Question

How do you simplify $ \dfrac{{\dfrac{4}{5}}}{{6\dfrac{2}{3}}} $ ?

Answer 1

Hint: Here first of all will simplify the given expression and will convert the given mixed fraction in the form of simple fraction and then will simplify both the fractions for the resultant required value.

Complete step-by-step answer:
Mixed number is the combination of a whole number and the fraction. Fraction is the number expressed in the form of the numerator and the denominator.
Convert the given mixed fraction in the form of fraction.
 $ 6\dfrac{2}{3} = \dfrac{{20}}{3} $
Now take the given expression and then place the above value in it.
 $ \dfrac{{\dfrac{4}{5}}}{{6\dfrac{2}{3}}} = \dfrac{{\dfrac{4}{5}}}{{\dfrac{{20}}{3}}} $
In the above expression denominator of the fraction of the numerator and the denominator’s denominator goes in the numerator.
 $ \dfrac{{\dfrac{4}{5}}}{{6\dfrac{2}{3}}} = \dfrac{4}{5} \times \dfrac{3}{{20}} $
Find the factors for the terms in the denominator.
 $ \dfrac{{\dfrac{4}{5}}}{{6\dfrac{2}{3}}} = \dfrac{4}{5} \times \dfrac{3}{{4 \times 5}} $
Common factors from the numerator and the denominator cancels each other. Therefore, remove from the numerator and the denominator in the above fraction.
 $ \dfrac{{\dfrac{4}{5}}}{{6\dfrac{2}{3}}} = \dfrac{1}{5} \times \dfrac{3}{5} $
Simplify the above equation-
 $ \dfrac{{\dfrac{4}{5}}}{{6\dfrac{2}{3}}} = \dfrac{3}{{25}} $
This is the required solution.
So, the correct answer is “ $ \dfrac{3}{{25}} $ ”.

Note: Fractions are the part of the whole. Generally, it represents any number of equal parts and it describes the part from a certain size and it is the number expressed in the form of numerator upon the denominator. Know the difference between the fraction and the percentage and apply accordingly.
Be careful while simplifying equations and always remember when its percentage is with respect to hundred. Convert the decimal point in the form of fraction. To convert decimal into fraction, place the decimal number over its place value. For example, for $ 0.2 $ the two is in the tenths place so that we place $ 2 $ over $ 10 $ to create the equivalent fraction i.e. $ \dfrac{2}{{10}} $ and similarly if there is two digits after decimal point, for $ 0.25 $ the $ 25 $ is in the hundredths place so that we place $ 25 $ over $ 100 $ to create the equivalent fraction i.e. $ \dfrac{{25}}{{100}} $ .