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

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What is the Distributive Property for Natural Numbers?

Grade Level:

Class 7

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

Definition

What is it?

The Distributive Property 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 sharing one thing with many people.

Simple Example

Quick Example

Imagine your school is ordering 3 new cricket bats. Each bat costs Rs 500 and a set of pads costs Rs 200. If you want to calculate the total cost for 3 bats and 3 sets of pads, you can either add the cost of one bat and one set of pads first (500 + 200 = 700) and then multiply by 3 (3 x 700 = Rs 2100). Or, using the distributive property, you can multiply 3 by the cost of bats (3 x 500 = 1500) and 3 by the cost of pads (3 x 200 = 600) and then add these amounts (1500 + 600 = Rs 2100). Both ways give the same answer!

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).
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Step 2: Multiply the number outside the bracket by the first number inside. So, 6 x 7 = 42.
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Step 3: Multiply the number outside the bracket by the second number inside. So, 6 x 3 = 18.
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Step 4: Add the results from Step 2 and Step 3. So, 42 + 18 = 60.
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Answer: 6 x (7 + 3) = 60.

Why It Matters

Understanding the Distributive Property makes mental math easier and is crucial for algebra, which is the foundation for advanced studies. Engineers use it to simplify complex calculations, and data scientists apply similar logic when processing large datasets. It helps in building efficient algorithms for computers.

Common Mistakes

MISTAKE: Multiplying the outside number by only the first number inside the bracket. For example, 5 x (2 + 4) = (5 x 2) + 4 = 10 + 4 = 14. | CORRECTION: Remember to distribute the multiplication to ALL numbers inside the bracket. So, 5 x (2 + 4) = (5 x 2) + (5 x 4) = 10 + 20 = 30.

MISTAKE: Confusing multiplication with addition when distributing. For example, trying to add the outside number to the numbers inside. | CORRECTION: The distributive property is about multiplication 'distributing' over addition or subtraction. Always multiply the outside number by each term inside.

MISTAKE: Not applying the property when there's subtraction inside the bracket. For example, 8 x (10 - 2) = (8 x 10) - 2 = 80 - 2 = 78. | CORRECTION: The property works for subtraction too. Distribute the multiplication to both terms and keep the subtraction. So, 8 x (10 - 2) = (8 x 10) - (8 x 2) = 80 - 16 = 64.

Practice Questions

Try It Yourself

QUESTION: Solve 4 x (5 + 8) using the Distributive Property. | ANSWER: (4 x 5) + (4 x 8) = 20 + 32 = 52

QUESTION: Calculate 7 x (12 - 5) using the Distributive Property. | ANSWER: (7 x 12) - (7 x 5) = 84 - 35 = 49

QUESTION: A shop sells 9 packets of laddoos. Each packet has 6 small laddoos and 4 medium laddoos. How many laddoos are there in total? Use the Distributive Property. | ANSWER: 9 x (6 + 4) = (9 x 6) + (9 x 4) = 54 + 36 = 90 laddoos

MCQ

Quick Quiz

Which of the following correctly shows the Distributive Property for 3 x (9 + 2)?

3 x 9 + 2

3 + 9 x 2

(3 x 9) + (3 x 2)

(3 + 9) x (3 + 2)

The Correct Answer Is:

Option C correctly applies the Distributive Property by multiplying the number outside the bracket (3) by each number inside the bracket (9 and 2) separately, and then adding the results. The other options do not follow this rule.

Real World Connection

In the Real World

Imagine you are a shop owner using a billing software. When a customer buys 5 items, and each item costs Rs 150 and has a GST of Rs 20, the software might calculate the total cost using the distributive property: 5 x (150 + 20) = (5 x 150) + (5 x 20). This helps process bills quickly and accurately, just like how UPI transactions are calculated behind the scenes.

Key Vocabulary

Key Terms

DISTRIBUTE: To spread something out among a group. | PROPERTY: A rule or characteristic in mathematics. | NATURAL NUMBERS: Counting numbers starting from 1 (1, 2, 3, ...). | BRACKETS: Symbols used to group numbers or terms together.

What's Next

What to Learn Next

Great job understanding the Distributive Property! Next, you can explore how this property applies to integers (positive and negative numbers) and then to algebraic expressions. This will make solving more complex math problems much easier and prepare you for higher classes!