Question

What should be subtract from $ \left( {\dfrac{3}{4} - \dfrac{2}{3}} \right) $ to get $ \dfrac{1}{6} $ ?

Answer 1

Hint: Form an equation by assuming a number and by simplifying the equation, find the value of the assumed number by using the basic rules of addition and subtraction of fractional numbers.

Complete step-by-step answer:
Let us assume a number be $ x $ that should be subtracted from $ \left( {\dfrac{3}{4} - \dfrac{2}{3}} \right) $ to get $ \dfrac{1}{6} $ .
From the given question, we know that the subtraction between the two numbers, one being \[\] and the other being, $ x $ is equal to $ \dfrac{1}{6} $ . The equation formed by using the above numbers is:
 $ \left( {\dfrac{3}{4} - \dfrac{2}{3}} \right) - x = \dfrac{1}{6} $
By rewriting the above equation, we get,
 $ x = \left( {\dfrac{3}{4} - \dfrac{2}{3}} \right) - \dfrac{1}{6} $
Now we take the LCM of the denominator and simplify the above equation, we get,
 $
\Rightarrow x = \dfrac{{\left( {3 \times 6} \right) - \left( {2 \times 8} \right) - \left( {6 \times 4} \right)}}{{24}}\\
 = \dfrac{{18 - 16 - 24}}{{24}}\\
 = - \dfrac{{22}}{{24}}
 $
After further simplification, we get,
 $ \Rightarrow x = - \dfrac{11}{12} $
Hence, the number that should be subtracted from $ \left( {\dfrac{3}{4} - \dfrac{2}{3}} \right) $ to get $ \dfrac{1}{6} $ is $ - \dfrac{11}{12} $ .

Note: In the given question, first we need to assume a number $ x $ then form an equation with the help of given values and simplify the equation to obtain the value of $ x $ .
The addition of subtraction of two or more fraction numbers is done by making their denominator the same, which is done by taking the LCM (lowest common factor) of their denominators or you can also multiply the numerator and denominator with the same number. Let us understand with an example:
\[
\dfrac{{14}}{5} - \dfrac{{11}}{4} = \dfrac{{14 \times 4 - 11 \times 5}}{{20}}\\
{\rm{or}}\\
\dfrac{{14}}{5} \times \dfrac{4}{4} - \dfrac{{11}}{4} \times \dfrac{5}{5}
\]