Multiplication and Division of Signed Mumbers: Multiplication of signed numbers

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

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

Let's reduce between the multiplication exercise 4X3 in the numerator and denominator and we get:

$38$

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 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 solve the division exercise:

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

Let's solve the exercise from left to right:

$7\times3=21$

Now we got the 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 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 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.