Solve Complex Fraction: [(15×8+15)÷27+45]×8÷20÷(-5)

Question

Solve the following equation:

$\frac{\lbrack(15\times8+15)\colon27+45\rbrack\times8\colon20}{-5}=$

00:00 Solve the following expression

00:03 Always solve parentheses first, even nested parentheses

00:07 Multiplication and division precede addition and subtraction

00:28 Continue to calculate the parentheses

00:47 Continue to solve the expression according to the proper order of operations, from left to right

01:07 Break down 50 into factors 10 and 5

01:20 Reduce wherever possible

01:26 Continue to solve the expression according to the proper order of operations, from left to right

01:31 This is the solution

Initially, we address the first parentheses in the numerator of the fraction:

$(15\times8+15)=$

According to the rules, we first must solve the multiplication exercise and then the addition:

$120+15=135$

We obtain the following exercise:

$\frac{(135:27+45)\times8:20}{-5}=$

We will again address the parentheses in the numerator of the fraction. First by solving the division and then addition exercise.

$5+45=50$

We are left with the following exercise:

$\frac{50\times8:20}{-5}=$

We divide 50 into a multiplication exercise:

$\frac{5\times10\times8:20}{-5}=$

We then simplify:

$-10\times8:20=$

Lastly we solve from left to right:

$-80:20=-4$