Question

How do you simplify $\dfrac{{\dfrac{5}{6}}}{{1\dfrac{1}{4}}}?$

Answer 1

Hint: As you can see this question can be solved in two parts. The numerator part will be solved first and then the denominator will be solved. The numerator is a proper fraction and the denominator is a mixed fraction. So, the mixed fraction (the combination of a whole number and the fraction) will be solved separately and the proper fraction (the numerator is smaller than the denominator) will be solved separately.

Complete step by step solution:
The given problem statement is $\dfrac{\dfrac{5}{6}}{1\dfrac{1}{4}}$
For the given problem, we will first solve the mixed fraction $1\dfrac{1}{4}$ into an improper fraction.
 $\Rightarrow 1\dfrac{1}{4}=1+\dfrac{1}{4}$
 After simplifying we get,
 $\Rightarrow \dfrac{4+1}{4}=\dfrac{5}{4}$
You can even solve the above part by the method, first multiply the denominator to the whole number and then add it to the numerator.
$\Rightarrow \dfrac{4\times 1+1}{4}=\dfrac{5}{4}$
Now, we have to simplify this $\dfrac{\dfrac{5}{6}}{\dfrac{5}{4}}$
We know that $\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a}{b}\times \dfrac{d}{c}$
Therefore, following the same rule, we will get,
 $=\dfrac{5}{6}\times \dfrac{4}{5}$
After cancelling the 5 in the numerator and denominator we will get,
 $=\dfrac{4}{6}$
Now, we need to bring it to the lowest terms, we get,
 $=\dfrac{2}{3}$

Therefore, after solving we get $\dfrac{{\dfrac{5}{6}}}{{1\dfrac{1}{4}}} = \dfrac{2}{3}$

Additional Information:
For this problem we have two parts, in the numerator, we have a proper fraction and the denominator has a mixed fraction. Here, we have solved the mixed fraction first. Afterwards, we have to reduce the fraction in the lowest form and then we get our solution.

Note:
The numerator in the given problem was already in the lowest form that’s why we have solved the denominator first. The denominator is in the form of a mixed fraction. So, we solved the mixed fraction first and then we have applied the rule of \[\dfrac{{\dfrac{a}{b}}}{{\dfrac{c}{d}}} = \dfrac{a}{b} \times \dfrac{d}{c}\] . After which we have solved the fraction to get the solution.