Then explain how to multiply and divide whole numbers step by step.
The peculiarity of multiplying and dividing integers with respect to multiplications and divisions with natural numbers is that we now multiply and divide also the sign that has each integer.
Therefore, before we learn to multiply and divide whole numbers, we need to know a very important law, known as the rule of signs or the law of signs, which we will explain below.
Índice de Contenidos
Rule of Signs
We use the rule of signs to know the result of multiplying and dividing the sign of integers:
- More for more is more
- More for less is less
- Less for more is less
- Less for less is more
For the division:
- More the more is more
- More the less is less
- Less the more the less
- Less the less is more
As a conclusion:
- When equal signs are multiplied or divided, the result is more
- When different signs are multiplied or divided the result is less
Multiplication of integers
To multiply integers follow these steps:
- The sign is multiplied, following the rule of signs
- Numbers are multiplied
Let’s see an example:
1. We multiply the signs: More by less is less:
2. Multiply the numbers: 5.3 = 15:
Y the integers would already be multiplied. In the same way, we would multiply these other multiplications:
Division of integers
To divide integers follow these steps:
- The sign is divided, taking into account the rule of signs
- Numbers are divided
Let’s look at another example of how to divide integers:
1. We divide the signs: More is less is less:
2. We divide the numbers: 8/4=2:
And we already have our integer division.
Here you have other examples, with the other combinations of signs you can find:
You may find that the minus sign is in front of the fraction. In that case, the minus sign can be in the numerator or denominator indistinctly, since the result does not vary:
Integer operations with parentheses
When we have integer operations with parentheses, we have a particular case of integer multiplication.
The minus sign in front of a parenthesis is equivalent to multiplying by -1 each number in the parenthesis, so it changes the sign to the numbers inside. Let’s see an example:
1. We remove parentheses, according to the hierarchy of operations. We multiply the minus sign by each sign of each number. The 2 is positive because it has nothing.
Now we can continue with the additions and subtractions of integers:
We can also add and subtract first within the parenthesis and then multiply the result by the minus sign, as in this example:
In the same way, a sign before the parenthesis is equivalent to multiplying by 1 and leaves the numbers inside the parenthesis with the same sign: