Question

Solve the following expression $a+3\dfrac{1}{2}=5$.

Answer 1

Hint:We will first convert mixed fraction into normal fraction as follows. Let us suppose, we have a mixed fraction, say, $a\dfrac{b}{c}$ then it can be converted into the normal fraction as, $\dfrac{a\times c+b}{c}$. After that, we will transfer the obtained normal fraction from the LHS to the RHS and then by solving it, we will get the value of a.

Complete step-by-step answer:
In this question, we have been asked to solve the expression, $a+3\dfrac{1}{2}=5$. To solve this question, we need to know about the conversion of a mixed fraction into its normal fraction. So, we can convert a mixed fraction into a normal fraction as follows. If we have a mixed fraction, say, $a\dfrac{b}{c}$ then it can be converted into the normal fraction as, $\dfrac{a\times c+b}{c}$. Therefore, by using this concept, we will convert the mixed fraction, that is, $3\dfrac{1}{2}$ into the normal fraction. So we get,
$3\dfrac{1}{2}=\dfrac{3\times 2+1}{2}=\dfrac{7}{2}$
Now, we will substitute this value back into our expression. So, we get,
$a+\dfrac{7}{2}=5$
Now, we will transfer $\dfrac{7}{2}$ from the LHS to the RHS. So, we get,
$a=5-\dfrac{7}{2}$
On taking the LCM, we get,
$a=\dfrac{10-7}{2}=\dfrac{3}{2}$
Thus the value of a in the expression is equal to $\dfrac{3}{2}$.

Note: This is one of the most basic types of questions which is asked related to linear equations. But, still it is noticed that some students make mistakes in these types of questions. The possible mistake that the students can make in this question is by converting the mixed fraction into the wrong normal fraction. They may convert $a\dfrac{b}{c}$ as $\dfrac{a\times b+c}{b}$, which is wrong, the correct formula is $\dfrac{a\times c+b}{c}$. Also, remember that while converting any mixed fraction into the normal fraction, the denominator always remains the same. So, the students must use the correct formula in order to avoid any mistakes.