Tag: fraction

Questions Related to fraction

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.

A fraction $\displaystyle\frac{x}{y}$ can be expressed as a terminating decimal if y has no prime factors other than _________.

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

  1. $2, 3$

  2. $3, 5$

  3. $2, 5$

  4. $2, 3, 5$

Show answer
Correct Option: C
Explanation:

If the denominator has a prime factor $2$ or $5$ then it is a terminating decimal

Hence the correct answer is option C

The value of $\left(\displaystyle 1-\frac{1}{3}\right)\left(\displaystyle 1-\frac{1}{4}\right)\left(\displaystyle 1-\frac{1}{5}\right)\left(\displaystyle 1-\frac{1}{6}\right).....\left(\displaystyle 1-\frac{1}{n}\right)$ is _________.

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

  1. $\displaystyle\frac{1}{n}$

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

  3. $\displaystyle\frac{2(n-1)}{4}$

  4. $\displaystyle\frac{2}{n(n+1)}$

Show answer
Correct Option: B
Explanation:
We need to find value of $\left(1-\dfrac {1}{3}\right)\left (1-\dfrac {1}{4}\right)\left (1-\dfrac {1}{5}\right)\left(1-\dfrac {1}{6}\right).....\left (1-\dfrac {1}{n}\right)$
Solving each bracket, we get 
$\dfrac{2}{3} \times \dfrac{3}{4} \times \dfrac{4}{5} . . . . ...\dfrac{n-3}{n-2}\times \dfrac{n-2}{n-1} \times \dfrac{n-1}{n}$
Starting from $1^{st}$ term each denominator is cancelled out by next numerator.
Finally, we get $\dfrac{2}{n}$

The product of the $9$ fractions $\left(\displaystyle 1-\frac{1}{2}\right)\left(\displaystyle 1-\frac{1}{3}\right)\left(\displaystyle 1-\frac{1}{4}\right)..........\left(\displaystyle 1-\frac{1}{10}\right)=$____________.

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

  1. $\displaystyle\frac{10}{11}$

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

  3. $\displaystyle\frac{1}{10}$

  4. $\displaystyle\frac{1}{2}$

Show answer
Correct Option: C
Explanation:
We need to simplify $\left (1-\dfrac {1}{2}\right)\left (1-\dfrac {1}{3}\right)\left (1-\dfrac {1}{4}\right).....\left (1-\dfrac {1}{10}\right)$
Simplifying each bracket, we get
$\dfrac{1}{2} \times \dfrac{2}{3} \times \dfrac{3}{4} . . . . ...\dfrac{7}{8}\times \dfrac{8}{9} \times \dfrac{9}{10}$
As we can see 
Starting from $1^{st}$ term, each denominator is cancelled out by next numerator.
Finally we get $\dfrac{1}{10}$

The standard form of $\displaystyle\frac{192}{-168}$ is _________.

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

  1. $\displaystyle\frac{-2}{3}$

  2. $\displaystyle\frac{-8}{7}$

  3. $\displaystyle\frac{-1}{7}$

  4. $\displaystyle\frac{-6}{7}$

Show answer
Correct Option: B
Explanation:

the standard form of $ - \dfrac{192}{168}$

$=-\dfrac{2 \times 3\times 4\times 8}{2\times 3\times 4\times 7}$
$-\dfrac{8}{7}$

Which of the following sum is in the simplest form?

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

  1. $\dfrac{4}{9}+\dfrac{-5}{9}$

  2. $\dfrac{-2}{5}+\dfrac{13}{20}$

  3. $\dfrac{-5}{12}+\dfrac{11}{-12}$

  4. $\dfrac{-7}{8}+\dfrac{1}{12}+\dfrac{2}{3}$

Show answer
Correct Option: A
Explanation:
A. $\dfrac{4}{9} + \dfrac{-5}{9} = \dfrac{-1}{9}$ Simplest Form

B. $\dfrac{-2}{5} + \dfrac{13}{20} = \dfrac{-8+13}{20} = \dfrac{5}{20}$ Not the simplest form

C. $\dfrac{-5}{12} + \dfrac{11}{-12} = \dfrac{-5-11}{12} = \dfrac{-16}{12}$ Not the simplest form

D. $\dfrac{-7}{8} + \dfrac{1}{12} + \dfrac{2}{3} = \dfrac{-21+2+16}{24} = \dfrac{-3}{24}$ Not the simplest form

$\Rightarrow$ Only A gives answer in simplest form

Which of the following is not equivalent to $\dfrac{4}{8}$ ?

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

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

  2. $\cfrac { 16 }{ 32 } $

  3. $1$

  4. $\cfrac { 12 }{ 24 } $

Show answer
Correct Option: C
Explanation:

we have, $\dfrac{4}{8}=$ $\dfrac{1}{2}=$$\dfrac{16}{32}=$$\dfrac{12}{24}$

Among the given values, the one which is not equivalent to $\dfrac{4}{8}$ is 1.

Simplify: $\dfrac{5}{11} + 4\dfrac{3}{9} $

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

  1. $\dfrac{158}{33}$

  2. $\dfrac{168}{33}$

  3. $\dfrac{178}{33}$

  4. $\dfrac{148}{33}$

Show answer
Correct Option: A
Explanation:
$\displaystyle \frac{5}{11}+4\frac{3}{9}=\frac{5}{11}+\frac{36+3}{9}=\frac{5}{11}+\frac{39}{9}$

$\displaystyle =\frac{5\times 9+11\times 39}{9\times 11}=\frac{45+429}{99}=\frac{474}{99}=\frac{158}{33}$