Solve the following exercise:
Solve the following exercise:
To solve for the sum of , we will proceed with the following steps:
Let's begin:
Step 1: Identify the least common denominator (LCD)
The denominators are 10 and 6. The least common multiple (LCM) of 10 and 6 can be found by evaluating their prime factors:
10 = 2 × 5
6 = 2 × 3
The LCM is found by taking the highest power of each prime that appears:
LCM = 2 × 3 × 5 = 30.
Thus, the common denominator is 30.
Step 2: Convert each fraction to an equivalent fraction with the common denominator of 30
For :
Multiply both the numerator and the denominator by 3 to make the denominator 30:
.
For :
Multiply both the numerator and the denominator by 5 to make the denominator 30:
.
Step 3: Add the numerators
Now that the fractions have the same denominator, add the numerators:
.
This fraction cannot be simplified further as 22 and 30 have no common factors besides 1.
Therefore, the sum of is .