Multiplication of negative numbers

Using the concept of the modulus of a number, we formulate the rules for multiplying positive and negative numbers .

Multiplication of numbers with the same characters

The first case you may encounter is the multiplication of numbers with the same signs.

To multiply two numbers with the same signs you need :

• multiply the modules of numbers;
• put the “+” sign before the received work (when recording the answer, the plus sign in front of the first number on the left can be omitted).

Examples of multiplying negative and positive numbers.

• (- 3) • (- 6) = + 18 = 18
• 2 • 3 = 6

Multiplication of numbers with different signs

The second possible case is the multiplication of numbers with different signs.

To multiply two numbers with different signs, you need :

• multiply the modules of numbers;
• put the “-” sign before the received work.

Examples of multiplying negative and positive numbers.

• (- 0.3) • 0.5 = - 1.5
• 1.2 • (- 7) = - 8.4

The rules of multiplication signs

Remembering the multiplication rule is easy. This rule is the same as the rule for opening parentheses.

In the "long" examples, in which there is only an action of multiplication, the sign of the work can be determined by the number of negative factors.

With an even number of negative factors, the result will be positive, and with an odd number - negative.

Example.

In the example, five negative factors. Hence, the sign of the result will be "minus".

Now we calculate the product of the modules, not paying attention to the signs.

The end result of multiplying the original numbers will be:

Multiplication by zero and one

If among the factors there is a number zero or a positive one, then the multiplication is performed according to the known rules.

• 0 • a = 0
• a • 0 = 0
• a • 1 = a

Examples:

• 0 • (- 3) = 0
• 0.4 • 1 = 0.4

A special role in multiplying rational numbers is played by a negative one (- 1).

When multiplied by (- 1) the number is reversed.

In alphabetic expression this property can be written:

When performing the addition, subtraction and multiplication of rational numbers together, the procedure established for positive numbers and zero is preserved.

An example of multiplying negative and positive numbers.