Tag: maths

Questions Related to maths

The fraction equivalent to $\displaystyle \frac {1} {3} $ is ................

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

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

  2. $\displaystyle \frac {5} {15} $

  3. $\displaystyle \frac {6} {18} $

  4. All the above

Show answer
Correct Option: D
Explanation:

3×3=9 so 3/9=1/3

5×3=15 so 5/15=1/3
6×3=18 so 6/18=1/3
So all the given options are equivalent to 1/3
Option D is the correct answer.

Which number should come in place of $\displaystyle \ \Box, \dfrac { 1 }{ 4 } +\dfrac { 2 }{ 4 } +\dfrac { \Box  }{ 4 } =1\dfrac { 1 }{ 2 } $

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: C
Explanation:

$=\displaystyle \frac { 3 }{ 2 } -\frac { 1 }{ 4 } -\frac { 2 }{ 4 }=  \frac { 6-1-2 }{ 4 }= \frac{3} {4} $ 

What is the value of $\dfrac {1}{1 + \sqrt {2} + \sqrt {3}} + \dfrac {1}{1 - \sqrt {2} + \sqrt {3}}$?

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $1$

  2. $\sqrt {2}$

  3. $\sqrt {3}$

  4. $2$

Show answer
Correct Option: A
Explanation:

The value of $\dfrac {1}{(1 + \sqrt {3})+\sqrt {2}} + \dfrac {1}{(1 + \sqrt {3}) - \sqrt {2}}$ is
$=\dfrac {(1 + \sqrt {3} - \sqrt {2}) + (1 + \sqrt {3} + \sqrt {2})}{(1 + \sqrt {3})^{2} - (\sqrt {2})^{2}}$
$= \dfrac {2(1 + \sqrt {3})}{1 + 3 + 2\sqrt {3} - 2}$
$= \dfrac {2(1 + \sqrt {3})}{2(1 + \sqrt {3})} = 1$

Reduce fraction to lowest form:
$\dfrac{144}{36}$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\dfrac{4}{1}$

  2. $\dfrac{12}{2}$

  3. $\dfrac{1}{36}$

  4. $\dfrac{4}{9}$

Show answer
Correct Option: A
Explanation:

$\dfrac{144}{36}$


Dividing numerator and denominator by $12$, we get
$\dfrac{144}{36} = \dfrac{12}{3}$

Dividing both numerator and denominator again by $3$, we get

$\dfrac{12}{3} = \dfrac{4}{1}$

This is the lowest form

Reduce fraction to lowest form:
$\dfrac{100}{200}$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\dfrac{1}{2}$

  2. $\dfrac{2}{3}$

  3. $\dfrac{2}{5}$

  4. $\dfrac{2}{6}$

Show answer
Correct Option: A
Explanation:

$\dfrac{100}{200}$


Dividing numerator and denominator by $100$, we get
$\dfrac{100}{200} = \dfrac{1}{2}$

This is the lowest form

Reduce fraction to lowest form:
$\dfrac{12}{16}$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

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

  2. $\dfrac{1}{4}$

  3. $\dfrac{1}{16}$

  4. $\dfrac{2}{8}$

Show answer
Correct Option: A
Explanation:

$\dfrac{12}{16}$


Dividing numerator and denominator by $4$, we get
$\dfrac{12}{16} = \dfrac{3}{4}$

This is the lowest form

Reduce fraction to lowest form:
$\dfrac{125}{625}$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\dfrac{1}{5}$

  2. $\dfrac{12}{625}$

  3. $\dfrac{5}{625}$

  4. $\dfrac{15}{25}$

Show answer
Correct Option: A
Explanation:

$\dfrac{125}{625}$


Dividing numerator and denominator by $25$, we get
$\dfrac{125}{625} = \dfrac{5}{25}$

Dividing again both numerator and denominator by $5$, we get

$\dfrac{5}{25} = \dfrac{1}{5}$

This is the lowest form

Reduce fraction to lowest form:
$\dfrac{25}{100}$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\dfrac{25}{10}$

  2. $\dfrac{1}{4}$

  3. $\dfrac{5}{10}$

  4. $\dfrac{5}{100}$

Show answer
Correct Option: B
Explanation:

$\dfrac{25}{100}$


Dividing numerator and denominator by $25$, we get
$\dfrac{25}{100} = \dfrac{1}{4}$

This is the lowest form

Reduce fraction to lowest form:
$\dfrac{81}{36}$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\dfrac{18}{2}$

  2. $\dfrac{1}{36}$

  3. $\dfrac{8}{36}$

  4. $\dfrac{9}{4}$

Show answer
Correct Option: D
Explanation:

$\dfrac{81}{36}$


Dividing numerator and denominator by $9$, we get
$\dfrac{81}{36} = \dfrac{9}{4}$

This is the lowest form

Which of these statements is CORRECT?

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\dfrac {3}{6}$ and $\dfrac {1}{2}$ are equivalent fractions

  2. $\dfrac {1}{2}$ of an hour is equal to $20$ minutes

  3. $\dfrac {5}{6}$ is equal to $\dfrac {6}{5}$

  4. $1\ mm$ is $\dfrac {1}{100}$ of $1\ cm$

Show answer
Correct Option: A
Explanation:

(A) $\dfrac {3}{6} = \dfrac {3\div 3}{6\div 3} = \dfrac {1}{2}$
(B) $\dfrac {1}{2}$ of an hour $= \dfrac {1}{2}\times 60$ minutes = $30$ minutes
(C) $\dfrac {5}{6} = 0.8333, \dfrac {6}{5} = 1.2$
$\therefore \dfrac {5}{6}\neq \dfrac {6}{5}$
(D) $\dfrac {1}{100}$ of $1$ cm = $\dfrac {1}{100}\times 10$ mm = $\dfrac {1}{10}$ mm.

Hence the correct answer is option A.