Question

what is \[\dfrac{1}{4}+\dfrac{1}{5}\]?

Answer 1

Hint: In the above mentioned question we need to find the sum of two fraction for this we will first make the denominator same then add both the terms (through numerator as the denominator is same) then check whether it is in simplest form if it is then that will become our final answer.

Complete step by step solution:
In the above mentioned question we will first see check whether the denominator of all the terms mentioned in the question is same or not if it same then we will add the numerators of all the terms and convert the resultant term in simplest form i.e. there is no common term present between the numerator and denominator, but if the denominator is not same then we will first make the denominator same then add the numerator and then change the resultant term into simplest term. Now when we see our question we can clearly see that there are two terms and both of them have different denominators i.e. 4 and 5 respectively, so we need to make the denominator the same, to do that we are going to take the LCM of both the numbers. The LCM of 4 and 5 is equal to 20 so the equivalent denominator is 20. Now to change the numerator, when we see the first term we need to multiply the denominator by 5 so to equalize that we will multiply the numerator also by 5 and we will get the equivalent first term as \[\dfrac{5}{20}\] , we are going to do the same thing in the second term i.e. we need to multiply the denominator by 4 to make it 20 and in order to equalize that we will multiply the numerator by 4 and we will get the equivalent second term as \[\dfrac{4}{20}\]. Now the denominator of both the terms are equal we will add the numerator and we get the equivalent term as:
\[\dfrac{5}{20}+\dfrac{4}{20}=\dfrac{9}{20}\]
\[\dfrac{9}{20}\] is in the simplest form as there is no common factor between 9 and 20.
So the value of \[\dfrac{1}{4}+\dfrac{1}{5}\] is \[\dfrac{9}{20}\].

Note: There might not be only two terms like in the above equation there can be many so while adding those fractions make the denominator of every single term equal and according to that remember to change the numerator then add those terms and check whether they are in simplest form or not.