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

  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:

$12.1280 < 12.129$

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.