Question

How do you write $6\dfrac{1}{2}$ miles and $1\dfrac{1}{4}$ miles as decimals?

Answer 1

Hint: To write $6\dfrac{1}{2}$ miles and $1\dfrac{1}{4}$ miles as decimals, we are going to write improper fractions into proper fractions. Like, one of the miles given in the above problem is: $6\dfrac{1}{2}$, let us convert this improper fraction into a proper fraction $6+\dfrac{1}{2}$. Now, taking 2 as L.C.M in this fraction and we get, $\dfrac{12+1}{2}=\dfrac{13}{2}$. Now, we are going to divide this fraction and will get the answer in decimals. Similarly, we are going to do it for the other miles.

Complete step by step answer:
The miles given in the above problem which we have to convert into decimals are as follows:
$6\dfrac{1}{2}$ miles and $1\dfrac{1}{4}$ miles
Now, we are going to convert these improper fractions into proper fractions as follows:
First of all, we are going to convert $6\dfrac{1}{2}$ miles into proper fraction as follows:
$\Rightarrow \left( 6+\dfrac{1}{2} \right)miles$
Taking L.C.M in the above expression we get,
$\begin{align}
  & \Rightarrow \left( \dfrac{12+1}{2} \right)miles \\
 & \Rightarrow \dfrac{13}{2}miles \\
\end{align}$
Now, dividing the above fraction by using division method we get,
$2\overset{6.5}{\overline{\left){\begin{align}
  & 13 \\
 & 12 \\
 & \overline{01}0 \\
 & \dfrac{010}{000} \\
\end{align}}\right.}}$
Hence, we have found the decimal for $6\dfrac{1}{2}$ miles as 6.5 miles.
Now, converting the second improper fraction i.e. $1\dfrac{1}{4}$ miles into proper fraction as follows:
$\Rightarrow \left( 1+\dfrac{1}{4} \right)miles$
Taking 4 as L.C.M in the above expression we get,
$\begin{align}
  & \Rightarrow \left( \dfrac{4+1}{4} \right)miles \\
 & =\dfrac{5}{4}miles \\
\end{align}$
Dividing each of the two fractions and then will get the answer in decimals we get,
Now, we are dividing 5 by 4 by division method we get,
$4\overset{1.25}{\overline{\left){\begin{align}
  & 5 \\
 & 4 \\
 & \overline{1}0 \\
 & 08 \\
 & \overline{\begin{align}
  & 020 \\
 & \dfrac{020}{000} \\
\end{align}} \\
\end{align}}\right.}}$
Hence, we have found the decimal form for the $1\dfrac{1}{4}$ miles as 1.25 miles.

Note:
The alternate approach to the above problem is that we will first convert these improper fractions:
$6\dfrac{1}{2}$ miles and $1\dfrac{1}{4}$ miles
First of all, we are solving the first improper fraction in the above:
$\Rightarrow \left( 6+\dfrac{1}{2} \right)miles$
In the above expression, we can write one half as 0.5 in the above expression and we get,
$\begin{align}
  & \Rightarrow \left( 6+0.5 \right)miles \\
 & =6.5miles \\
\end{align}$
Similarly, we are going to find the decimal representation for $1\dfrac{1}{4}$ miles:
$\Rightarrow \left( 1+\dfrac{1}{4} \right)miles$
Now, we know that one half and one fourth in the decimal form is 0.5 and 0.25 so substituting these fraction values in the decimal form we get,
$\begin{align}
  & \Rightarrow \left( 1+0.25 \right)miles \\
 & =1.25miles \\
\end{align}$
As you can see that we have got the same decimal form as that we have got in the above solution.