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Add the following fractions. $\dfrac{3}{2},\dfrac{13}{17}$

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Last updated date: 13th Jul 2024
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Answer
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Hint: We solve this question by using basic concepts fractional addition. We are required to solve this question by adding the given two fractions. This is done by considering the LCM or least common multiple of their denominators, then we make the denominators equal to the LCM by multiplying it with a common factor. This is multiplied with the numerator too to make sure that the fraction does not change. Then we add the numerators and obtain the answer.

Complete step by step answer:
In order to solve this question, let us consider the sum or addition of the two given fractions.
$\Rightarrow \dfrac{3}{2}+\dfrac{13}{17}$
Now, we cannot add these directly as they have a different denominator so the fractions are not a part of the same whole number. To add them, we need to take the LCM of the denominators and since both the denominators are prime numbers, we shall multiply them to obtain the LCM.
$\Rightarrow LCM\left( 2,17 \right)=2\times 17=34$
Now, we need to make both the denominators equal to this value. In order to do so, we multiply the numerator and denominator of the first fraction by 17 and the numerator and denominator of the second fraction by 2.
$\Rightarrow \dfrac{3\times 17}{2\times 17}+\dfrac{13\times 2}{17\times 2}$
Taking the product,
$\Rightarrow \dfrac{51}{34}+\dfrac{26}{34}$
Since the denominators are the same, we can just add the two numerators.
$\Rightarrow \dfrac{51+26}{34}=\dfrac{77}{34}$
This is the result of adding the two fractions. Hence, by adding $\dfrac{3}{2},\dfrac{13}{17}$ we get $\dfrac{77}{34}.$

Note: We need to know the concept of addition of two fractions to solve such sums. To add two fractions, we need to ensure the denominators are the same. To do so, we take the LCM of the denominators. Care must be taken to always represent the final answer in the simplest terms. This means that if there is any common factor between the numerator and denominator, we are required to cancel them and represent the fraction in its reduced form.