Adding fractions with different denominators
To solve the expression 7/10 + 3/2 + 3/5, we first need to find a common denominator for all the fractions.

Finding a common denominator
The common denominator for 10, 2, and 5 is 10. To make the denominators the same, we need to adjust the fractions accordingly.

Adjusting the fractions
- 7/10 remains the same
- To convert 3/2 to have a denominator of 10, we multiply the numerator and denominator by 5, resulting in 15/10
- To convert 3/5 to have a denominator of 10, we multiply the numerator and denominator by 2, resulting in 6/10

Adding the adjusted fractions
Now that all the fractions have a common denominator of 10, we can add them together:
7/10 + 15/10 + 6/10 = 28/10

Simplifying the final answer
By dividing both the numerator and denominator by their greatest common factor, we can simplify the fraction 28/10. The greatest common factor of 28 and 10 is 2.
28 ÷ 2 = 14
10 ÷ 2 = 5
Therefore, the final answer is 14/5 or 2 4/5.