Charles ate of the plum cake in the morning and of the cream cake in the evening. The amount of cake he ate in all is__________.

The correct answer is:

Step1: First we will write all the fractions and then we will write the denominator and then we will use prime factorization method to add the fraction.
Fractions are: and 
In this question the denominators are  and .
Factors of  are:
Factors of  are:
Step2:  For calculating the LCM we will multiply the factors by considering the common factors only one time with the highest exponent.
In this case the factor  is common in both  and  so we will multiply it only once with the highest exponent
LCM (,) = 
LCM (,) = 
Step3: Now what we do is divide the LCM by each denominator and multiply the numerator by quotient and then add them
So, 
and 
So, we will multiply the numerator of  by  and numerator of  by .

So, Charles ate a total of  plum cake which can be further simplified by dividing both numerator and denominator by  which gives