Final answer:
To evaluate the expressions, multiply and simplify the fractions for 2/5 x 5/9 to get 2/9, and add the fractions for 1/4 + 5/8 after finding a common denominator to get 7/8.
Step-by-step explanation:
To evaluate the expressions 2/5 x 5/9 and 1/4 + 5/8, we perform multiplication for the first and addition for the second.
Multiplying Fractions
Multiplication of fractions involves multiplying the numerators together and the denominators together. So, for 2/5 x 5/9, you multiply 2 by 5 and 5 by 9:
2/5 x 5/9 = (2*5) / (5*9)
= 10 / 45
Now we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
10 / 45 = 2 / 9
Adding Fractions
For the addition of fractions 1/4 + 5/8, we first need to have a common denominator. The least common denominator for 4 and 8 is 8. Therefore, we convert 1/4 to 2/8:
1/4 + 5/8 = 2/8 + 5/8
Then we add the numerators:
2/8 + 5/8 = 7/8