Question

How do you simplify $\dfrac{2}{7} + \dfrac{1}{2}$ ?

Answer 1

Hint: To simplify this fraction we have two methods one is by converting fractions to decimals or by taking the least common factor LCM . after converting them add the obtained terms.

Complete step by step solution:
The objective of the problem is to simplify the $\dfrac{2}{7} + \dfrac{1}{2}$
About the fraction: A fraction is the part of a whole number. A fraction has two parts; they are numerator and denominator. A numerator is one that is above the line and a denominator is one that is below the line and the line indicates division. There are three types of functions. They are proper fractions, improper fractions, and mixed fractions.
About the decimal: A decimal number is a number where a number is followed by a dot point followed by one or more numbers. The number before the dot is called the integral part and the number after the dot is called the fractional part.
Method 1: converting fractions to decimals.
Now, to convert fraction numbers into decimal numbers simply divide the numerator by the denominator. Use the basic division processor to solve this.
Converting $\dfrac{2}{7}$ as a decimal.
 \[\begin{gathered}
  \,\,7\mathop{\left){\vphantom{1\begin{gathered}
  20 \\
  \underline {14} \\
\end{gathered} }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}
  20 \\
  \underline {14} \\
\end{gathered} }}}
\limits^{\displaystyle \,\,\, {0.285}} \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,60 \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\underline {56} \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,40 \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline {35} \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5\,\,\,\,\,\,\,\,\, \\
\end{gathered} \]
In above we take zero beside 2 because we take zero in the quotient so we put zero beside the 2.
Therefore, the decimal number of the fraction $\dfrac{2}{7}$ is 0.285 approximately.
Similarly , we can find the value of $\dfrac{1}{2}$. The value of half is 0.5
now add the terms 0.285 and 0.5 we get
$ \Rightarrow 0.285 + 0.5 = 0.785$
Therefore the value of $\dfrac{2}{7} + \dfrac{1}{2}$ is 0.785 approximately.
Method 2: By taking least common factor
We have to find the value of $\dfrac{2}{7} + \dfrac{1}{2}$
Now take the least common factor of 7 and 2 . the LCM of 7 and 2 is 14
Now we get
$\dfrac{2}{7} + \dfrac{1}{2} = \dfrac{{2\left( 2 \right) + 1\left( 7 \right)}}{{14}}$
On simplifying above we get
$ \Rightarrow \dfrac{{11}}{{14}}$
By using the above division method or by using a calculator we get the value of 11/14.
The value of 11/14 is 0.785 approximately.

Therefore, the value of $\dfrac{2}{7} + \dfrac{1}{2}$ is 0.785 approximately.

Note:
A fraction is said to be a proper fraction if the numerator is less than the denominator.
A fraction is said to be an improper fraction if the numerator is greater than or equal to the denominator. And a fraction is said to be a mixed fraction if a whole number and the proper fractions are sides by side.