Tag: lowest form of a fraction

Questions Related to lowest form of a fraction

Express in simpest from

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

  1. $-247/228$

  2. $-68/119$

  3. $87/116$

  4. $299/161$

Show answer
Correct Option: B

If $\displaystyle\,5\,\dfrac{7}{x}\,\times\,y\,\dfrac{1}{13}\,=\,12$, where fractions are in their lowest terms, then $x - y$ is equal to 

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

  1. $2$

  2. $4$

  3. $7$

  4. $9$

Show answer
Correct Option: C
Explanation:

$\displaystyle 5\,\frac{7}{x}\,\times\,y\,\frac{1}{13}\,=\,12$
By Hit and Trial method. 
Let $x = 9, y = 2$
Where the fractions are in their lowest terms, then x should be maximum possible single digit and $y$ is minimum possible single digit.
Putting this value in equ. (1)
$\displaystyle \,5\,\times\,\frac{7}{9}\,\times\,2\,\times\,\frac{1}{13}\,=\,\frac{52}{9}\,\times\,\frac{27}{13}\,=\,12
$
$\therefore \,x\,-\,y\,=7$
Hence, option 'C' is correct.

Simplest form of the ratio 140 : 24 is__

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

  1. 1 : 3

  2. 70 :12

  3. 6 : 35

  4. 35 : 6

Show answer
Correct Option: D
Explanation:

We have, $ 140:24 $
Dividing by $ 4 $ we get $ 35:6 $
As there is no other common factor  to divide with, so $ 35:6 $ is the simplest form.

What is the reciprocal of $-3$?

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

  1. $-3$

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

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

  4. $3$

  5. Undefined

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Correct Option: B
Explanation:

Reciprocal of $ -3 = \dfrac {1}{-3} $ or $ \dfrac {-1}{3} $

The value of $\left[\left(-2\displaystyle\frac{3}{4}\right)-\left(\displaystyle -1\frac{3}{4}\right)\right]+\left[\left(\displaystyle -2\frac{3}{4}\right)-\left(\displaystyle -1\frac{3}{4}\right)\right]+......$ upto $30$ times is:

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

  1. $-1$

  2. $1$

  3. $30$

  4. $-30$

Show answer
Correct Option: D
Explanation:
Consider the given expression.

$\left [ \left ( -2\dfrac{3}{4} \right )- \left ( -1\dfrac{3}{4} \right )\right ]+\left [ \left ( -2\dfrac{3}{4} \right )- \left ( -1\dfrac{3}{4} \right )\right ]+.......$ upto $30$ times

Sum $=\left[\left(\dfrac{-11}{4}\right)-\left(\dfrac{-7}{4}\right)\right]+\left[\left(\dfrac{-11}{4}\right)-\left(\dfrac{-7}{4}\right)\right]+......$ upto $30$ times

        $=[-1]+[-1]+......upto\ 30\ times$

        $=-30$

Hence, the value of the expression is $-30$. 

The number $2.525252$ can be written as a fraction, when reduced to the lowest term, the sum of the numerator and denominator is:

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

  1. $7$

  2. $29$

  3. $141$

  4. $349$

Show answer
Correct Option: D
Explanation:
Let the given number be $x=2.525252....$
multiplying with $100$ on both sides
$\Rightarrow 100x=252.525252...$
$\Rightarrow 100x=250+2.5252...$
$\Rightarrow 100x=250+x\Rightarrow 99x=250$
$\Rightarrow x=\dfrac{250}{99}$
$\therefore$ Sum of numerator and denominator $=25099=349$

The fraction $\dfrac {a^{2} + b^{2} - c^{2} + 2ab}{a^{2} + c^{2} - b^{2} + 2ac}$ is (with suitable restrictions on the values of $a, b,$ and $c$).

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

  1. Irreducible

  2. Reducible to $-1$

  3. Reducible to a polynomial of three terms

  4. Reducible to $\dfrac {a - b + c}{a + b - c}$

  5. Reducible to $\dfrac {a + b - c}{a - b + c}$

Show answer
Correct Option: E
Explanation:

$\dfrac {a^{2} + b^{2} - c^{2} + 2ab}{a^{2} + c^{2} - b^{2} + 2ac} = \dfrac {(a + b)^{2} - c^{2}}{(a + c)^{2} - b^{2}} = \dfrac {(a + b + c)(a + b - c)}{(a + c + b)(a + c - b)}$
$= \dfrac {a + b - c}{a + c - b}$ with $(a + c)^{2} \neq b^{2}$.

The simplest rationalizing factor of $\sqrt{75}$ is.

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

  1. $(75)^{1/3}$

  2. $5\sqrt3$

  3. $3$

  4. $\sqrt{150}$

Show answer
Correct Option: B
Explanation:

Let us first factorize $75$ as shown below:


$75=3\times 5\times 5=3\times { 5 }^{ 2 }$

Now consider $\sqrt {75}$ as follows:

$\sqrt { 75 } =\sqrt { 3\times 5\times 5 } =\sqrt { 3\times { 5 }^{ 2 } } =\sqrt { 3 } \times \sqrt { { 5 }^{ 2 } } =5\sqrt { 3 }$

Hence, the simplest rationalizing factor of $\sqrt {75}$ is $5\sqrt { 3 }$.