What is the Distributive Property? | Simple Explanation for Class 6

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What is the Distributive Property of Rational Numbers?

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The Distributive Property of Rational Numbers tells us how multiplication behaves with addition or subtraction. It means you can multiply a number by a sum (or difference) by multiplying that number by each part of the sum (or difference) separately, and then adding (or subtracting) the results. It's like distributing a common factor to each term inside brackets.

Simple Example

Quick Example

Imagine you are buying 2 packets of biscuits and each packet costs Rs 10. Also, in each packet, there's a small chocolate worth Rs 5. You want to find the total cost. You can either add the biscuit cost and chocolate cost first (10+5 = 15) and then multiply by 2 (2 x 15 = Rs 30), OR you can multiply the biscuit cost by 2 (2 x 10 = 20) and the chocolate cost by 2 (2 x 5 = 10) and then add them (20 + 10 = Rs 30). Both ways give you the same answer!

Worked Example

Step-by-Step

Let's use the distributive property to solve: 4 x (5 + 3/2)

Step 1: Identify the number outside the bracket and the numbers inside. Here, 4 is outside, and 5 and 3/2 are inside.
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Step 2: Distribute the number outside to each number inside the bracket using multiplication. This means 4 will multiply 5, AND 4 will multiply 3/2. So, we get (4 x 5) + (4 x 3/2).
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Step 3: Perform the multiplications separately. (4 x 5) = 20. And (4 x 3/2) = (12/2) = 6.
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Step 4: Now add the results from Step 3: 20 + 6.
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Step 5: Calculate the final sum: 20 + 6 = 26.

So, 4 x (5 + 3/2) = 26.

Why It Matters

This property simplifies complex calculations and is a basic building block for algebra. Understanding it helps in fields like Computer Science for optimizing code, in Economics for calculating costs efficiently, and even in Physics for solving equations. It's a key skill for problem-solving in many future careers.

Common Mistakes

MISTAKE: Multiplying the outside number by only the first term inside the bracket and ignoring the rest. For example, 2 x (3 + 4) becomes (2 x 3) + 4. | CORRECTION: Remember to multiply the outside number by EVERY term inside the bracket. So, 2 x (3 + 4) should be (2 x 3) + (2 x 4).

MISTAKE: Confusing distribution with simple multiplication. For example, treating 2 x (3 x 4) as (2 x 3) x (2 x 4). | CORRECTION: The distributive property applies to multiplication over addition or subtraction, not over another multiplication. For 2 x (3 x 4), you just multiply the numbers in order: 2 x 12 = 24.

MISTAKE: Forgetting to handle signs correctly when distributing a negative number. For example, -2 x (3 - 4) becomes (-2 x 3) - (2 x 4). | CORRECTION: The negative sign also gets distributed. So, -2 x (3 - 4) should be (-2 x 3) - (-2 x 4), which simplifies to -6 - (-8) = -6 + 8 = 2.

Practice Questions

Try It Yourself

QUESTION: Use the distributive property to solve: 5 x (7 + 1/5) | ANSWER: 36

QUESTION: Simplify using the distributive property: (2/3) x (9 - 6) | ANSWER: 2

QUESTION: A shopkeeper sells 3 identical school bags. Each bag costs Rs 450 and has a small lunchbox worth Rs 50 inside. Use the distributive property to find the total cost of the bags and lunchboxes. | ANSWER: Rs 1500

MCQ

Quick Quiz

Which of the following correctly shows the distributive property for 6 x (2 + 1/3)?

(6 x 2) + 1/3

6 + (2 + 1/3)

(6 x 2) + (6 x 1/3)

6 x 2 x 1/3

The Correct Answer Is:

Option C correctly shows that the 6 is multiplied by both the 2 and the 1/3, and then the results are added. Options A, B, and D do not apply the distributive property correctly.

Real World Connection

In the Real World

Imagine you are calculating your monthly mobile phone bill. Your plan costs Rs 299 per month, and you also pay Rs 50 for a data add-on each month. If you want to calculate the total cost for 3 months, you can use the distributive property: 3 x (299 + 50) = (3 x 299) + (3 x 50). This helps billing systems in companies like Jio or Airtel calculate charges efficiently for millions of users.

Key Vocabulary

Key Terms

RATIONAL NUMBER: A number that can be written as a fraction p/q, where p and q are integers and q is not zero. | DISTRIBUTE: To spread something out or apply it to each part. | PROPERTY: A characteristic or rule in mathematics. | EXPRESSION: A combination of numbers, variables, and operation symbols. | BRACKETS: Symbols like () used to group parts of a mathematical expression.

What's Next

What to Learn Next

Great job learning about the Distributive Property! Next, you can explore the Associative and Commutative Properties of Rational Numbers. These properties also help simplify calculations and are essential for solving more complex algebraic equations in higher classes.