Question

How do you simplify \[\dfrac{12\dfrac{3}{4}}{2\dfrac{5}{16}}\]?

Answer 1

Hint: From the question we have been asked to simplify the given fraction. To solve these kinds of fraction questions we will take the mixed fractions and convert them into improper fractions. After converting them into improper fractions then we will use basic operation in mathematics which is division and simplify further to get the answer.

Complete step-by-step answer:
We are given mixed fractions in the questions.
Firstly, as we mentioned above we will convert the mixed fractions in the numerator and denominator into improper fractions.
So, the mixed fraction in the numerator is \[12\dfrac{3}{4}\] . so, we will convert it as follows.
We will multiply the four with \[12\] and add it to the numerator three. So, we get,
\[\Rightarrow 12\dfrac{3}{4}\]
\[\Rightarrow \dfrac{12\times 4+3}{4}\]
\[\Rightarrow \dfrac{51}{4}\]
Now, in the similar manner we will convert the mixed fraction of denominator into improper fraction as follows.
\[\Rightarrow 2\dfrac{5}{16}\]
We will multiply the two with \[16\] and add the five in the numerator. So, we get the expression reduced as follows.
\[\Rightarrow \dfrac{16\times 2+5}{16}\]
\[\Rightarrow \dfrac{37}{16}\]
Now, as given in the question we will divide these both improper fractions using the basic operation in division and get the required solution.
So, we get the expression as follows.
\[\Rightarrow \dfrac{\dfrac{51}{4}}{\dfrac{37}{16}}\]
Now, we will multiply the denominator to the numerator after reversing the fraction in the denominator.
So, we get,
\[\Rightarrow \dfrac{51}{4}\times \dfrac{16}{37}\]
\[\Rightarrow \dfrac{204}{37}\]

Note: Students should be very careful in doing the calculations. Students should have good knowledge in the concept of fractions like mixed fractions and improper fractions etc..and also should perform the division of fractions very carefully. If we do mistakes like for example after this step \[\Rightarrow \dfrac{\dfrac{51}{4}}{\dfrac{37}{16}}\] if we write the next step as \[\Rightarrow \dfrac{51}{4}\times \dfrac{37}{16}\] instead of \[\Rightarrow \dfrac{51}{4}\times \dfrac{16}{37}\] our solution will be wrong.