Home Overview SiteMap Math Dictionary

# Closure Property of Real Number Addition and Multiplication

## Definition of Closure Property of Real Number Addition and Multiplication

• Closure property of real number addition states that the sum of any two real numbers equals another real number.
• Closure property of real number multiplication states that the product of any two real numbers equals another real number.

### Examples of Closure Property of Real Number Addition and Multiplication

• 2, 5 are real numbers.

2 + 5 = 7, another real number.

• 4, 7 are real numbers.

4 × 7 = 28, another real number.

### Solved Example on Closure Property of Real Number Addition

Determine the set that does not satisfy closure property of addition.

Choices:

A. Real number

B. Irrational numbers

C. Rational numbers

D. Integers

Solution:

Step 1: Among the sets listed, only the set of irrational numbers does not satisfy closure property of addition.

Step 2: For example, consider the irrational numbers

and .

Step 3: is a rational number.

Step 4: So, the set of irrational numbers does not satisfy the Closure property under addition.

Solved Example on Closure Property of Real Number Multiplication

Determine whether the set {0, 11, - 11} satisfies closure property with respective to multiplication.

Choices:

A. Yes

B. No

Solution:

Step 1: {0, 11, - 11}

Step 2: 0 × 11 = 0          [0 is an element of the set.]

Step 3: - 11 × 0 = 0        [0 is an element of the set.]

Step 4: - 11 × 11 = - 121, not an element of the given set.

Step 5: So, the given set does not satisfy the closure property with respective to multiplication.

• Real Number
• Sum
• Product