![]() This property also does not apply to division. For instance, \(5-3\) does not yield the same as \(3-5\). Real numbers are closed with respect to addition and multiplication. According to the commutative property of multiplication, the result remains the same if we interchange the position of the numbers multiplied. It is important to note this distinction because the commutative property does not apply to the operation of subtraction. Definition Of Closure Property Of Real Numbers Addition. ![]() Note that there is a very important distinction between the addition of a negative integer and the operation of subtraction. if a and b are any two whole numbers, a + b will be a whole number. Closure property of whole numbers under addition: The sum of any two whole numbers will always be a whole number, i.e. Let’s alter one of our terms a bit for this next example. Closure property holds for addition and multiplication of whole numbers. But if we switch our terms and make it \(3 + 5\), we still get \(8\). To prove that moving, or rearranging, terms is acceptable, let’s look at a few examples of the commutative property being used in addition problems. Let’s take a minute to remember the definition of an algebraic term: it is the number, variable, or product of coefficients and variables. The commutative property of multiplication: \(a\cdot b=b\cdot a\) The commutative property of addition: \(a+b=b+a\) The commutative property looks like this, mathematically: That word reminds me of “move,” which is pretty much what the commutative property allows you to do when adding or multiplying algebraic terms. What do you think of when you see this word? When I look at this word, I see the word commute. The names of the properties that we’re going to be looking at are helpful in decoding their meanings. In this video, we will go back to the basics to review the commutative, associative, and distributive properties of real numbers, which allow for the math mechanics of algebra and beyond. As you’re building these concepts over time, the math process may become automatic, but the reason, or justification for the work, may be long forgotten. Arithmetic skills are necessary to conquer algebraic concepts, which are then developed further to be used in calculus, and so on. The closure property states that if a set of numbers (integers, real numbers, etc.) is closed under some operation (such as addition, subtraction, or multiplication, etc.), then performing that operation on any two numbers in the set results in the element belonging to the set. As you may have already realized through the years of math classes and homework, math is sequential in nature, meaning that each concept is built upon prior work. ![]()
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