Multiplication and division of whole numbers. Exercises solved.

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.

Rule of Signs

We use the rule of signs to know the result of multiplying and dividing the sign of integers:

For multiplication:

  • More for more is more
  • More for less is less
  • Less for more is less
  • Less for less is moremultiplication and division of integer numbers

For the division:

  • More the more is more
  • More the less is less
  • Less the more the less
  • Less the less is more

multiplications and divisions with integer numbers

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:

  1. The sign is multiplied, following the rule of signs
  2. Numbers are multiplied

Let’s see an example:multiplication and division with integer numbers

1. We multiply the signs: More by less is less:

resolution of multiplications and divisions with integer numbers

2. Multiply the numbers: 5.3 = 15:

multiplications and divisions of integers

Y the integers would already be multiplied. In the same way, we would multiply these other multiplications:

division and multiplication of integer numbers

multiplicación de números ínos

how to divide integers

Division of integers

To divide integers follow these steps:

  1. The sign is divided, taking into account the rule of signs
  2. Numbers are divided

Let’s look at another example of how to divide integers:

integer division

1. We divide the signs: More is less is less:

operations with integers multiplication and division

2. We divide the numbers: 8/4=2:

integers multiplication and division

And we already have our integer division.

Here you have other examples, with the other combinations of signs you can find:

integer division

whole number division

multiplication of integers

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:

law of signs to multiply and divide whole numbers

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:

multiply and divide integers1. 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.
multiply and divide integers

Now we can continue with the additions and subtractions of integers:

Multiply and divide integers

We can also add and subtract first within the parenthesis and then multiply the result by the minus sign, as in this example:

Whole number multiplication and division exercises

multiplication with integer numbers

producto y división de enteros

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:

how to divide integers
regla de mas por menos

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