Adding Fractions
We are required to find the sum:
[tex]\frac{7}{8}+\frac{9}{10}[/tex]In order to be able to find the sum, we first need to make both denominators with the same value, or a common denominator.
The procedure is called Least Common Multiple of the denominators and consists of finding the lowest multiple of both denominators, in this case:
LCM(8,10)
To find the LCM, we write the prime divisors of each number as follows:
8 = 2*2*2
10 = 2*5
Now we select all the divisors the maximum number of times they appear, that is:
LCM = 2*2*2*5 = 40
Now we divide the LCM by each denominator and multiply the result by each numerator:
[tex]\frac{7}{8}+\frac{9}{10}=\frac{5\cdot7}{40}+\frac{4\cdot9}{40}[/tex][tex]\frac{7}{8}+\frac{9}{10}=\frac{35}{40}+\frac{36}{40}[/tex]Operating:
[tex]\frac{7}{8}+\frac{9}{10}=\frac{35+36}{40}=\frac{71}{40}[/tex]The result is 71/40
