Distributive Property Calculator with Steps

Distributive Property Calculator

Factor (a):

First Term (b):

Operation: Addition (+) Subtraction (-)

Second Term (c):

function calculateDistributiveProperty() { var factorA = parseFloat(document.getElementById('factorA').value); var termB = parseFloat(document.getElementById('termB').value); var termC = parseFloat(document.getElementById('termC').value); var operation = document.getElementById('operation').value; var resultDiv = document.getElementById('distributiveResult'); var outputHtml = "; if (isNaN(factorA) || isNaN(termB) || isNaN(termC)) { resultDiv.innerHTML = 'Please enter valid numbers for all fields.'; return; } // Original Expression outputHtml += '

Steps:

'; outputHtml += 'Original Expression: ' + factorA + ' * (' + termB + ' ' + operation + ' ' + termC + ')'; // Step 1: Apply distributive property var step1_term1 = factorA + ' * ' + termB; var step1_term2 = factorA + ' * ' + termC; outputHtml += 'Step 1: Apply Distributive Property'; outputHtml += '(' + step1_term1 + ') ' + operation + ' (' + step1_term2 + ')'; // Step 2: Multiply terms var product1 = factorA * termB; var product2 = factorA * termC; outputHtml += 'Step 2: Multiply Terms'; outputHtml += " + product1 + ' ' + operation + ' ' + product2 + "; // Step 3: Perform final addition/subtraction var finalResult; if (operation === '+') { finalResult = product1 + product2; outputHtml += 'Step 3: Add Terms'; } else { // operation === '-' finalResult = product1 – product2; outputHtml += 'Step 3: Subtract Terms'; } outputHtml += " + finalResult + "; outputHtml += '

Final Result:

'; outputHtml += " + finalResult + "; resultDiv.innerHTML = outputHtml; } .calculator-container { background-color: #f9f9f9; border: 1px solid #ddd; padding: 20px; border-radius: 8px; max-width: 500px; margin: 20px auto; font-family: Arial, sans-serif; } .calculator-container h2 { text-align: center; color: #333; margin-bottom: 20px; } .form-group { margin-bottom: 15px; } .form-group label { display: block; margin-bottom: 5px; font-weight: bold; color: #555; } .form-group input[type="number"], .form-group select { width: calc(100% – 22px); padding: 10px; border: 1px solid #ccc; border-radius: 4px; box-sizing: border-box; } button { background-color: #007bff; color: white; padding: 12px 20px; border: none; border-radius: 4px; cursor: pointer; font-size: 16px; width: 100%; box-sizing: border-box; } button:hover { background-color: #0056b3; } .result-container { margin-top: 20px; padding: 15px; border: 1px solid #e0e0e0; border-radius: 4px; background-color: #eef; } .result-container h3 { color: #333; margin-top: 0; border-bottom: 1px solid #ccc; padding-bottom: 10px; margin-bottom: 10px; } .result-container p { margin-bottom: 8px; line-height: 1.5; color: #444; } .result-container p.error { color: #dc3545; font-weight: bold; } .result-container p.final-result { font-size: 1.4em; font-weight: bold; color: #28a745; text-align: center; margin-top: 15px; }

Understanding the Distributive Property in Mathematics

The distributive property is a fundamental concept in algebra that allows you to simplify expressions by multiplying a single term by two or more terms inside a set of parentheses. It's one of the most frequently used properties in mathematics and is crucial for solving equations and simplifying complex algebraic expressions.

What is the Distributive Property?

In its simplest form, the distributive property states that multiplying a number by a sum (or difference) is the same as multiplying that number by each term in the sum (or difference) and then adding (or subtracting) the products. Mathematically, it can be expressed as:

For Addition: a * (b + c) = a*b + a*c
For Subtraction: a * (b - c) = a*b - a*c

Here, 'a' is the factor outside the parentheses, and 'b' and 'c' are the terms inside. The property essentially "distributes" the multiplication across the terms within the parentheses.

Why is it Important?

The distributive property is vital for several reasons:

Simplifying Expressions: It allows you to remove parentheses and combine like terms, making expressions easier to work with.
Solving Equations: It's often the first step in solving equations that involve parentheses.
Factoring: It's the reverse process of factoring, where you pull out a common factor from multiple terms.
Foundation for Advanced Math: Understanding this property is essential for more complex algebraic concepts, polynomial multiplication, and calculus.

How to Use the Distributive Property Calculator

Our Distributive Property Calculator simplifies the process of applying this property and shows you the step-by-step breakdown. Here's how to use it:

Enter the Factor (a): Input the number that is outside the parentheses. This is the term that will be distributed.
Enter the First Term (b): Input the first number inside the parentheses.
Select the Operation: Choose whether the operation between the terms inside the parentheses is addition (+) or subtraction (-).
Enter the Second Term (c): Input the second number inside the parentheses.
Click "Calculate": The calculator will then display the original expression, each step of applying the distributive property, and the final simplified result.

Example Calculation:

Let's walk through an example to illustrate the distributive property:

Problem: Simplify the expression 5 * (7 + 2)

Original Expression: 5 * (7 + 2)
Step 1: Apply Distributive Property
Multiply the factor (5) by each term inside the parentheses:
(5 * 7) + (5 * 2)
Step 2: Multiply Terms
Perform the multiplications:
35 + 10
Step 3: Add Terms
Perform the addition:
45

So, 5 * (7 + 2) = 45. You can verify this by first adding inside the parentheses: 5 * (9) = 45.

Using the calculator above, you would input '5' for Factor (a), '7' for First Term (b), select 'Addition (+)', and '2' for Second Term (c). The calculator will then show you these exact steps and the final result.