Tag: maths

Questions Related to maths

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

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

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

  2. $\displaystyle \frac{5}{10}$

  3. $\displaystyle \frac{9}{18}$

  4. all the above

Show answer
Correct Option: D
Explanation:

Doing the simplest form of all these options..

$\dfrac{3}{6} = \dfrac{1}{2}$
$\dfrac{5}{10}= \dfrac{1}{2}$ 
$\dfrac{9}{18} = \dfrac{1}{2}$
hence option D is correct..

Which one is greater?
$\cfrac { 1 }{ 2 } $  $ of \, \cfrac { 4 }{ 7 } $ or $\cfrac { 2 }{ 3 } \, of $$\cfrac { 3 }{ 7 } $


Both are equal

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

$\dfrac{1}{2}\ \ \ of \ \ \dfrac{4}{7}$


$=\dfrac{1}{2}\ \ \ \times \ \ \dfrac{4}{7}$


$=\dfrac{2}{7}$

Similarly,

$\dfrac{2}{3}\ \ \ of \ \ \dfrac{3}{7}$

$=\dfrac{2}{3}\ \ \ \times \ \ \dfrac{3}{7}$

$=\dfrac{2}{7}$

So, both are equal

Which of the following orders are the fractions from the smallest to the largest?

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

  1. $\cfrac { 1 }{ 8 } ,\cfrac { 2 }{ 8 } ,\cfrac { 5 }{ 8 } $

  2. $\cfrac { 1 }{ 2 } ,\cfrac { 4 }{ 2 } ,\cfrac { 3 }{ 2 } $

  3. $\cfrac { 3 }{ 4 } ,\cfrac { 1 }{ 4 } ,\cfrac { 2 }{ 4 } $

  4. $\cfrac { 4 }{ 16 } ,\cfrac { 2 }{ 16 } ,\cfrac { 1 }{ 16 } $

Show answer
Correct Option: A
Explanation:

In option A, denominator of all the fractions are same and numerator are in increasing order

So, option A is correct.

$\displaystyle\frac{15}{\square}$ is a fraction that lies between $\displaystyle\frac{1}{7}$ and $\displaystyle\frac{1}{8}$. What is the missing whole number in the box?

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

  1. $112$

  2. $56$

  3. $32$

  4. $65$

Show answer
Correct Option: A
Explanation:

Let the missing number be $x$

$\dfrac{1}{7}<\dfrac{15}{x}<\dfrac{1}{8}$
Multiplying  numerator and denominator by 15
$\therefore$ $\dfrac{15}{105}<\dfrac{15}{x}<\dfrac{15}{120}$
So any number between $105$ and $120$ will be the value of $x$.
Hence the correct answer is option A

Which of the following statements is true?

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

  1. $\displaystyle\frac{5}{7} <\frac{7}{9} <\frac{9}{11} <\frac
    {11}{13}$

  2. $\displaystyle\frac{11}{13} < \frac{9}{11} < \frac{7}{9} < \frac{5}{7}$

  3. $\displaystyle\frac{5}{7} < \frac{11}{13} < \frac{7}{9} < \frac{9}{11}$

  4. $\displaystyle\frac{5}{7} < \frac{9}{11} <\frac{11}{13} < \frac{7}{9}$

Show answer
Correct Option: A
Explanation:

$\dfrac{5}{7} , \dfrac{7}{9} , \dfrac{9}{11}, \dfrac{11}{13}$

making same deomenator,
$\dfrac{5}{7}= \dfrac{5\times 9 \times 11 \times 13}{7\times 9\times 11\times 13}$
$=\dfrac{6435}{9009}$ ...........................(1)


$\dfrac{7}{9}= \dfrac{7\times 7\times 11\times 13}{9\times 7\times 11\times 13}$

$=\dfrac{7007}{9009}$ ............................(2)

$\dfrac{9}{11}=\dfrac{9\times 7\times 9\times 13}{7\times 9\times 11\times 13}$

$=\dfrac{7371}{9009}$................................(3)

$\dfrac{11}{13}=\dfrac{11\times 7 \times 9 \times 11}{7 \times 9 \times 11 \times 13}$

$=\dfrac{7623}{9009}$.................................(4)

From equations (1), (2), (3) and (4);
$\dfrac{5}{7}$  <  $\dfrac{7}{9} $< $\dfrac{9}{11}$ < $\dfrac{11}{13}$

Which of the following fractions has the highest value $3/5$, $4/3$, $2/5$, $1/2$.

