Tag: lowest form of a fraction

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

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 

  1. $2$
  2. $4$
  3. $7$
  4. $9$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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:

  1. $-1$
  2. $1$
  3. $30$
  4. $-30$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $-30$. 

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

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

  1. $7$
  2. $29$
  3. $141$
  4. $349$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $=25099=349$
Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

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 $c$).

  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 $\dfrac {a + b - c}{a - b + c}$
Reveal answer Fill a bubble to check yourself
E Correct answer
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 $(a + c)^{2} \neq b^{2}$.

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

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

  1. $(75)^{1/3}$
  2. $5\sqrt3$
  3. $3$
  4. $\sqrt{150}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $5\sqrt { 3 }$.