# Closure Property Worksheets

What is the Closure Property? (In Algebra) The term closure is a term that is used extensively in many fields. In the field of mathematics, closure is applied in many sub-branches. The property states that when you perform any operation (like an arithmetic one) on any two numbers from the same set, the result will be another number in the same set. For instance, if we multiply two numbers from a set of even numbers, the answer will always be an even number. However, this property is only valid for a few conditions and not all of them.

• ### Basic Lesson

Demonstrates how to determine if a set is closed through a rule system. A set is considered closed, under an operation, if the operation on two elements of the set produces another element of the set. If an element outside the set is created, then the operation is not closed.

• ### Intermediate Lesson

Explores how to use the same concept in a visual set. If we divide one even number and one odd number and the answer is even than the property is not closed.

• ### Independent Practice 1

Determine if the given sets are closed or not closed. The answers can be found below.

• ### Independent Practice 2

Features another 20 Closure Property problems.

• ### Homework Worksheet

Example problems are provided and explained. Does this table display a closed property? The elements in a binary table are displayed horizontally and vertically outside the table .If the elements inside the table are limited to the elements P, Q, R, and S, the table is closed under the indicated operation.

• ### Topic Quiz

10 Closure Property problems. A math scoring matrix is included.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### Question?

In the movie 'The Princess Diaries,' what does Joe say after Mia says, 'The Princess is late for algebra,' and Michael is playing his harmonica? Answer: watch the movie to find out!