# The Distributive Property In Arithmetic

mathantics2016-02-20

Mathematics (Field Of Study)#Math#Math Antics#Education#arithmetic#distributive property

1M views|8 years ago

💫 Short Summary

This Math Antics video explains the distributive property in mathematics, demonstrating how it allows for the rearrangement of expressions and the simplification of calculations. The concept is illustrated through examples, highlighting its practical applications and importance in algebra.

✨ Highlights

📊 Transcript

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Introduction to the distributive property in math.

00:06The distributive property is the same as the distributive law or the distributive property of multiplication over addition.

Distributing something means giving it to each member of a group.

The concept of the distributive property allows us to change the order of operations in certain types of problems.

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Example of using the distributive property to simplify an expression.

02:09Distributing the factor of 3 to each member of the group (4 and 6) individually.

Simplifying the expression by multiplying and adding the results.

The original expression and the simplified expression using the distributive property are equivalent.

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The distributive property provides an alternate path to the same answer.

04:27Two ways to get to the same answer using the distributive property and the regular method.

The distributive property can make some calculations easier to do mentally for certain basic multi-digit multiplication problems.

Breaking up the factor into a group sum and distributing the other factor can simplify the calculation.

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The distributive property works for subtraction and for group members that are being added or subtracted.

07:09Example of the distributive property with subtraction: 7 times (10 - 4)

Distributive property works for group members that are being added or subtracted, even with a mixture of addition and subtraction in the group.

The distributive property doesn't work when the members of a group are being multiplied or divided.

💫 FAQs about This YouTube Video

### 1. What is the distributive property in mathematics?

The distributive property in mathematics allows us to distribute a factor to each term inside a group, which is particularly useful when multiplying or adding. It is a fundamental concept that provides a way to simplify and manipulate algebraic expressions.

### 2. How does the distributive property work?

The distributive property states that a(b + c) = ab + ac, where a, b, and c are numbers or variables. This means that we can distribute the factor a to both b and c when they are added together. The same principle applies to subtraction as well: a(b - c) = ab - ac.

### 3. What are the practical applications of the distributive property?

The distributive property has wide-ranging practical applications in various mathematical calculations, including simplifying expressions, solving equations, and factoring algebraic expressions. It also plays a crucial role in areas such as geometry, finance, and computer science.

### 4. How is the distributive property related to algebra?

In algebra, the distributive property is a fundamental tool for expanding and simplifying expressions, solving equations, and understanding the relationships between different mathematical operations. It is a key concept that forms the basis for many algebraic manipulations and transformations.

### 5. Can you provide an example of the distributive property in action?

Certainly! An example of the distributive property is 3(x + 2), which can be expanded to 3x + 6 by distributing the 3 to both x and 2. This showcases how the distributive property allows us to work with individual terms within parentheses when performing multiplication.

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