We explain what are the whole numbers, the different properties they have and some examples of this numerical set.
What are whole numbers?
The numerical set that contains all natural numbers , their negative inverse and zero is known as integers or simply integers . This numerical set is designated by the letter Z, from the German word z ahlen (“numbers”).
Integers are represented on a number line , with zero in the middle and positive numbers (Z +) to the right and negative numbers (Z-) to the left, both sides extending to infinity. Negatives are usually transcribed with their sign (-), which is not necessary for positives, but can be done to highlight the difference.
In this way, the positive integers are larger to the right, while the negative integers are getting smaller as we move to the left . You can also talk about the absolute value of an integer (represented by bars | z |), which is equivalent to the distance between its location within the number line and zero, regardless of its sign: | 5 | is the absolute value of +5 or -5.
The incorporation of whole numbers to natural numbers makes it possible to enlarge the spectrum of quantifiable things, including negative figures that serve to keep track of absences or losses, or even for certain quantities such as temperature, which uses values above and below zero.
Properties of whole numbers
Whole numbers can be added, subtracted, multiplied or divided just like natural numbers, but always following the rules that determine the resulting sign, as follows:
Suma . To determine the sum of two integers, attention should be paid to their signs, as follows:
- If both are positive or one of the two is zero, they must simply add their absolute values and the positive sign is retained. For example: 1 + 3 = 4.
- If both signs are negative or one of the two is zero, their absolute values must simply be added and the negative sign is preserved. For example: -1 + -1 = -2.
- If they have different signs, on the other hand, the absolute value of the minor to that of the major must be subtracted, and the sign of the major will be retained in the result. For example: -4 + 5 = 1.
Resta . The subtraction of whole numbers also attends to the sign, depending on which one is greater and which minor in terms of absolute value, obeying the rule that two equal signs together become the opposite:
- Subtract two positive numbers with a positive result : 10 – 5 = 5
- Subtract two positive numbers with negative result : 5 – 10 = -5
- Subtraction of two negative numbers resulting negative (-5) – (-2) = (-5) + 2 = -3
- Subtract two negative numbers with positive result : (-2) – (-3) = (-2) + 3 = 1
- Subtract two numbers of different sign and negative result : (-7) – (+6) = -13
- Subtract two numbers of different sign and positive result : (2) – (-3) = 5.
Multiplying . Integer multiplication is done by multiplying the absolute values normally, and then applying the sign rule, which stipulates the following:
- More for more equal to more . For example: (+2) x (+2) = (+4)
- More for less equal to less . For example: (+2) x (-2) = (-4)
- Less for more equal to less . For example: (-2) x (+2) = (-4)
- Less for less equals more . For example: (-2) x (-2) = (+4)
Division . It works the same as multiplication. For example:
- (+10) / (-2) = (-5)
- (-10) / 2 = (-5)
- (-10) / (-2) = 5.
- 10/2 = 5.
Examples of whole numbers
Examples of whole numbers are any natural number: 1, 2, 3, 4, 5, 10, 125, 590, 1926, 76409, 9,483,920, along with each corresponding negative number: -1, -2, -3, – 4, -5, -10, -590, -1926, -76409, -9.483.920. This includes, of course, zero (0).