E - Properties Lesson

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A numerical expression is a mathematical phrase that contains only numbers and operation symbols.   When you evaluate a numerical expression, you're finding its value. When there is more than 1 operation, you have to know what order to perform the operations in. For this, we use the order of operations.

Order of Operations

() Parenthesis 5bsquared Exponents x Multiplication OR ÷ Division + Addition OR - Subtraction

  1. Perform operations in parentheses.
  2. Find the values of numbers with exponents.
  3. Multiply or divide from left to right in the order it appears in the problem.
  4. Add or subtract from left to right in the order it appears in the problem.

A fun way to remember the order of operations is the phrase "Please Excuse My Dear Aunt Sally." The first letter in each word can help you remember the order of operations.

When simplifying numerical expressions, it is useful to know properties that can help you perform the operations quickly, and often using only mental math. These properties are the commutative property, associative property, and distributive property. Let's look at each of these properties individually.

First, watch the videos in the video showcase below that will walk you through each property.

Commutative Property

This property states that you can add or multiply numbers in any order.  

  • For example, 3 + 5 = 5 + 3.  
  • Similarly, 4 x 7 = 7 x 4.  

Associative Property

When you are only adding or multiplying, you can group any of the numbers together.  

  • For example, (2 + 4) + 6 = 2 + (4 + 6).  
  • Similarly, (3 x 6) x 9 = 3 x (6 x 9).
  • When adding, look for ways to regroup to get sums that are multiples of 10.  
  • When multiplying, look for ways to regroup to get products that are multiples of 10.  

Watch the video below to learn more about the commutative and Associative Properties.

Distributive Property

  • The distributive property allows you to break up multiplication problems and solve two simpler problems
  • You can solve equations in the form of a(b + c)

Watch the video below to learn more about the Distributive Property:

Exponents and Properties Assignment

Download the "Exponents and Properties Assignment " by clicking here. Be sure to work all of the problems on paper. You will use these problems and solutions to complete the "Exponents and Properties Homework Quiz 1." Links to an external site.

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