Question

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

Answer 1

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 solution:
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.

\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 $$\dfrac{3}{2}$$.