Tag: lowest form of fractions

Questions Related to lowest form of fractions

Simplify: $\dfrac{{4 + \sqrt 5 }}{{4 - \sqrt 5 }} + \dfrac{{4 - \sqrt 5 }}{{4 + \sqrt 5 }}$

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

  1. $\dfrac {42}{11}$

  2. $\dfrac {40}{11}$

  3. $\dfrac {39}{25}$

  4. $\dfrac {16}{25}$

Show answer
Correct Option: A
Explanation:

$\dfrac{4+\sqrt5}{4-\sqrt5} = \dfrac{(4+\sqrt5)}{(4-\sqrt5)} \dfrac{(4+\sqrt5)}{(4+\sqrt5)}$    ...... rationalizing numerator and the denominator


$= \dfrac{(4+\sqrt5)^2}{16-5} = \dfrac{(4+\sqrt5)^2}{11} $

$\dfrac{4-\sqrt5}{4+\sqrt5} = \dfrac{(4-\sqrt5)}{(4+\sqrt5)} \dfrac{(4-\sqrt5)}{(4-\sqrt5)}$    ...... rationalizing numerator and the denominator, 

$= \dfrac{(4-\sqrt5)^2}{16-5} = \dfrac{(4-\sqrt5)^2}{11} $


$\dfrac{4+\sqrt5}{4-\sqrt5} +\dfrac{4-\sqrt5}{4+\sqrt5} = \dfrac{(4+\sqrt5)^2 +(4-\sqrt5)^2}{11} =\dfrac{16+5+16+5}{11} = \dfrac{42}{11}$

What fraction of a day is $16$ hours?

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

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

  2. $\dfrac{1}{24}$

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

  4. $\dfrac{16}{60}$

Show answer
Correct Option: C
Explanation:

A complete day has $24$ hours so

$Required\>ratio\>=\>\dfrac{16}{24}\>=\>\dfrac23$

Hence option $'C'$ is the answer.

Which of the following are true?

(a) $\displaystyle \frac{35}{16}=2.1875$
(b) $\displaystyle \frac{17}{8}=2.125$
(c) $\displaystyle \frac{327}{500}=0.654$
(d) $\displaystyle \frac{14588}{625}=23.3408$

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

  1. $a,b,c,d$

  2. $a,c,d$

  3. $a,b,c$

  4. $a,b,d$

Show answer
Correct Option: A
Explanation:

(i) $\displaystyle \frac{35}{16} = \frac{35 \times 5^4}{2 \times 5^4}= \frac{35 \times 625}{(10)^4}= \frac{21875}{10000}=2.1875$
(ii) $\displaystyle \frac{17}{8} = \frac{17 \times 5^3}{2^3 \times 5^3} = \frac{17 \times 125}{(10)^3}=\frac{2125}{1000}=2.125$
(iii) $\displaystyle \frac{327}{500} = \frac{327}{5\times 5 \times 5 \times 2 \times 2}$
$=\displaystyle \frac{327}{5^3 \times 2^2} = \frac{327}{5^3 \times 2^3}= \frac{654}{(10)^3} = 0.654$
(iv) $\displaystyle \frac{14588}{625} = \frac{2^2 \times 7 \times 521}{5^4} = \frac{2^6 \times 7 \times 521}{2^4 \times 5^4}$
$\displaystyle =\frac{233408}{10^4}=23.3408$

Solve: $8\dfrac{2}{3}+9\dfrac{3}{8}$

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

  1. $40$

  2. $\dfrac{433}{24}$

  3. $24$

  4. $\dfrac{437}{24}$

Show answer
Correct Option: B
Explanation:

Given, $\displaystyle 8\frac{2}{3} + 9\frac{3}{8}$


Could be written as,


$\displaystyle \frac{26}{3} + \frac{75}{8}$

LCM of 3 and 8 is 24,

= $\displaystyle \dfrac{208}{24} + \dfrac{225}{24}$

= $\displaystyle\dfrac{433}{24}$

Three number $ A, B$ and $C$ are in the ratio of $12 : 15 : 25 .$ If the some of these numbers be $364$ find the ratio between the difference of $B$ and $A$ and the difference of $C$and $B ?$

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

  1. $3 : 2$

  2. $3 : 10$

  3. $3 : 5$

  4. $4 : 2$

Show answer
Correct Option: B
Explanation:

Let $A=12k,B=15k, C=25k$

Now $A+B+C=364$
$12k+15k+25k=364$
$52k=364$
$k=\dfrac{364}{52}=7$
$\dfrac{B-A}{C-B}=\dfrac{15k-12k}{25k-15k}=\dfrac{3k}{10k}=\dfrac{3}{10}$
Hence the correct option is (B).

The standard from of a rational number -225 / 465 is 

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

  1. $\frac { -4 }{ 7 } $

  2. $\frac { -6 }{ 7 } $

  3. $\frac { -6 }{ 17 } $

  4. none of these

Show answer
Correct Option: D
Explanation:

$\dfrac{-225}{465}=\dfrac{-45}{93}=-\dfrac{15}{31}$


Thus, option D is correct.

Which of the following numbers is in standard form?

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

  1. $\dfrac { -24 }{ 52 } $

  2. $\dfrac { -49 }{ 71 } $

  3. $\dfrac { -27 }{ 48 } $

  4. $\dfrac { 28 }{ -105 } $

Show answer
Correct Option: B
Explanation:
Here option $A) \frac{-24}{52}=\frac{-6}{13}$

$B) \frac{-49}{71}$

$C) \frac{-27}{48}=\frac{-9}{16}$

$D) \frac{28}{-105}=\frac{4}{-15}$

Here (B) is in the standard form.

State whether true or false
Simplest form of the ratio 225% in form of ratio is $\displaystyle \frac{9}{4}$

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Given percentage is $ 225 % $

In fraction form, $ 225  % $ $  = \dfrac {225}{100} $

Simplifying it by dividing the numerator and denominator by $ 25  $, we get the fraction $ = \dfrac {9}{4} $

If $2a-5b = 0$ then find the value of $\displaystyle \frac{a+b}{a-b}$.

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

  1. $\displaystyle \frac{7}{2}$

  2. $\displaystyle \frac{7}{3}$

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

  4. $\displaystyle \frac{7}{5}$

Show answer
Correct Option: B
Explanation:

Given, $ 2a-5b = 0 $

$=>2a = 5b $

$ => \dfrac {a}{b} = \dfrac {5}{2} $

Applying componendo and dividendo,

Now, $ \dfrac {a+b}{a-b} = \dfrac{5+2}{5-2} =

\dfrac {7}{3} $

If $2a-5b = 0$ then find the value of  $\displaystyle \frac{a-b}{b}$

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

  1. $\displaystyle \frac{7}{2}$

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

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

  4. $\displaystyle \frac{7}{5}$

Show answer
Correct Option: B
Explanation:

Given, $ 2a-5b = 0 $
$=> 2a = 5b $
$ => \dfrac {a}{b} = \dfrac {5}{2} $
 
Now, $ \dfrac {a-b}{b} = \dfrac {a}{b} - 1 = \dfrac {5}{2} - 1 = \dfrac{5-2}{2} = \dfrac {3}{2} $