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

  1. $3/5$

  2. $4/3$

  3. $2/5$

  4. $1/2$

Show answer
Correct Option: B
Explanation:
Given fractions, $\dfrac{3}{5},  \dfrac{4}{3},  \dfrac{2}{5},  \dfrac{1}{2}$

LCM of $2, 3$ and $5$ is $30 $

So, 
$\dfrac{3}{5} \times \dfrac{6}{6} = \dfrac{18}{30}$

$\dfrac{4}{3} \times \dfrac{10}{10} = \dfrac{40}{30}$

$\dfrac{2}{5} \times \dfrac{6}{6} = \dfrac{12}{30}$

$\dfrac{1}{2} \times \dfrac{15}{15} = \dfrac{15}{30}$

As in above fraction all denominators are same and $40$ is the biggest numerator. 

So, $\dfrac{4}{3}$ is the biggest fraction.

While comparing like fractions, fraction with greater numerator is:

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

  1. greater

  2. smaller

  3. equal

  4. can't compare

Show answer
Correct Option: A
Explanation:

Fractions with the same denominators (bottom numbers) are called like fractions.

so, while comparing like fractions, the fraction with greater number/numerator will be greater.

If $ \dfrac {1}{a} < \dfrac {1}{b} ,$ then :

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

  1. $|a| > |b| $

  2. $ a < b$

  3. $ a > b $

  4. None of these

Show answer
Correct Option: C
Explanation:

$\begin{array}{l} We\, have \ \frac { 1 }{ a } <\frac { 1 }{ b }  \ by\, reciprocal\, both\, side\, we\; get \ \frac { a }{ 1 } >\frac { b }{ 1 }  \ \therefore a>b \ Hence,\, the\, option\, C\, is\, the\, correct\, answer. \end{array}$

A student was asked to solve the fraction $\cfrac { \cfrac { 7 }{ 3 } +\left( 1\cfrac { 1 }{ 2 }  \times\cfrac { 5 }{ 3 } \right) }{ 2+1\cfrac { 2 }{ 3 }  } $ and his answer was $\cfrac{1}{4}$. By how much was his answer wrong?

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

  1. $1$

  2. $\cfrac{1}{55}$

  3. $\cfrac{1}{220}$

  4. None of these

Show answer
Correct Option: D
Explanation:
$ \dfrac{\dfrac{7}{3}+(1\dfrac{1}{2}\times \dfrac{5}{3})}{2+1\dfrac{2}{3}}$

$ = \dfrac{\dfrac{7}{3}+(\dfrac{3}{2}\times \dfrac{5}{3})}{(2+\dfrac{5}{3})}$

$  = \dfrac{\dfrac{7}{3}+\dfrac{5}{2}}{\dfrac{11}{3}} = \dfrac{14+15}{6}\times \dfrac{3}{11} = \dfrac{29}{22}$

$ \Rightarrow $ His answer was wrong by

$ \dfrac{29}{22}-\dfrac{1}{4} = \dfrac{116-22}{88} = \dfrac{94}{88} = \dfrac{47}{44}$


Which of the following fraction is the smallest? $\dfrac{7}{6}, \dfrac{7}{9}, \dfrac{4}{5}, \dfrac{5}{7}$

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

  1. $\dfrac{7}{6}$

  2. $\dfrac{7}{9}$

  3. $\dfrac{4}{5}$

  4. $\dfrac{5}{7}$

Show answer
Correct Option: D
Explanation:
let the fractions be a, b, c, d
$ \dfrac{a}{b} = \dfrac{7}{6}\times \dfrac{9}{7} = \dfrac{9}{6}> 1\Rightarrow a> b$
a is not smallest
$ \dfrac{b}{c} = \dfrac{7}{9}\times \dfrac{4}{5} = \dfrac{28}{45}< 1\Rightarrow c> b$
 c is not smallest
$ \dfrac{b}{d} = \dfrac{7}{9}\times \dfrac{7}{5} = \dfrac{49}{45}> 1\Rightarrow b> d$
$ \Rightarrow $ d  is smallest $\Rightarrow (D)$