All Operations in the Order of Operations: Using negative numbers

Solve the following equation:

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

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:

$-80:20=-4$

4-

Solve the following equation:

$\frac{400\colon(-5)-\lbrack-2(93-61)\rbrack}{4}=$

We begin by addressing the numerator of the fraction.

First we solve the division exercise and the exercise within the parentheses:

$400:(-5)=-80$

$(93-61)=32$

We obtain the following:

$\frac{-80-(-2\times32)}{4}=$

We then solve the parentheses in the numerator of the fraction:

$\frac{-80-(-64)}{4}=$

Let's remember that a negative times a negative equals a positive:

$\frac{-80+64}{4}=$

$\frac{-16}{4}=-4$

$-4$

Solve the following equation:

$\frac{(32\times4+8)\colon(-27+35)}{-2}=$

We begin by solving the two parentheses in the numerator of the fraction:

$(32\times4+8)=128+8=136$

$(-27+35)=8$

We obtain the following exercise:

$\frac{136:8}{-2}=$

$\frac{17}{-2}=-8.5$

-8.5

Solve the following equation:

$-9-(15-3-\lbrack17-14\rbrack+4)+12\colon3\times7=$

According to the order of arithmetic operations, we begin by solving the innermost parenthesis and the division exercise first:

$-9-(15-3-3+4)+4\times7=$

We then solve the parenthesis exercise from left to right:

$15-3-3+4=12-3+4=9+4=13$

We obtain the following exercise:

$-9-13+(4\times7)=$

We then solve the multiplication exercise and obtain:

$-9-13+28=$

Lastly we solve the exercise from left to right:

$-9-13=-22$

$-22+28=6$

6

$6\times15-142-\frac{7}{14}+20\colon5=$

According to the order of operations, first we solve the multiplication and division exercises.

We will put them in parentheses to avoid confusion later in the solution:

$(6\times15)-142-\frac{7}{14}+(20:5)=$

We solve the exercises in parentheses:

$90-142-\frac{7}{14}+4=$

We will rewrite the denominator of the fraction as a multiplication exercise:

$90-142-\frac{7}{7\times2}+4=$

We simplify and obtain:

$90-142-\frac{1}{2}+4=$

Now we solve the exercise from left to right:

$-52-\frac{1}{2}+4=$

$-52\frac{1}{2}+4=-48\frac{1}{2}$

$$-48.5