Question

Sarita bought $\dfrac{2}{5}$ meters of ribbon and Lalita bought $\dfrac{3}{4}$ meters of ribbon. What is the total length of ribbon they bought?

Answer 1

Hint: We will first note the length of the ribbon bought by both of them individually. After that, we will need to add both the quantities using LCM in order to find the required answer.

Complete step by step answer:
We are given that Sarita bought $\dfrac{2}{5}$ meters of ribbon.
Also, Lalita bought $\dfrac{3}{4}$ meters of ribbon.
They will obviously buy the addition of both the quantities.
Therefore, they together bought = $\dfrac{2}{5} + \dfrac{3}{4}$.
Since, the denominators of both the fractions are not the same, therefore, we cannot just directly add these. We will first require the LCM of their denominators.
Since, 4 and 5 have no common factor other than 1.
Therefore, LCM of 4 and 5 = $4 \times 5 = 20$.
Now, we see that 5 can be multiplied by 4 to get the required LCM and 4 can be multiplied to 5 to get the same LCM.
Therefore, we have:-
$ \Rightarrow \dfrac{2}{5} + \dfrac{3}{4} = \dfrac{{(2 \times 4) + (3 \times 5)}}{{20}}$
On simplifying the RHS, we will then get:-
$ \Rightarrow \dfrac{2}{5} + \dfrac{3}{4} = \dfrac{{8 + 15}}{{20}}$
On simplifying the RHS further, we will then get:-
$ \Rightarrow \dfrac{2}{5} + \dfrac{3}{4} = \dfrac{{23}}{{20}}$

Hence, they together bought $\dfrac{{23}}{{20}}m$ of ribbon.

Note:
The students must not forget to put the units that are meters here in this question because just writing any number does not make any sense, it would not represent any length but just a number.
The students must wonder how the addition with LCM did make it possible to add two numbers which have different denominators.
Let us give it a thought:-
We have the first number as: $\dfrac{2}{5}$ and the second number as: $\dfrac{3}{4}$.
Now, to add them simply, we need to make their denominators equal. We can write $\dfrac{2}{5}$ as: $\dfrac{2}{5} \times \dfrac{4}{4} = \dfrac{8}{{20}}$.
Also, we can write $\dfrac{3}{4}$ as: $\dfrac{3}{4} \times \dfrac{5}{5} = \dfrac{{15}}{{20}}$.
Now, we have got ourselves two fractions with equal denominators.
$ \Rightarrow \dfrac{2}{5} + \dfrac{3}{4} = \dfrac{8}{{20}} + \dfrac{{15}}{{20}} = \dfrac{{8 + 15}}{{20}}$
On simplifying it, we have:-
$ \Rightarrow \dfrac{2}{5} + \dfrac{3}{4} = \dfrac{{23}}{{20}}$.