Simplifying Expressions
RUNNINGHEAD: SIMPLIFYING EXPRESSIONS
In arithmetic we use only positive numbers and zero, but with algebra, we use both positive and negative numbers. The numbers we use in algebra are called the “real numbers” or integers {… , -3, -2, -1, 0, 1, 2, 3…}. In this paper I am going to explain the properties of real numbers using three examples. I will also be explaining how to solve these examples step by step, all while discussing why these properties are so important to begin with. The properties of real numbers are the commutative, associative, identity, and additive inverse properties of addition, distributive law, and the commutative, associative, identity, and the multiplicative inverse (reciprocal) of multiplication.
What these properties mean is that order and grouping don 't matter for addition and multiplication, but they certainly do matter for subtraction and division. In this way, addition and multiplication are much cleaner than subtraction or division. This is extremely important when talking about simplifying algebraic expressions. Often what we will want to do with an algebraic expression involves rearranging it somehow, and combining like terms. If the operations are all addition and multiplication, we don 't have to worry so much that we might be changing the value of an expression by rearranging its terms or factors. Fortunately, we have the option to think of subtraction as an addition problem (adding the opposite), and we can always think of division as a multiplication problem (multiplying by the reciprocal). The additive identity property of addition has the rule that you can add zero to any number and its original identity will always remain the same. The additive inverse property rules that any numbers plus that numbers negative will equal zero. ex. 5 + -5=0 or -5 + 5=0
You may have noticed that the commutative and associative properties read exactly the same way for addition and multiplication, as if there was
In arithmetic we use only positive numbers and zero, but with algebra, we use both positive and negative numbers. The numbers we use in algebra are called the “real numbers” or integers {… , -3, -2, -1, 0, 1, 2, 3…}. In this paper I am going to explain the properties of real numbers using three examples. I will also be explaining how to solve these examples step by step, all while discussing why these properties are so important to begin with. The properties of real numbers are the commutative, associative, identity, and additive inverse properties of addition, distributive law, and the commutative, associative, identity, and the multiplicative inverse (reciprocal) of multiplication.
What these properties mean is that order and grouping don 't matter for addition and multiplication, but they certainly do matter for subtraction and division. In this way, addition and multiplication are much cleaner than subtraction or division. This is extremely important when talking about simplifying algebraic expressions. Often what we will want to do with an algebraic expression involves rearranging it somehow, and combining like terms. If the operations are all addition and multiplication, we don 't have to worry so much that we might be changing the value of an expression by rearranging its terms or factors. Fortunately, we have the option to think of subtraction as an addition problem (adding the opposite), and we can always think of division as a multiplication problem (multiplying by the reciprocal). The additive identity property of addition has the rule that you can add zero to any number and its original identity will always remain the same. The additive inverse property rules that any numbers plus that numbers negative will equal zero. ex. 5 + -5=0 or -5 + 5=0
You may have noticed that the commutative and associative properties read exactly the same way for addition and multiplication, as if there was
Cited: Cool math pre-algebra. (n.d.). Retrieved from coolmath.com