Step-by-Step Solution for 6 + 9 - 5 * 10 / 5 + 1 / 2 of ( 90 - 25 + 5 ):

Step 1: Simplify the expression inside the parentheses first. 90 - 25 + 5 = 70

Step 2: Calculate 1/2 of 70. 1/2 * 70 = 35

Step 3: Substitute the value of 1/2 of (90 - 25 + 5) into the original expression. 6 + 9 - 5 * 10 / 5 + 35

Step 4: Perform multiplication and division from left to right. 6 + 9 - 50 / 5 + 35 6 + 9 - 10 + 35

Step 5: Perform addition and subtraction from left to right. 15 - 10 + 35 5 + 35 40

Therefore, the value of the expression 6 + 9 - 5 * 10 / 5 + 1 / 2 of (90 - 25 + 5) is 40.

Step-by-Step Solution for 105/15 * 4 + 32 + 1/4 of (15 * 4 - 16):

Step 1: Simplify the expression inside the parentheses first. 15 * 4 - 16 = 60 - 16 60 - 16 = 44

Step 2: Calculate 1/4 of 44. 1/4 * 44 = 11

Step 3: Substitute the value of 1/4 of (15 * 4 - 16) into the original expression. 105/15 * 4 + 32 + 11

Step 4: Perform multiplication and division from left to right. 7 * 4 + 32 + 11 28 + 32 + 11

Step 5: Perform addition from left to right. 28 + 32 = 60 60 + 11 = 71

Therefore, the value of the expression 105/15 * 4 + 32 + 1/4 of (15 * 4 - 16) is 71.

Step-by-Step Solution for 4 * (3 + 4 - 5) + 5 * (8 - 3 - 2):

Step 1: Simplify the expressions inside the parentheses first. 3 + 4 - 5 = 7 - 5 7 - 5 = 2

8 - 3 - 2 = 5 - 2 5 - 2 = 3

Step 2: Substitute the simplified values into the original expression. 4 * 2 + 5 * 3

Step 3: Perform multiplication from left to right. 8 + 15

Step 4: Perform addition. 8 + 15 = 23

Therefore, the value of the expression 4 * (3 + 4 - 5) + 5 * (8 - 3 - 2) is 23.