Let a = {2/3÷ -4/5+7/12+-11/6}{1/9+5/3× -8/15+7/27} Then, the value of a is

Correct Answer is : 675168675/168168675

Correct Answer is : 675168675/168168675

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CTET Paper II (Mathematics and Science) 10 Jan 2022 Solved Paper

Question : 34 of 150

Marks: +1, -0

Let a =

\frac{\frac{2}{3}\div \frac{-4}{5}+\frac{7}{12}+\frac{-11}{6}}{\frac{1}{9}+\frac{5}{3}\times \frac{-8}{15}+\frac{7}{27}}

Then, the value of a is

Solution:

Concept:

Simplify complex fractions by handling division and multiplication before addition/subtraction, using common denominators to combine terms.

Explanation:

First, change the division into multiplication:

\frac{2}{3} \div \frac{-4}{5} = \frac{2}{3} \times \frac{5}{-4} = \frac{-10}{12} = -\frac{5}{6}

In the numerator:

-\frac{5}{6} + \frac{7}{12} + \frac{-11}{6} = -\frac{5}{6} - \frac{11}{6} + \frac{7}{12} = -\frac{16}{6} + \frac{7}{12} = -\frac{32}{12} + \frac{7}{12} = -\frac{25}{12}

In the denominator:

\frac{5}{3} \times \frac{-8}{15} = -\frac{40}{45} = -\frac{8}{9}

. Then

\frac{1}{9} - \frac{8}{9} + \frac{7}{27} = -\frac{7}{9} + \frac{7}{27} = -\frac{21}{27} + \frac{7}{27} = -\frac{14}{27}

Now divide:

a = \frac{-\frac{25}{12}}{-\frac{14}{27}} = \frac{25}{12} \times \frac{27}{14} = \frac{25 \times 27}{12 \times 14} = \frac{675}{168}

Answer:

\frac{675}{168}

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