}{8}, \dfrac{5}{6}, \dfrac{1}{2}$

LCM $8, 6, 2$ is $24$

So, 

$\dfrac{5}{8} \times \dfrac{3}{3}$ = $\dfrac{15}{24}$

$\dfrac{5}{6} \times \dfrac{4}{4}$ = $\dfrac{20}{24}$

$\dfrac{1}{2} \times \dfrac{12}{12}$ = $\dfrac{12}{25}$

As we know, $12 < 15 < 20$

So, 

$\dfrac{1}{2} < \dfrac{5}{8} < \dfrac{5}{6}$

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

State whether true or false


$\cfrac { 2 }{ 5 } $ of $\cfrac { 4 }{ 7 } $  is smaller than $\cfrac { 3 }{ 4 } $ of $\cfrac { 1 }{ 2 } $

  1. True

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

$\dfrac{2}{5}$ of $\dfrac{4}{7}=\dfrac{2\times 4}{5\times 7}=\dfrac{8}{35}$


$\dfrac{3}{4}$ of $\dfrac{1}{2}=\dfrac{3\times 1}{4\times 2}=\dfrac{3}{8}$


To compare two fractions let us make the denominators same.

LC.M of $8,35=280$

$\therefore \dfrac{8\times 8}{35 \times 8}=\dfrac{64}{280}$

And $\dfrac{3\times 35}{8\times 35}=\dfrac{105}{280}$

We have $\dfrac{105}{280}>\dfrac{64}{280}$

Hence $\dfrac{3}{8}>\dfrac{8}{35}$

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

Akshit, Rajat, Sanjay and Nikunj each took the same spelling test.
$\bullet$ Akshit spelled $\displaystyle\frac{7}{10}$ of the words correctly.
$\bullet$ Rajat spelled $\displaystyle\frac{3}{4}$ of the words correctly.
$\bullet$ Sanjay spelled $\displaystyle\frac{4}{5}$ of the words correctly.
$\bullet$ Nikunj spelled $\displaystyle\frac{2}{3}$ of the words correctly.
Who spelled the least number of words correctly?

  1. Akshit

  2. Rajat

  3. Sanjay

  4. Nikunj
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Descending order of the fraction of words spelled correctly is,

$\Rightarrow$  $\dfrac{4}{5}>\dfrac{3}{4}>\dfrac{7}{10}>\dfrac{2}{3}$

$\Rightarrow$  $Sanjay>Rajat>Akshit>Nikunj$

$\therefore$    $Nikunj$ spelled least number of words correctly.