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What is the Distributive Law?
Grade Level:
Class 5
Maths, Computing, AI, Logic, Abstract Algebra
Definition
What is it?
The Distributive Law tells us how multiplication works with addition or subtraction. It means you can multiply a number by a group of numbers added or subtracted together, or you can multiply that number by each number in the group separately and then add or subtract the results. It helps break down big problems into smaller, easier ones.
Simple Example
Quick Example
Imagine you buy 3 packets of biscuits, and each packet has 2 cream biscuits and 3 plain biscuits. Instead of counting all biscuits one by one, you can use the Distributive Law. You can find total cream biscuits (3 x 2) and total plain biscuits (3 x 3) and then add them up.
Worked Example
Step-by-Step
Let's solve 5 x (6 + 4) using the Distributive Law.
1. Identify the number outside the bracket and the numbers inside: 5 is outside, 6 and 4 are inside.
---2. Multiply the outside number by the first number inside the bracket: 5 x 6 = 30.
---3. Multiply the outside number by the second number inside the bracket: 5 x 4 = 20.
---4. Add the results from step 2 and step 3: 30 + 20 = 50.
---5. So, 5 x (6 + 4) = 50.
(Just to check, 5 x (6 + 4) = 5 x 10 = 50. Both methods give the same answer!)
Why It Matters
The Distributive Law is fundamental for algebra and solving equations, which are crucial in higher maths. Engineers use it to design structures, and computer programmers use it to write efficient code for apps and games. It helps in logical thinking for fields like AI and data science.
Common Mistakes
MISTAKE: Multiplying only the first number inside the bracket. For example, in 3 x (2 + 5), students might do 3 x 2 + 5 = 6 + 5 = 11. | CORRECTION: Remember to multiply the number outside by EVERY number inside the bracket. So, 3 x (2 + 5) = (3 x 2) + (3 x 5) = 6 + 15 = 21.
MISTAKE: Forgetting the operation sign inside the bracket. For example, in 4 x (7 - 3), students might write (4 x 7) + (4 x 3). | CORRECTION: The operation sign (plus or minus) between the terms inside the bracket must be carried over. So, 4 x (7 - 3) = (4 x 7) - (4 x 3) = 28 - 12 = 16.
MISTAKE: Applying the Distributive Law when there's only multiplication inside the bracket, e.g., 2 x (3 x 4). | CORRECTION: The Distributive Law applies to multiplication over ADDITION or SUBTRACTION. For 2 x (3 x 4), you simply multiply: 2 x 12 = 24. It's not (2 x 3) x (2 x 4).
Practice Questions
Try It Yourself
QUESTION: Solve 6 x (7 + 2) using the Distributive Law. | ANSWER: (6 x 7) + (6 x 2) = 42 + 12 = 54
QUESTION: A shopkeeper sells 4 boxes of pens. Each box has 5 blue pens and 3 black pens. How many pens are there in total? Use the Distributive Law. | ANSWER: 4 x (5 + 3) = (4 x 5) + (4 x 3) = 20 + 12 = 32 pens
QUESTION: Find the value of 8 x (10 - 4 + 2) using the Distributive Law. | ANSWER: (8 x 10) - (8 x 4) + (8 x 2) = 80 - 32 + 16 = 48 + 16 = 64
MCQ
Quick Quiz
Which of these correctly shows the Distributive Law for 7 x (9 - 3)?
7 x 9 - 3
(7 x 9) - (7 x 3)
(7 - 9) x (7 - 3)
7 x 9 + 7 x 3
The Correct Answer Is:
B
Option B correctly applies the Distributive Law by multiplying 7 with both 9 and 3 separately, and keeping the subtraction sign in between. Options A, C, and D do not follow the rule correctly.
Real World Connection
In the Real World
When budgeting for a school trip, if 20 students are going and each needs 150 rupees for bus fare and 100 rupees for snacks, you can use the Distributive Law. You can calculate total bus fare (20 x 150) and total snack money (20 x 100) and then add them, instead of adding fare and snacks first (150+100) and then multiplying by 20.
Key Vocabulary
Key Terms
DISTRIBUTIVE LAW: A rule showing how multiplication spreads over addition or subtraction | BRACKETS: Symbols () used to group numbers or terms together | MULTIPLICATION: The process of finding the product of two or more numbers | ADDITION: The process of combining numbers to find their sum | SUBTRACTION: The process of taking one number away from another
What's Next
What to Learn Next
Great job learning the Distributive Law! Next, you can explore the Commutative and Associative Laws of arithmetic. These laws, along with the Distributive Law, are the building blocks for understanding more complex algebra and problem-solving in maths.
