All Operations in Signed Numbers: Using order of arithmetic operations

In order to solve the equation we must follow the order of operations beginning with the parentheses:

$-7+4=-3$

We should obtain the following expression:

$-(-3):(-9)=$

Let's remember the rule:

$-(-x)=+x$

Therefore:

$-(-3)=3$

Resulting in the following expression:

$3:(-9)=$

Let's proceed to write the expression as a simple fraction:

$\frac{+3}{-9}=$

Note that we are dividing a positive number by a negative number, so the result must be a negative number:

$\frac{+}{-}=-$

Next let's expand the 9 in the denominator of the fraction:

$-\frac{3}{3\times3}=$

Finally let's reduce the 3 in both the numerator and denominator of the fraction:

$-\frac{1}{3}$

First, let's solve the expression in parentheses from left to right:

$-7-13=-20$

$-20+10=-10$

Now the expression we have is:

$-400:-10=$

Let's note that we are dividing two negative numbers, so the result must be a positive number:

$\frac{-}{-}=+$

Therefore:

$\frac{400}{10}=40$

Let's solve the exercise from left to right.

We'll write the division problem as a simple fraction in the following way:

$\frac{-3.5}{-7}+14=$

Let's note that we are dividing a negative number by a negative number, so the result will necessarily be a positive number:

$\frac{-}{-}=+$

We'll break down 7 into a multiplication problem:

$\frac{3.5}{3.5\times2}+14=$

We'll reduce the 3.5 in both the numerator and denominator of the fraction and get:

$\frac{1}{2}+14=14\frac{1}{2}$

Let's first solve the expression in parentheses:

$-8+4=-4$

Now the expression is:

$-12:-6\times-4=$

Let's solve the expression from left to right.

We'll write the division as a simple fraction like this:

$\frac{-12}{-6}=$

Note that we are dividing between two negative numbers, so the result must be a positive number:

$\frac{-}{-}=+$

Therefore:

$\frac{12}{6}=2$

Now the expression we got is:

$2\times-4=$

Note that we are multiplying a positive number by a negative number, so the result must be a negative number:

$+\times-=-$

Therefore the result is:

$2\times-4=-8$

First, let's solve what's inside the parentheses:

$-3+2=-1$

Now the exercise looks like this:

$-7:-49:+14:-1=$

Let's treat the exercise as division between two simple fractions:

$(-7:-49):(+14:-1)=$

$\frac{-7}{-49}:\frac{+14}{-1}=$

Let's look at the simple fraction on the left side.

Since we are dividing a negative number by a negative number, the result will be positive.

Let's break down 49 into a multiplication exercise:

$\frac{7}{7\times7}=$

Let's reduce the 7 in the numerator and denominator and we get:

$\frac{1}{7}$

Now the exercise we got is:

$\frac{1}{7}:\frac{+14}{-1}=$

Let's convert the division to multiplication, don't forget to switch between numerator and denominator:

$\frac{1}{7}\times\frac{-1}{+14}=$

Let's reduce to one exercise:

$\frac{1\times-1}{7\times14}=\frac{-1}{+98}$

Since we are dividing a negative number by a positive number, the result will be negative:

$-:+=-$

Therefore we get:

$-\frac{1}{98}$