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Is Distributive Property Applicable for Subtraction?

Published in Distributive Property 2 mins read

Yes, the distributive property is indeed applicable for subtraction. It is a fundamental principle in mathematics that extends to both addition and subtraction operations.

Understanding the Distributive Property

The distributive property states that multiplying a number by a sum or difference yields the same result as multiplying that number by each term within the sum or difference and then performing the respective operation. This means you can "distribute" the multiplication operation over the terms inside parentheses.

How it Works with Subtraction

For subtraction, the property is expressed as:

a × (b - c) = (a × b) - (a × c)

Here, 'a' is the number being distributed, and '(b - c)' represents the difference between two numbers. The property allows you to multiply 'a' by 'b' and 'a' by 'c' separately, and then subtract the results.

Practical Example

Let's illustrate with a numerical example:

Suppose you need to calculate 5 × (7 - 3).

  1. Without Distributing (Order of Operations):

    • First, perform the subtraction inside the parentheses: 7 - 3 = 4
    • Then, multiply: 5 × 4 = 20
  2. Using the Distributive Property:

    • Distribute the multiplication (5) to each term inside the parentheses:
      • Multiply 5 by 7: 5 × 7 = 35
      • Multiply 5 by 3: 5 × 3 = 15
    • Subtract the results: 35 - 15 = 20

As shown, both methods yield the exact same result, confirming that the distributive property holds true for subtraction.

Summary Table

The table below summarizes the application of the distributive property for subtraction:

Concept General Form Numerical Example Calculation Method Result
Original Expression a × (b - c) 5 × (7 - 3) 5 × 4 20
Distributed Form (a × b) - (a × c) (5 × 7) - (5 × 3) 35 - 15 20

This property is a cornerstone of algebraic manipulation, simplifying complex expressions and calculations. It's widely used in various mathematical fields, from basic arithmetic to advanced algebra and calculus.