Closure is when an operation (for example addition) on a member of a set will always produce a member of the same set. Sets of integers are always considered closed under the operation of addition, because when you add integers you will always get another integer. This doesn't hold true for subtraction or division. When you subtract integers by integers that are larger than themselves, they result in negative numbers. Division is also not considered closed because you can often create fractions from taking the quotient of simple integers.

Closure Property for Addition Problems: When a & b are real numbers, then a + b will be unusual and real. Closure Property for Multiplication Problems: When a and b are real numbers, then a × b will be unusual and real. It means addition & multiplication of two real numbers gives the answer in real numbers. Also, most probably answer will be unusual. This fact is true according to the Textbooks methods as it uses additional mathematical symbols (like; aa, bb ∈R∈ℝ, and so on). It is more difficult method. Understand the examples below then you will perceive vital this concept is. Example#1: 5+6=11 is real. Both 5 and 6 are real numbers. After mutual addition, answer will be 11, that is also real number, and 11 is the only answer we can obtain by adding 5+6. The value 5+6 =11 is real, representing the Closure Property for Addition. Example#2: 5×6=30 is real. Both 55 and 66 are real numbers. After multiplying together, the answer will be 30, that is also real number, and 30 is the only answer we can obtain by multiplying 5×6. The value 5 x 6=30 is real, representing the Closure Property for Multiplication These worksheets explain the closure property of operations. Students will answer questions featuring addition, subtraction, multiplication, and division, as well as several tables.