They start at 0 and continue counting upwards infinitely. On the other hand, whole numbers include 0 along with positive integers. Natural numbers are only positive integers and do not include 0 or negative ones. They represent counting numbers in real-life scenarios, such as counting apples or students in a classroom. They start at 1 and continue counting upwards infinitely. Natural numbers are a subset of whole numbers. There are other properties of whole numbers which you can add to your lessons, and they are:ĭifference between Whole Numbers and Natural Numbers We can distribute the 2 to the 3 and 4 inside the parentheses, then add the results. If we have 2 and want to multiply it by the sum of 3 and 4, we can use the distributive property to simplify the calculation. That is, a x (b + c) = a x b + a x c and a x (b – c) = a x b – a x c, where a, b, and c are whole numbers. Distributive propertyĪccording to distributive property, the product of a whole number and the sum or difference of two whole numbers is the same as the sum or difference of the product of that whole number and each of the whole numbers. And if we look at the right side, we get 2 + 7 = 9. Looking at the left side, we get 5 + 4 = 9. According to the associative property, we can group them in any way we want when performing addition. That is (a + b) + c = a + (b + c) and (a x b) x c = a x (b x c), where a, b, and c are whole numbers.įor example, we have three whole numbers, 2, 3, and 4. The principle of associative property states that the sum and product of three or more whole numbers remain the same irrespective of how you group them. According to the commutative property, we can add them in any order and still get the same answer. Let’s say we have two whole numbers, 2 and 3. That is, a + b = b + a and a x b = b x a, where a and b are whole numbers. The commutative property states that the order of the numbers does not affect the sum and product of any two whole numbers. So, if you take any two whole numbers, a and b, and add them together (a + b) or multiply them (a x b), the result will always be a whole number. This pattern holds for any two numbers you add or multiply. If we multiply them, we get 10, which is also a whole number. If we add them together, we get 7, which is also a whole number. For example, we have two whole numbers, 2 and 5. The closure property states that the sum and product of any two whole numbers is also a whole number. Here are some of the properties of whole numbers: Closure property It also aids in performing operations with whole numbers, such as addition and subtraction, and comparing and ordering them. The number line helps us understand the relationship between whole numbers and their position on the natural number line. Similarly, to plot the whole number -3, we start at zero, count three units to the left, and mark the point corresponding to -3 on the number line. The point that corresponds to 4 is then marked on the number line. For example, to plot the whole number 4, we start at zero and count four units to the right. To plot a whole number on a number line, we can find its position by counting the number of units to the right of zero for positive whole numbers or to the left of zero for negative whole numbers. The number line starts at zero and extends in both directions to infinity. On a number line, each whole number is represented by a point placed at an equal distance from the other points. The number line visually represents the actual number system, and whole numbers are plotted on this line. “ℤ” represents the set of all integers, including positive and negative whole numbers, while “ℤ⁺” represents only the positive numbers. The symbol used to represent whole numbers is “W” or “ℤ⁺” (pronounced as “Z plus”). In addition, they are the foundation for arithmetic operations such as addition, subtraction, division, and multiplication. Whole numbers are essential in mathematics as they are used to count, label, and order items or values. They do not include fractions or decimals. What is a whole number? Whole numbers are a set of positive integers which can be described as the primary number sequence, 1,2,3… and their negative counterparts -1, -2, -3, … A simple whole numbers definition is that they are numbers that can also be called non-negative integers or counting numbers. One of these basic structures is whole numbers. In kindergarten and through the grade levels, kids explore these foundations and use them as a stepping stone before they counter more challenging math problems. Math evolves into more complex structures that would confuse anyone who has no basic foundation in the subject.
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