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Number Properties – Definition, Types, Chart

Jo-ann Caballes

Updated on January 12, 2024

Welcome to Brighterly, the extraordinary and interactive platform designed exclusively for children! Our mission is to make learning an enjoyable and exciting experience. In this article, we’ll embark on an adventure to explore the captivating world of numbers and their properties. Understanding number properties is a cornerstone in developing a solid foundation in math skills, and here at Brighterly, we’ve transformed this learning process into a delightful and engaging journey.

With a blend of creativity, burstiness, and human-like touch, Brighterly offers a unique approach to help children grasp number properties and unlock their potential in mathematics. As we dive into this wonderful world of numbers, children will not only strengthen their math skills but also develop a genuine appreciation for the subject. So, buckle up and join us as we embark on this thrilling adventure to uncover the magical properties of numbers with Brighterly!

About Number Properties

Number properties are rules and characteristics that help us work with and understand numbers in mathematics. These properties make it easier for us to perform operations like addition, subtraction, multiplication, and division. We’ll cover some essential number properties in this article, including the commutative, associative, distributive, and identity properties.

What are Number Properties?

Number properties are basic rules that describe how numbers behave in mathematical operations. By learning these properties, we can better understand how to work with numbers and solve math problems efficiently.

Commutative Property

The commutative property states that the order of numbers in addition or multiplication does not affect the result. In other words, changing the order of numbers won’t change the answer. This property applies to both addition and multiplication, but not to subtraction or division.

For example:

• For addition: 5 + 3 = 3 + 5
• For multiplication: 4 × 7 = 7 × 4

Associative Property

The associative property tells us that when adding or multiplying three or more numbers, the way we group them does not affect the result. Like the commutative property, this rule applies only to addition and multiplication, not subtraction or division.

For example:

• For addition: (2 + 3) + 4 = 2 + (3 + 4)
• For multiplication: (6 × 2) × 3 = 6 × (2 × 3)

Distributive Property

The distributive property states that when a number is multiplied by the sum of two other numbers, it’s the same as multiplying the number by each of the two numbers and then adding the results. This property is particularly useful when simplifying expressions in algebra.

For example: 5 × (3 + 2) = (5 × 3) + (5 × 2)

Identity Property

The identity property defines special numbers called “identity elements” that, when combined with other numbers through certain operations, do not change the value of the other numbers. For addition, the identity element is 0, and for multiplication, it’s 1.

For example:

• For addition: 7 + 0 = 7
• For multiplication: 9 × 1 = 9

Distributive Property of Multiplication Over Addition

The distributive property of multiplication over addition is another way to describe the distributive property. It emphasizes that multiplication distributes over addition, as we saw in the previous example.

For example: 4 × (6 + 3) = (4 × 6) + (4 × 3)

Formula Chart of Basic Number Properties

Here’s a quick reference chart with the basic number properties and their formulas:

1. Commutative Property
   • Addition: a + b = b + a
   • Multiplication: a × b = b × a
2. Associative Property
   • Addition: (a + b) + c = a + (b + c)
   • Multiplication: (a × b) × c = a × (b × c)
3. Distributive Property
   • a × (b + c) = (a × b) + (a × c)
4. Identity Property
   • Addition: a + 0 = a
   • Multiplication: a × 1 = a

Solved Examples of Number Properties

1. Commutative Property:
   • 8 + 12 = 12 + 8 (Addition)
   • 9 × 5 = 5 × 9 (Multiplication)
2. Associative Property:
   • (7 + 6) + 4 = 7 + (6 + 4) (Addition)
   • (3 × 8) × 2 = 3 × (8 × 2) (Multiplication)
3. Distributive Property:
   • 6 × (4 + 10) = (6 × 4) + (6 × 10)
4. Identity Property:
   • 15 + 0 = 15 (Addition)
   • 11 × 1 = 11 (Multiplication)

Practice Problems of Number Properties

1. Apply the commutative property to the following numbers:
   • 7 + 9
   • 6 × 4
2. Apply the associative property to the following numbers:
   • (2 + 8) + 5
   • (10 × 3) × 7
3. Apply the distributive property to the following numbers:
   • 3 × (6 + 4)
4. Identify the identity elements in the following problems:
   • 13 + ?
   • 5 × ?

Fun Facts!

• The word “commutative” comes from the Latin word “commutare,” which means “to change” or “to exchange.”
• The associative property is named after the word “associate,” which means “to group” or “to connect.”
• Identity elements are unique to each operation: 0 is the identity element for addition, and 1 is the identity element for multiplication.

Conclusion

Number properties are the building blocks of mathematics, paving the way for a deeper understanding of numbers and their interactions. Grasping these essential concepts will not only enhance your math skills but also empower you to tackle complex problems with ease. At Brighterly, we’re committed to nurturing your mathematical prowess, transforming you into a true math maestro!

As you immerse yourself in the vibrant world of numbers, you’ll uncover the hidden patterns and relationships that govern their behavior. By conquering these properties, you’ll unlock the door to a realm of endless possibilities and creative problem-solving approaches.

At Brighterly, our unique, engaging, and interactive approach to learning ensures that you’ll not only master the fundamentals of number properties but also develop a genuine passion for mathematics. Our carefully designed resources, activities, and challenges will keep you enthralled and motivated, fostering a love for numbers that will last a lifetime.

So, don’t hesitate to embark on this thrilling journey into the captivating universe of numbers with Brighterly by your side. Together, we’ll explore, learn, and conquer the fascinating world of mathematics, one number property at a time!

Frequently Asked Questions of Number Properties

Why are number properties important in mathematics?

• • Number properties are important because they help us understand and work with numbers more efficiently. They provide a foundation for solving mathematical problems and simplify calculations.

Do number properties apply to all mathematical operations?

• • No, some number properties only apply to specific operations. For example, the commutative and associative properties apply to addition and multiplication but not to subtraction or division.

What is the difference between the distributive property and the distributive property of multiplication over addition?

• • They are the same concept. The distributive property of multiplication over addition is just another way to describe the distributive property, emphasizing that multiplication distributes over addition.

Jo-ann Caballes

6 articles

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.