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

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What is the Distributive Property of Integers?

Grade Level:

Class 6

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

Definition

What is it?

The Distributive Property of Integers tells us how multiplication works 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.

Simple Example

Quick Example

Imagine you buy 3 packets of biscuits, and each packet has 5 chocolate biscuits and 2 plain biscuits. Instead of finding total biscuits in one packet first (5+2=7, then 3*7=21), you can multiply 3 by the chocolate biscuits (3*5=15) and 3 by the plain biscuits (3*2=6) separately, then add them (15+6=21). Both ways give you 21 biscuits!

Worked Example

Step-by-Step

Let's solve 5 * (8 + 3) using the Distributive Property.

Step 1: Identify the number outside the bracket and the numbers inside.
Here, 5 is outside, and 8 and 3 are inside, connected by addition.
---Step 2: Distribute the number outside to each number inside the bracket by multiplication.
This means we multiply 5 by 8, and 5 by 3.
---Step 3: Write down the new expression with the multiplication results.
(5 * 8) + (5 * 3)
---Step 4: Perform the multiplications.
40 + 15
---Step 5: Perform the addition.
55

So, 5 * (8 + 3) = 55.

Why It Matters

Understanding the Distributive Property helps simplify complex calculations in daily life and in advanced subjects. It's crucial for coding in Computer Science, solving equations in Physics, and managing data in AI/ML. Engineers use it to design efficient systems and economists to model financial situations.

Common Mistakes

MISTAKE: Multiplying the number outside only by the first term inside the bracket. For example, solving 4 * (2 + 5) as (4 * 2) + 5 = 8 + 5 = 13. | CORRECTION: Remember to multiply the number outside by EVERY term inside the bracket. So, 4 * (2 + 5) = (4 * 2) + (4 * 5) = 8 + 20 = 28.

MISTAKE: Forgetting to apply the property to subtraction. For example, solving 6 * (7 - 3) as (6 * 7) - 3 = 42 - 3 = 39. | CORRECTION: The Distributive Property works for both addition AND subtraction. So, 6 * (7 - 3) = (6 * 7) - (6 * 3) = 42 - 18 = 24.

MISTAKE: Changing the operation between the distributed terms. For example, solving 3 * (4 + 2) as (3 * 4) * (3 * 2). | CORRECTION: The operation (addition or subtraction) inside the bracket remains the same between the distributed terms. So, 3 * (4 + 2) = (3 * 4) + (3 * 2) = 12 + 6 = 18.

Practice Questions

Try It Yourself

QUESTION: Use the Distributive Property to solve 7 * (10 + 2). | ANSWER: (7 * 10) + (7 * 2) = 70 + 14 = 84

QUESTION: Calculate 9 * (15 - 5) using the Distributive Property. | ANSWER: (9 * 15) - (9 * 5) = 135 - 45 = 90

QUESTION: A chai shop sells 8 cups of chai every hour. If each cup costs Rs 10 and has an extra Rs 2 for a biscuit, how much money does the shop make in an hour from 8 customers using the Distributive Property? | ANSWER: 8 * (10 + 2) = (8 * 10) + (8 * 2) = 80 + 16 = Rs 96

MCQ

Quick Quiz

Which of the following correctly shows the Distributive Property for 6 * (4 + 7)?

6 * 4 + 7

6 + 4 * 7

(6 * 4) + (6 * 7)

(6 + 4) * (6 + 7)

The Correct Answer Is:

Option C correctly applies the Distributive Property by multiplying 6 with both 4 and 7, and then adding the results. The other options show incorrect applications of the property.

Real World Connection

In the Real World

When a caterer in India plans for a big event, they might use the Distributive Property. If they need to prepare 20 thalis, each with 3 rotis and 1 bowl of sabzi, they can calculate total rotis (20 * 3) and total sabzi bowls (20 * 1) separately and then add them up. This helps manage ingredients and costs efficiently, just like managing inventory for a Kirana store.

Key Vocabulary

Key Terms

DISTRIBUTIVE PROPERTY: A rule that lets you multiply a sum or difference by multiplying each term separately | INTEGER: A whole number (positive, negative, or zero) | TERM: A single number or variable in an expression | BRACKETS: Symbols used to group parts of an expression, like ( )

What's Next

What to Learn Next

Great job understanding the Distributive Property! Next, you can explore the Associative and Commutative Properties of Integers. These properties, along with the Distributive Property, are fundamental building blocks for all of algebra and will make solving bigger math problems much easier!