Multiplication and Division of Signed Mumbers: Using order of arithmetic operations

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:

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

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 apply 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:

$-\frac{1}{3}$

We must solve the exercise from left to right.

First, we will rewrite the division as a simple fraction in the following way:

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

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

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

We will then break down 7 into a multiplication exercise:

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

Finally, we will reduce the 3.5 in both the numerator and denominator of the fraction to get our answer:

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

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:

$2\times-4=-8$

Let's begin by writing the two division exercises as a multiplication of two simple fractions:

$(38:(-4))\times(12:(-3))=$

$\frac{38}{-4}\times\frac{12}{-3}=$

Let's proceed to combine them into one exercise:

$\frac{38\times12}{-4\times-3}=$

Note that in the denominator of the fraction we are multiplying two negative numbers, therefore the result must be positive:

$\frac{38\times12}{4\times3}=$

Let's now break down the 12 in the fraction's numerator into a multiplication exercise:

$\frac{38\times4\times3}{4\times3}=$

Finally let's reduce the multiplication exercise 4X3 in the numerator and denominator and we should obtain the following:

$38$

Let's begin by writing the division exercise as a simple fraction:

$\frac{-49}{-7}\times3\times(-\frac{1}{4})=$

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

$\frac{49}{7}\times3\times(-\frac{1}{4})=$

Let's proceed to solve the division exercise:

$7\times3\times-\frac{1}{4}=$

Let's now solve the exercise from left to right:

$7\times3=21$

We should obtain the following exercise:

$21\times-\frac{1}{4}=$

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

$-\frac{21}{4}$

Let's write the result as a mixed fraction:

$-\frac{21}{4}=-5\frac{1}{4}$

Let's solve the exercise from left to right.

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

$-13\times4=-52$

Now we got the exercise:

$-52:-8=$

Let's write the exercise as a simple fraction:

$\frac{-52}{-8}=$

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

$\frac{52}{8}=$

Let's convert it to an addition exercise:

$6+\frac{4}{8}=$

Let's break down the 8 into a multiplication exercise:

$6+\frac{4}{4\times2}=$

Let's reduce the 4 in both eight and the fraction's denominator:

$6+\frac{1}{2}=6\frac{1}{2}$

Let's solve the exercise from left to right.

First, we'll write the division problem in the form of a fraction:

$\frac{200}{-200}\times200=$

We should note that we are dividing a positive number by a negative number, so the result will necessarily be a negative number:

$-\frac{200}{200}\times200=$

Let's simplify the 200 and we get:

$-200$

Let's write the exercise as a multiplication of fractions:

$(-81:-27)\times(6:-2)=$

$\frac{-81}{-27}\times\frac{6}{-2}=$

Note that in the first fraction we are dividing between two negative numbers, therefore the result must be a positive number.

Note that in the second fraction we are dividing between a positive number and a negative number, therefore the result must be a negative number.

Therefore:

$\frac{81}{27}\times-\frac{6}{2}=$

Let's break down 81 into a multiplication exercise and 6 into a multiplication exercise:

$\frac{27\times3}{27}\times-\frac{2\times3}{2}=$

Let's reduce the 27 and the 2 in the numerator and denominator of the fraction and we get:

$3\times-3=$

Note that we are multiplying between a positive number and a negative number, therefore the result must be a negative number:

$-9$

Let's write the exercise in the following way:

$\frac{-5\times-49}{14}\times-10=$

Note that in the numerator of the fraction we are multiplying two negative numbers, therefore the result must be a positive number:

$\frac{5\times49}{14}\times-10=$

Break down 49 and 14 into multiplication exercises:

$\frac{5\times7\times7}{7\times2}\times-10=$

Reduce the 7 in the numerator and denominator of the fraction and proceed to break down the 10 into a multiplication exercise:

$\frac{5\times7}{2}\times-5\times2=$

Reduce the 2 and note that we are multiplying a positive number by a negative number, therefore the result must be negative:

$-5\times7\times5=$

Let's solve the exercise from left to right.

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

$-5\times7=-35$

We obtain the following:

$-35\times5=$

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

$-175$

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:

$-\frac{1}{98}$

Let's write the exercise in the following form:

$\frac{400\times(-4)}{-16}:-6=$

Let's factor -16 in the denominator as a multiplication exercise:

$\frac{400\times(-4)}{4\times(-4)}:-6=$

Let's reduce -4 in both the numerator and denominator and get:

$\frac{400}{4}:-6=$

Let's factor the 100 in the numerator as a multiplication exercise:

$\frac{100\times4}{4}:-6=$

Let's reduce the 4 in both the numerator and denominator and get:

$100:-6=$

Let's write the exercise as a fraction:

$\frac{100}{-6}=$

Note that we are dividing a positive number by a negative number, therefore the result must be negative.

Let's factor the 100 as an addition exercise:

$-\frac{96+4}{6}=$

Let's write the exercise in the following way:

$-(\frac{96}{6}+\frac{4}{6})=$

Let's solve the first fraction and in the second fraction let's factor the numerator and denominator as multiplication exercises:

$-(16+\frac{2\times2}{2\times3})=$

Let's reduce the 2 in both the numerator and denominator:

$-(16+\frac{2}{3})=$

Let's pay attention to the appropriate sign since we are multiplying by a negative number:

$-16\frac{2}{3}$

Let's begin by rewriting the exercise as follows:

$\frac{-3\times8}{0}\times-14=$

One should consider that it's not possible to divide a number by zero thus the expression has no meaning.