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This is one of our many quizzes on Fraction operations. Click on this to access more such competitive quizzes on Number System.

Fraction operations Quiz 2

mathematics

 If the sum of three fractions  is $2\dfrac{{11}}{{12}}$. Then As the greatest fraction is divided by the smallest fraction, the result is $\dfrac{7}{{12}}$ , which is greater than the middle fraction by $\dfrac{1}{6}$. Find all the three fractions.

 Use all given conditions appropriately. Then apply LCM rules and rearrange to solve.

Middle $= \dfrac{7}{{12}} - \dfrac{1}{6} = \dfrac{5}{{12}}$ $ \\ $  Let, Greatest $= \dfrac{a}{b}$ and smallest $= \dfrac{x}{y}$ $ \\ \dfrac{ay}{bx} = \dfrac{7}{12} \\  \dfrac{a}{b} + \dfrac{x}{y} + \dfrac{5}{{12}} = \dfrac{{35}}{{12}} \\   \Rightarrow \dfrac{a}{b} + \dfrac{x}{y} = \dfrac{5}{3} \\ $ Taking LCM $ \\ \dfrac{{7x}}{{12y}} + \dfrac{x}{y} = \dfrac{5}{3} \\   \Rightarrow \dfrac{x}{y} = \dfrac{{20}}{{19}} \\   \Rightarrow \dfrac{a}{b} = \dfrac{{35}}{{57}}  $ 

 $\dfrac{5}{7}$ of the pole is in the mud. When $\dfrac{2}{3}$ of it is pulled out, 250 cm is still in the mud. Find the total length of the pole. 

 Solve by reading the conditions correctly and equate it to $x$.

&nbsp;$x = $ Length of pole $ \\\dfrac{5}{7}x - \dfrac{2}{3}x = 250 \\  \dfrac{1}{{21}}x = 250 \\  x = 5250 $  

 $\dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{7} + \dfrac{1}{{14}} + \dfrac{1}{{28}} = ?$.

 Get the LCM of the denominators to solve left to right.

&nbsp;$\dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{7} + \dfrac{1}{{14}} + \dfrac{1}{{28}}  \\ \Rightarrow  \dfrac{3}{4} + \dfrac{1}{7} + \dfrac{1}{{14}} + \dfrac{1}{{28}}  \\ \Rightarrow  \dfrac{3}{4} + \dfrac{3}{{14}} + \dfrac{1}{{28}} = 1$

 If the numerator of fraction is increased by $150\% $ and the denominator is decreased by $75\% $, the resultant fraction is $\dfrac{8}{15}$. Find the original fraction.

 Find the increase in percentage and add.

Initial $= \dfrac{a}{b}$ $ \\ $  final $= \dfrac{{2.5a}}{{0.25b}} = \dfrac{8}{{15}}$ $ \\ \Rightarrow \dfrac{a}{b} = \dfrac{4}{{75}}  $ 

 If the numerator is 3 times less than the denominator. If the numerator is decreased by 1 and denominator is increased by 3, then the denominator becomes 6 times the numerator?

 Reduce to the prime factors. Solve step by step using given conditions.

T: Let fraction $= \dfrac{a}{b}$ $ \\  b = a + 3 \\  b + 4 = 8(a - 1) \\   \Rightarrow b + 3 = 8(b - 4) \\   \Rightarrow 7b = 35 \\  \therefore b = 5,a = 2$ 