Simplifying Expressions - Speech or Presentation Example

Simplifying Expressions Using Properties of Real Numbers School Simplifying Expressions Using Properties of Real Numbers Knowledge of the properties of real numbers is very important to solve algebraic expressions. This paper simplifies the given expressions discussing the properties of real numbers that are applied on every step in the process. Simplification of the given expressions is followed by a discussion of the importance of properties of real numbers. In the following examples, the mathematical expressions are shown on the left side and the properties of real numbers applied to reach the next stage are discussed on the right side.

Example 12a(a – 5) + 4(a – 5) The given expression= 2a2 - 10a + 4a – 20 The distributive property removes the parentheses= 2a2 -6a – 20 Like terms are combined by adding coefficients This expression is now fully simplifiedIn this example, terms did not need to be reordered since the like terms were together already as can be seen in the step 2.Example 22w – 3 + 3(w – 4) – 5(w – 6) The given expression= 2w – 3 +3w – 12 – 5w + 30 The distributive property removes the parentheses= 2w + 3w – 5w – 3 – 12 + 30 Combining like terms = 5w – 5w – 15 + 30 Like terms are combined by adding coefficients= 0 – 15 Applying additive identity property.

“In other words, adding “0” to any number will always yield that number” (coedu.usf.edu, n.d., p. 1). = -15 This expression is now fully simplifiedIn this example, there was a need to rearrange like terms since they were not together as can be seen in the step 2. In step 3, like terms have been rearranged so that like terms are together.Example 30.05(0.3m + 35n) – 0.8(-0.09n – 22m) The given expression= 0.015m + 1.75n + 0.072n + 17.6m The distributive property removes the parentheses= 0.015m + 17.6m + 1.75n + 0.072n Combining like terms = 17.615m + 1.822n Like terms are combined by adding coefficients This expression is now fully simplifiedIt is important to know the properties of real numbers because their knowledge is a pre-requisite of performing the arithmetic operations including algebra.

Properties of the real numbers apply in the simplification and solution of expressions. Expressions are solved by moving terms around, combining like terms, applying the real numbers’ properties. There are several ways in which the properties of real numbers help in the simplification of the algebraic expressions. For instance, the distributive property of real numbers is applied to multiply the terms inside the parenthesis with the real numbers outside them which results into the parenthesis removal.

Likewise, terms are moved to different places in the expressions with the help of the commulative property of real numbers. Concluding, we have to deal with real numbers in everyday life as the principles discussed in this assignment have application in matters as simple as totaling the price of items bought at a grocery store for the bill to as complex matters as engineering designs and calculations. In all the cases, expressions are solved using the same distributive and commulative properties of real numbers that have been discussed.

Hence, knowledge of the principles of real numbers is essential to achieve accurate results in mathematics including algebra.References:coedu.usf.edu. (n.d.). Properties of Real Numbers. Retrieved from http://www.coedu.usf.edu/main/departments/sped/PROPEL/documents/MicrosoftWord- PropertiesofRealNumbers.pdf.