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# Properties of Real Numbers

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In this lesson, we will learn about the various properties of real numbers. We begin by talking about the commutative property of addition/multiplication. The commutative property of addition/multiplication states that we can add/multiply in any order without changing the answer. Typically, we will see this written as: a + b = b + a (addition) or ab = ba (multiplication). We will also discuss the associative property of addition/multiplication. This property tells us that we can group the addition/multiplication of three or more numbers in any order without changing the answer. We will see this written as: a + (b + c) = (a + b) + c (addition) or (ab)c = a(bc) (multiplication). We will also talk about the identity and inverse properties. Zero is the additive identity; we can add zero to anything and the number remains unchanged. One is the multiplicative identity; multiplying a number by 1 leaves the number unchanged. The inverse properties tell us that a number plus its opposite or additive inverse results in zero and a non-zero number times its reciprocal gives us 1. Lastly, we will learn about the distributive property of multiplication. The distributive property of multiplication tells us that we can distribute multiplication over addition or subtraction. This property allows us to change a product such as: a(b + c) into a sum: ab + ac or reverse this process and write a sum: ab + ac as a product: a(b + c).
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