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

Question

27(140:353+360:(89))=? 27-(140:\frac{35}{3}+360:(8\cdot9))=\text{?}

Video Solution

Solution Steps

00:00 Solve
00:05 Division is also multiplication by the reciprocal
00:12 Move the division to the denominator
00:19 Factor 140 into 7 and 20
00:25 Factor 35 into 7 and 5
00:30 Factor 360 into 8, 9 and 5
00:42 Reduce what's possible
00:57 Factor 20 into 4 and 5
01:06 Reduce what's possible
01:16 And this is the solution to the question

Step-by-Step Solution

The problem asks us to evaluate the expression 27(140:353+360:(89)) 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:

  • 140:353 140 : \frac{35}{3} means 140÷353 140 \div \frac{35}{3} , which is equivalent to 140×335 140 \times \frac{3}{35} .

Simplifying 140×335 140 \times \frac{3}{35} :

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

Now, calculate the second division:

  • 360:(89) 360 : (8 \cdot 9) involves calculating 89=72 8 \cdot 9 = 72 .
  • Then, divide 360÷72=5 360 \div 72 = 5 .

So, our expression within the parentheses simplifies to:

  • 12+5=17 12 + 5 = 17 .

Now go back to the main expression: 2717 27 - 17 .

Calculate the final subtraction:

  • 2717=10 27 - 17 = 10 .

Thus, the solution to the problem is 10 10 .

Answer

10 10