What is the Distributive Property? | Simple Explanation for Class 7

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What is the Distributive Property for Whole Numbers?

Grade Level:

Class 7

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

Definition

What is it?

The Distributive Property for Whole Numbers tells us that multiplying a number by a sum (or difference) gives the same result as multiplying that number by each part of the sum (or difference) separately and then adding (or subtracting) the products. It essentially 'distributes' the multiplication over addition or subtraction. For example, a x (b + c) = (a x b) + (a x c).

Simple Example

Quick Example

Imagine you buy 3 packets of biscuits, and each packet has 2 cream biscuits and 5 plain biscuits. Instead of first adding 2 + 5 = 7 biscuits per packet and then multiplying by 3 (3 x 7 = 21), you can multiply 3 by the cream biscuits (3 x 2 = 6) and 3 by the plain biscuits (3 x 5 = 15), then add them (6 + 15 = 21). Both ways give 21 biscuits!

Worked Example

Step-by-Step

Let's solve 6 x (7 + 3) using the Distributive Property.
---Step 1: Identify the number outside the bracket (6) and the numbers inside the bracket (7 and 3).
---Step 2: Distribute the multiplication (6) to each number inside the bracket.
---Step 3: This means we will calculate (6 x 7) + (6 x 3).
---Step 4: Perform the multiplications: 6 x 7 = 42 and 6 x 3 = 18.
---Step 5: Now, add the results: 42 + 18.
---Step 6: 42 + 18 = 60.
---Answer: So, 6 x (7 + 3) = 60.

Why It Matters

Understanding the Distributive Property helps simplify complex calculations and is fundamental in algebra. It's used by software engineers to optimize code, by economists to model market behavior, and even in data science to process information efficiently. Learning this now will make your future studies in AI/ML and Computer Science much smoother!

Common Mistakes

MISTAKE: Multiplying only the first number inside the bracket. For example, in 5 x (2 + 4), students might only do (5 x 2) + 4. | CORRECTION: Remember to multiply the outside number by *every* term inside the bracket. It should be (5 x 2) + (5 x 4).

MISTAKE: Forgetting the operation inside the bracket when distributing. For example, writing 3 x (8 - 2) as (3 x 8) x (3 x 2). | CORRECTION: The operation (addition or subtraction) inside the bracket remains the same between the distributed terms. It should be (3 x 8) - (3 x 2).

MISTAKE: Incorrectly applying it to division. For example, thinking 10 / (2 + 3) = (10 / 2) + (10 / 3). | CORRECTION: The Distributive Property works only for multiplication over addition or subtraction, not for division. Always perform the operation inside the bracket first for division.

Practice Questions

Try It Yourself

QUESTION: Use the Distributive Property to solve 4 x (5 + 8). | ANSWER: (4 x 5) + (4 x 8) = 20 + 32 = 52

QUESTION: Simplify 7 x (10 - 3) using the Distributive Property. | ANSWER: (7 x 10) - (7 x 3) = 70 - 21 = 49

QUESTION: A grocery store sells 6 cartons of eggs. Each carton has 12 white eggs and 6 brown eggs. How many eggs are there in total? Solve using the Distributive Property. | ANSWER: 6 x (12 + 6) = (6 x 12) + (6 x 6) = 72 + 36 = 108 eggs.

MCQ

Quick Quiz

Which of the following correctly shows the Distributive Property for 9 x (15 + 5)?

(9 + 15) x (9 + 5)

(9 x 15) + 5

(9 x 15) + (9 x 5)

9 x 15 + 5

The Correct Answer Is:

Option C correctly distributes the multiplication of 9 to both 15 and 5, then adds the products. Options A, B, and D show incorrect applications of the property.

Real World Connection

In the Real World

When a small business owner in India calculates their daily earnings, they might use this property. If they sell 'chai' for Rs. 10 and 'samosas' for Rs. 15, and on a busy day, 50 customers buy both, they can calculate total sales as 50 x (10 + 15) = (50 x 10) + (50 x 15). This helps them quickly sum up different product sales.

Key Vocabulary

Key Terms

DISTRIBUTE: To spread out or give out to each part. | WHOLE NUMBERS: Numbers without fractions or decimals (0, 1, 2, 3...). | PRODUCT: The result of multiplication. | SUM: The result of addition. | DIFFERENCE: The result of subtraction.

What's Next

What to Learn Next

Great job understanding the Distributive Property! Next, you should explore the Associative and Commutative Properties of Whole Numbers. These properties, along with the Distributive Property, form the bedrock of arithmetic and algebra, helping you solve more complex problems with ease.