Final answer:
To evaluate the expression 7/9-9/5x10/27, we need to follow the order of operations and simplify the fractions step by step. The final answer is 1/9.
Step-by-step explanation:
To evaluate the expression 7/9-9/5x10/27, we need to follow the order of operations, which is parentheses, multiplication/division from left to right, and addition/subtraction from left to right. Let's break it down step by step:
- First, we simplify 9/5x10/27 by multiplying the fractions:
9/5x10/27 = (9x10)/(5x27) = 90/135 - Next, we simplify 7/9:
7/9 = 63/81 - Now, we can subtract 90/135 from 63/81:
63/81 - 90/135 - To subtract fractions, we need a common denominator. The common denominator for 81 and 135 is 405. We adjust the fractions accordingly:
(63/81)(5/5) - (90/135)(3/3) = 315/405 - 270/405 = (315-270)/405 = 45/405 - Finally, we simplify the fraction 45/405 by dividing both the numerator and denominator by their greatest common divisor, which is 45:
45/405 = 1/9
Therefore, the answer to 7/9-9/5x10/27 is 1/9.