Question

How do you simplify the fraction $1\dfrac{10}{21}+4\dfrac{5}{7}$ ?

Answer 1

Hint: The given problem consists of mixed fractions which are to be summed to get a simplified answer. As both the numbers in the given expression are nothing but mixed fractions, we first need to convert them into simple fractions. After doing that we must make the denominators of both the fractions the same to do the summation and get a simplified result of the given expression.

Complete step-by-step solution:
The expression we are given is
$1\dfrac{10}{21}+4\dfrac{5}{7}$
In the above expression both the numbers are given in the form of mixed fractions. So, to do the above summation we must convert both the numbers into simple fractions first from mixed fractions.
$1\dfrac{10}{21}$ is a mixed fraction that must be converted into a simple fraction.
This can also be written as
$=1+\dfrac{10}{21}$
$=\dfrac{21+10}{21}$
$=\dfrac{31}{21}$
Also, the second number $4\dfrac{5}{7}$ is a mixed fraction that must be converted into a simple fraction.
This can also be written as
$=4+\dfrac{5}{7}$
$=\dfrac{28+5}{7}$
$=\dfrac{33}{7}$
Now, after simplifying we can rewrite the main expression as
$=\dfrac{31}{21}+\dfrac{33}{7}$
As, the denominator of both the fractions are not same we must make the denominator same.
The LCM of $21$ and $7$ is $21$ . Hence, to get $21$ in the denominator in the second fraction we multiply $3$ with both the numerator and denominator as shown below
$=\dfrac{31}{21}+\dfrac{33\times 3}{7\times 3}$
$=\dfrac{31}{21}+\dfrac{99}{21}$
$=\dfrac{130}{21}$
Therefore, the simplified form of the given expression is $\dfrac{130}{21}$.

Note: While converting the mixed fractions into simple fractions we must be very careful about adding the whole number to the fraction, as students often get confused whether to add that number or to multiply. Also, we must keep in mind that it is necessary to get the same number in the denominator of both the fractions to complete the summation.