You negative numbers belong to the set of whole numbers and, among them, we can carry out operations of multiplication It is division.
There are some practical rules that allow us to perform these calculations in a simple and quick way and we will show you what they are and how to use them.
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However, in addition to knowing how to use the rules, it is important to understand what multiplying and dividing negative numbers and why these rules work.
Keep reading this post to understand everything about this subject!
Rules of signs in multiplying and dividing negative numbers
To the sign rules for multiplying and dividing negative numbers are:
Equal signs ⇒ the product or division will have a plus sign.
(+). (+) = +
(–). (–) = +
(+): (+) = +
(–): (–) = +
Different signs ⇒ the product or division will have a minus sign.
(+). (–) = –
(+). (–) = –
(+): (–) = –
(+): (–) = –
One observation is that the plus sign does not always appear in a positive number. It is common for the plus sign and parentheses to be omitted in operations.
So (+ 1) is just written as 1; (+ 2) appears as 2 only; and so on.
Examples:
(- 2). 3 = – 6
(- 2). (- 1) = 2
7. (- 3) = – 21
(- 9). (- 2) = 18
6: (- 2) = -3
(-8): (- 4) = 2
(-12): 3 = – 4
(- 21): (- 7) = 3
What is multiplication and division of negative numbers
Negative numbers have been used since the 17th century, but it took around 200 years for the multiplication and, consequently, division, was fully understood and accepted by mathematicians.
Fortunately, we saw that sign rules were created to perform these operations in a simple way and the results are obtained almost like magic.
But why do the rules work? What does it mean to multiply and divide negative numbers?
To understand this, we need to remember that multiplication is a sum of equal parts, for example, 3. 5 = 5 + 5 + 5 = 15.
With negative numbers, the principle is the same. See the possible cases:
positive number × negative number
4. (-2) = ?
4. (-2) = (-2) + (-2) + (-2) + (-2) = – 8
Negative number × positive number
(-2). 4 = ?
(-2). 4 = 4. (-2) = – 8
Also, see that (-2). 0 = 0 and that (-2). 1 = -2, because every number multiplied by 0 equals 0 and every number multiplied by 1 equals itself.
Thus, we can continue the sequence, always subtracting two units, and arrive at the same result:
(-2). 0 = 0
(-2). 1 = – 2
(-2). 2 = – 4
(-2). 3 = – 6
(-2). 4 = – 8
negative number × negative number
(-2). (-4) = ?
Here, we can do the reverse of the previous sequence and add 2 units:
(-2). 1 = – 2
(-2). 0 = 0
(-2). (-1) = 2
(-2). (-2) = 4
(-2). (-3) = 6
(-2). (-4) = 8
If you multiply other numbers, you will see that whenever the signs are the same, the result will be positive, and whenever the signs are different, the result will be negative.
You may also be interested:
- Adding and subtracting negative numbers with a number line
- Decimal numbers and percent
- Facts about numbers
