Question

Find the value of the following:
\[5 + 3\dfrac{4}{7}\]

Answer 1

Hint: In order to solve the given problem convert the mixed fraction in form of improper fraction by using the method of conversion and take the base of the integer as 1 to convert it in form of fraction and further by taking the LCM of the two fractions proceed to solve the given term.

Complete step-by-step answer:
Given that:
\[5 + 3\dfrac{4}{7}\]
Let us first divide the problem in two parts.
1. Conversion part
2. Simplification part
First let us proceed with conversion.
Let us convert the integer in fraction by taking the denominator as 1.
\[5 = \dfrac{5}{1}\]
Now let us convert the mixed number in some improper fraction by the use of conversion method.
\[3\dfrac{4}{7} = \dfrac{{\left( {3 \times 7} \right) + 4}}{7} = \dfrac{{21 + 4}}{7} = \dfrac{{25}}{7}\]
Now let us proceed with the simplification part of the problem.
Given problem was:
\[5 + 3\dfrac{4}{7}\]
Now the problem has changed to:
\[\dfrac{5}{1} + \dfrac{{25}}{7}\]
We have to add two fractions now.
Let us take the LCM of the denominators of the given two fractions.
LCM of 1 and 7 is 7.
So let us now proceed with the simplification by converting the denominator as LCM which is equal to 7.
\[
   = \dfrac{5}{1} + \dfrac{{25}}{7} \\
   = \dfrac{{35 + 25}}{7} \\
   = \dfrac{{60}}{7} \\
 \]
Hence, the simplified result is \[\dfrac{{60}}{7}\]

Note:In order to solve these types of problems related to simplification of the fractions; never try to directly solve the problem. First convert it in terms of fraction with the same denominator by taking the LCM of the denominator and then proceed further. These types of problems can also be solved by directly converting the fraction in decimal and further after addition of decimal conversion of decimal back to fraction but that is a more troublesome method as dealing with fraction is quite easier as compared to dealing with decimals.