Question

Solve:\[\dfrac{3}{5}+\dfrac{2}{7}\]
\[A.\dfrac{3}{5}\]
\[B.\dfrac{31}{35}\]
\[C.\dfrac{2}{7}\]
\[D.\dfrac{5}{7}\]

Answer 1

Hint: To solve this kind of questions, we need to know about basic concepts like fractions and decimal form. Here we can solve the question in fraction form by taking the LCM of denominators and then simplifying it into a simple fraction.

Complete step by step solution:
Fraction is defined as it represents any number with equal parts in a set of whole numbers.
It is represented in the form of ‘/’, for example a/b. The number on the top is known as ‘numerator’, and the number below is called ‘denominator’. There are 6 different types of fractions namely proper fractions, improper, like, unlike and mixed fractions.
Here, the given question is \[\dfrac{3}{5}+\dfrac{2}{7}\],
The numbers on the left-hand side of addition symbol i.e., \[\dfrac{3}{5}\]are labelled as
3= numerator
5= denominator
The numbers on the left-hand side of addition symbol i.e., \[\frac{2}{7}\] are labelled as
2= numerator
7= denominator
To make answer it in a fraction form, we need to add the two fractions, then
\[\dfrac{3}{5}+\dfrac{2}{7}\]
First, we need to take the LCM of 5 and 7
The LCM of 5 and 7 is 35,
we are multiplying the 3 with 7 and 2 with 5, we get
\[\Rightarrow \dfrac{\left( 3\times 7 \right)+\left( 2\times 5 \right)}{5\times 7}\]
We have done the LCM and made it as a simple fraction, on further calculation
\[\Rightarrow \dfrac{21+10}{35}\]
\[\Rightarrow \dfrac{31}{35}\]
Therefore, the correct option is (B).

Note: The common mistake done in fractions concept is believing that fractions’ denominators and denominators should be managed as a set of whole numbers. Most of the mistakes happen here. Students leave the denominator unchanged in fraction multiplication problems. And also failing to understand the reciprocate-and multiply procedure for solving fraction-based division problems.