Question

How do you add \[1\dfrac{1}{4} + 1\dfrac{1}{2}\]?

Answer 1

Hint: The above question is an addition between two mixed fractions where this type of fraction can be solved by splitting it into terms in such a way that it reduces to a normal fraction and further it can be solved by equating the denominators.

Complete step by step answer:
Mixed fraction is a combination of whole a whole number and a fraction. It can also be called a mixed number. The expression is given below
\[1\dfrac{1}{4} + 1\dfrac{1}{2}\]
Here, in this expression if looking into the first term i.e., \[1\dfrac{1}{4}\]
1 is the whole number and \[\dfrac{1}{4}\] is the fraction.
Similarly, for the second term \[1\dfrac{1}{2}\]
1 is the whole number and \[\dfrac{1}{2}\] is the fraction.
So, now the first step is to convert the mixed fraction into improper fractions. These improper fractions look like a mixed fraction without the whole number but having a fraction in it.
\[\left( {\left( {\dfrac{4}{4}} \right) \times 1 + \dfrac{1}{4}} \right) + \left( {\left( {\dfrac{2}{2}} \right) \times 1 + \dfrac{1}{2}} \right)\]
In the above step, the fractions are generated in such a way that its division is 1 and also it adds with the other fraction having the same denominator.
\[
  \left( {\dfrac{4}{4} + \dfrac{1}{4}} \right) + \left( {\dfrac{2}{2} + \dfrac{1}{2}} \right) \\
   = \dfrac{5}{4} + \dfrac{3}{2} \\
 \]
So further for making the denominator equal we need to multiply the second term with 2 in both numerator and denominator so that both the terms denominator is 4.
\[
   = \dfrac{5}{4} + \left( {\left( {\dfrac{2}{2}} \right)\left( {\dfrac{3}{2}} \right)} \right) \\
   = \dfrac{5}{4} + \dfrac{6}{4} = \dfrac{{11}}{4} \\
 \]
Therefore, the solution for the above question is \[\dfrac{{11}}{4}\].

Note: In the above solved mixed fraction can be solved in an easier or direct way. In the first term we can multiply denominator 4 with whole number 1 and then add it to 1 i.e.
\[(4 \times 1) + 1 = 5\]. Therefore, we get an improper fraction\[\dfrac{5}{4}\].Similarly , solving for the second term \[(2 \times 1) + 1 = 3\].
Hence, we get \[\dfrac{3}{2}\].