The Distributive property of Algebraic expressions
Janet Mency
MAT 221
Instructor: Amy Glidewell
January 25, 2014

Completing algebra problems can be difficult if you don’t understand the properties of real numbers. There are several properties in algebra dealing with both integers and real numbers; one that will be the focus of this report will be the distributive property. We use this property when we are combining addition and multiplication in an algebraic expression. Let’s say that you are presented with the expression 6x(2 + y) = 9x + 5xy, now with this problem the order of operation would have you to add the terms in parenthesis first, by using the distributive property it allows to simplify the problem by multiplying all the numbers in parenthesis with the multiplier. That’s why it is so important to understand the properties because completing algebra problems can be difficult if you don’t understand the properties of real numbers. When solving problems in algebra it is really important to know the properties of real numbers. Each property tells you the rules in which to use in order to solve that particular expression. For instance you have the commutative properties of addition which tell us that numbers in the problem can be rearranged in any order, for an example 5a + 7 = 7 + 5a and in commutative properties of multiplication, it’s pretty much the same idea we can multiply the numbers in any order and come out with the same result, for an example would be something like 8y x 9 x 4 = 9 x 4 x 8y. Another property that would be part of the basics of pre-algebra would be associative properties. It have the same concept but it deals more with grouping number. An example of this would be something like (9x + 2x) + 3x = 9x + (3x + 2x). Associative properties of addition allows you to do two number at one time and it doesn’t matter which two you want to start off with, you will come out with the same results, this also applies with the associative properties of multiplication as well. So far the properties that were discuss seems very simple, you have just simple addition or either multiplication but using distributive properties we are combining the two. There is also the concept of removing the parenthesis’s if it applies to the expression. Here are several problems that will be explained more in depth.
2a(a-5) + 4(a-5) The algebraic expression that will be simplified.
2a^2-10+4a-20 The distributive property removes the parentheses.
2a^2+4a-10-20 The next stage is to combine the like terms by adding 2a^2 + 4a - 30 coefficients. As you see in the problem we arrange the like terms together in order by using commutative property to complete the expression. That’s the property where we can rearrange the numbers where we want them. The next example will be a little more challenging because you have move variable in the expression.
2w-3+3(w-4)-5(w-6) The algebraic expression that will be simplified.
2w-3+3w-12-5w+30 The distributive property removes the parentheses.
2w+3w-5w-12+30 Combine the like terms by adding coefficients.
18 Once the like terms are added then the expression is simplified. Because 2w + 3w – 5w give you 0 then the answer would be 18, it kind of like it 0 out. My final expression that demonstrates the use of distributive property will be using decimals. Even though it uses decimals the concept is the same.
0.05(0.3m+35n) – 0.8(-0.09n–22m) The algebraic expression that will be simplified.
0.015m+1.15n+0.072n+17.6m The distributive property removes the parentheses.
0.015m+17.6m+1.15n+0.072n Combine the like terms by adding coefficients.
17.615m+1.222n The expression with decimals simplified notice that we completed we completed each one by using the same concept.
In conclusion we have learn about some of the basic pre-algebra properties of real numbers. We have discussed the how important of knowing what each property allows you to do. Not knowing about the properties of real numbers would be like, just looking at a bunch of numbers and letters. So understanding them helps you to know and understand how algebra works. Reading and applying these properties have helped me to understand algebra a little bit better. We only talked about three of the properties, which are commutative, associative and distributive properties. These properties are some of the basics in pre-algebra that I liked and that helped me to be able to simplify expression in algebra. When it’s all said and done it really all boils down to one thing completing algebra problems can be difficult if you don’t understand the properties of real numbers.