Question

What is a real life situation that could be expressed by adding two rational expressions that are fractions?

Answer 1

Hint: We are given a question asking us to give a real life example that could be expressed as the sum of two fractions. There are many examples around. Suppose, we are given Rs.1000 and we spent two-thirds for groceries, three-fourths for clothes and one-fourths for bath essentials. So how much was spent in each of the categories can be found by adding up the fraction and solving it further. Hence, we have a real life example for the given question.

Complete step-by-step answer:
According to the given question, we are asked to give a real life example which can be expressed by adding two rational expressions which are fractions.
There are many things around us that can be expressed by using the sum of the fractions. One such attribute can be our shopping expenditure details.
Suppose if we went shopping, we spent two thirds of the money for purchasing grocery items. Then, we spent three-fourths purchasing clothes on sale and lastly we spent one-fourths purchasing bath essentials. And we took only Rs.1000 with. What is the amount of money spent on each of the categories? The answer to this question can be solved using fractions.
We will simply add up the fractions and we will get the value of the money spent on each of the categories.
Let ‘x’ be the amount spent, so we have,
\[\dfrac{2}{3}x+\dfrac{3}{4}x+\dfrac{1}{4}x=1000\]
\[\Rightarrow \dfrac{8x+9x+3x}{12}=1000\]
\[\Rightarrow 20x=12000\]
\[\Rightarrow x=600\]
So, the amount spent on grocery items \[=\dfrac{2}{3}(600)=400\]
The amount spent on clothes \[=\dfrac{3}{4}(600)=450\]
And the amount spent on bath essentials \[=\dfrac{1}{4}(600)=150\]
Therefore, we have the real life example as per the requirement.

Note: In the above solution, the fractions had to be added to get the total expenditure and then have the value of money spent on each of the categories. Also, the use of fraction is nearly in every sector in some or the other way. And while adding up the fractions make sure that the denominators are the same, else addition won’t happen.