Applying the Distributive Property: A Step-by-Step Guide

Understanding the Distributive Property

The Distributive Property is a useful rule in algebra that helps you simplify expressions. It states that when you multiply a number by a sum (or difference), you can distribute the multiplication across each term inside the parentheses. In simpler terms, it allows you to break down complex problems into smaller, more manageable parts.

The formula looks like this:

a(b + c) = ab + ac
a(b - c) = ab - ac

Let’s dive into some practical examples to see how this works!

Example 1: Distributing a Sum

Imagine you have 3 baskets, and each basket contains 4 apples and 2 oranges. To find the total number of fruits, you can use the Distributive Property:

Step 1: Identify the expression

Here, you can think of the total number of fruits as:

Total Fruits = 3(4 + 2)

Step 2: Apply the Distributive Property

Using the Distributive Property, multiply 3 by both 4 and 2:

Total Fruits = 3 * 4 + 3 * 2

Step 3: Calculate the results

Now, do the math:

• 3 * 4 = 12 (apples)
• 3 * 2 = 6 (oranges)

Step 4: Add them together

Total Fruits = 12 + 6 = 18
So, you have a total of 18 fruits!

Example 2: Distributing a Difference

Let’s say you’re planning to buy 5 packs of gum, and each pack costs \(2 for regular gum and \)1 for sugar-free gum. How much will you spend in total?

Step 1: Identify the expression

You can represent your total cost as:

Total Cost = 5(2 - 1)

Step 2: Apply the Distributive Property

Using the Distributive Property, multiply 5 by both 2 and -1:

Total Cost = 5 * 2 - 5 * 1

Step 3: Calculate the results

• 5 * 2 = 10 (for regular gum)
• 5 * 1 = 5 (for sugar-free gum)

Step 4: Subtract the costs

Total Cost = 10 - 5 = 5
You will spend a total of $5 on gum!

Conclusion

The Distributive Property is a powerful tool that can simplify your algebraic expressions, making calculations faster and easier. With practice, applying this property will become second nature. Remember, if you can break down a problem into smaller parts, you can tackle even the most complex algebra with confidence. Happy solving!