Inaugurated by IN-SPACe
ISRO Registered Space Tutor
S3-SA4-0367
What is the Distributive Property (Numbers)?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
The Distributive Property helps us solve multiplication problems involving addition or subtraction inside a bracket. It says that multiplying a number by a sum (or difference) is the same as multiplying that number by each part inside the bracket 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 first adding 5 + 2 = 7 biscuits per packet and then multiplying by 3 (3 x 7 = 21), you can multiply 3 by the chocolate biscuits (3 x 5 = 15) and 3 by the plain biscuits (3 x 2 = 6), then add them (15 + 6 = 21). Both ways give you 21 biscuits!
Worked Example
Step-by-Step
Let's solve 6 x (10 + 3) using the Distributive Property.
1. Identify the number outside the bracket (6) and the numbers inside the bracket (10 and 3).
---
2. Multiply the number outside (6) by the first number inside (10): 6 x 10 = 60.
---
3. Multiply the number outside (6) by the second number inside (3): 6 x 3 = 18.
---
4. Add the results from step 2 and step 3: 60 + 18 = 78.
---
5. So, 6 x (10 + 3) = 78.
Answer: 78
Why It Matters
Understanding the Distributive Property makes calculations faster and is a basic building block for algebra. It's used in computer programming to optimize code, in data science to process large datasets efficiently, and even in economics to model how costs are distributed. Many engineers and scientists use this daily to solve complex problems.
Common Mistakes
MISTAKE: Multiplying the number outside the bracket by only the first number inside. For example, in 5 x (2 + 4), doing 5 x 2 + 4 = 10 + 4 = 14. | CORRECTION: Remember to multiply the number outside by EVERY number inside the bracket. It should be 5 x 2 + 5 x 4 = 10 + 20 = 30.
MISTAKE: Forgetting to use the correct operation (addition or subtraction) between the multiplied terms. For example, in 7 x (8 - 3), doing 7 x 8 + 7 x 3. | CORRECTION: Keep the original operation from inside the bracket. It should be 7 x 8 - 7 x 3 = 56 - 21 = 35.
MISTAKE: Applying the property when there's only multiplication inside the bracket, e.g., 2 x (3 x 4). | CORRECTION: The Distributive Property applies to multiplication over addition or subtraction, not over another multiplication. For 2 x (3 x 4), just multiply the numbers inside first: 2 x 12 = 24.
Practice Questions
Try It Yourself
QUESTION: Solve 4 x (5 + 2) using the Distributive Property. | ANSWER: 20 + 8 = 28
QUESTION: A shop sells a combo pack with a toy car for Rs 75 and a small book for Rs 25. If 8 such combo packs are sold, how much money did the shop earn in total? Use the Distributive Property to solve. | ANSWER: 8 x 75 + 8 x 25 = 600 + 200 = 800. The shop earned Rs 800.
QUESTION: Calculate 12 x 105 using the Distributive Property by breaking 105 into (100 + 5). | ANSWER: 12 x (100 + 5) = 12 x 100 + 12 x 5 = 1200 + 60 = 1260
MCQ
Quick Quiz
Which of these correctly shows the Distributive Property for 9 x (7 - 3)?
9 x 7 + 3
9 x 7 - 3
9 x 7 - 9 x 3
9 x 7 + 9 x 3
The Correct Answer Is:
C
Option C correctly applies the Distributive Property by multiplying 9 by both 7 and 3, and keeping the subtraction operation between them. The other options either miss multiplying one term or use the wrong operation.
Real World Connection
In the Real World
When you calculate your monthly mobile bill, which might have a fixed plan cost plus charges for extra data usage, the telecom company uses a form of distributive calculation. Or, if a delivery app like Swiggy or Zomato calculates the total cost for multiple items in your order, they're essentially using this property to sum up individual item costs plus any delivery charges for each item.
Key Vocabulary
Key Terms
DISTRIBUTE: To spread out or give to each part | BRACKET: A symbol (like parentheses) used to group numbers or terms | OPERATION: A mathematical process like addition, subtraction, multiplication, or division | SUM: The result of adding numbers | DIFFERENCE: The result of subtracting numbers
What's Next
What to Learn Next
Great job understanding the Distributive Property with numbers! Next, you can explore how this property applies to variables in algebra. It's the same idea but with letters instead of just numbers, which will open up a whole new world of problem-solving!
