Solve Complex Expression: 27-(140÷(35/3)+360÷72) Step-by-Step

The problem asks us to evaluate the expression $27-(140:\frac{35}{3}+360:(8\cdot9))$.

Following the order of operations (PEMDAS/BODMAS), we first focus on operations within the parentheses.

Calculate each division inside the parentheses:

• $140 : \frac{35}{3}$ means $140 \div \frac{35}{3}$, which is equivalent to $140 \times \frac{3}{35}$.

Simplifying $140 \times \frac{3}{35}$:

• Calculate $140 \div 35 = 4$.
• Then, multiply $4 \times 3 = 12$.

Now, calculate the second division:

• $360 : (8 \cdot 9)$ involves calculating $8 \cdot 9 = 72$.
• Then, divide $360 \div 72 = 5$.

So, our expression within the parentheses simplifies to:

• $12 + 5 = 17$.

Now go back to the main expression: $27 - 17$.

Calculate the final subtraction:

• $27 - 17 = 10$.

Thus, the solution to the problem is $10$.