Questions On Distributive Property For Class 7

The distributive property is a fundamental concept in mathematics that helps simplify expressions and solve problems efficiently. It states that multiplication distributes over addition or subtraction. This property is widely used in algebra arithmetic and real-life calculations.

For Class 7 students mastering the distributive property is crucial as it lays the foundation for more advanced mathematical concepts. This topic provides a detailed explanation of the distributive property along with important questions and answers to help students strengthen their understanding.

1. Understanding the Distributive Property

Q: What is the distributive property?

A: The distributive property states that when a number is multiplied by a sum or difference the number is distributed to each term inside the parentheses.

Mathematically it is expressed as:

Q: Why is the distributive property important?

A: The distributive property helps in:

• Simplifying expressions
• Making mental calculations easier
• Solving algebraic equations
• Understanding the relationship between multiplication and addition/subtraction

Q: Can you give an example of the distributive property?

A: Sure! Let’s take an example:

Applying the distributive property:

2. Applying the Distributive Property

Q: How can the distributive property be used in real-life scenarios?

A: The distributive property is useful in everyday calculations such as:

• Distributing discounts while shopping
• Splitting food portions equally
• Calculating area in geometry

Q: How do you use the distributive property with variables?

A: When variables are involved the property works the same way.

Example:

For instance if x = 2 y = 3 and z = 4:

3. Important Questions on Distributive Property

Basic Questions

1. Solve using the distributive property:

   4 times (2 + 6)

2. Expand the expression:

   3 times (7 – 5)

3. Write an equivalent expression using the distributive property:

   6 times 8 + 6 times 2

4. Apply the distributive property:

   9 times (5 + 3)

5. Simplify using the distributive property:

   2 times (x + 4)

Intermediate Questions

6. Use the distributive property to expand:

   7 times (4 + 9)

7. Solve the equation using the distributive property:

   5 times (x + 3) = 35

8. Simplify the expression:

   (6 + 2) times 5

9. Factorize using the distributive property:

   12x + 18

10. Expand and simplify:

Advanced Questions

11. Solve for x:

$$
4(x + 5) = 32
$$

12. Expand the algebraic expression:

$$
2(a + b) - 3(a - b)
$$

13. If y = 3 simplify:

$$
5(y + 2) - 2(y - 1)
$$

14. Use the distributive property to find the missing number:

6 \times (___ + 4) = (6 \times 3) + (6 \times 4)

15. Factorize the expression:

$$
15m + 20n
$$

4. Common Mistakes and How to Avoid Them

Q: What are some common mistakes when applying the distributive property?

A: Some common mistakes include:

• Forgetting to multiply every term inside the parentheses
• Confusing addition and multiplication
• Incorrectly distributing negative numbers

Q: How can we avoid these mistakes?

A:

• Always double-check each term.
• Use brackets to keep track of operations.
• Practice with different numbers and variables.

5. Practice Problems for Students

Try solving these additional problems:

1. Expand using the distributive property:

   8 times (x + 5)

2. Solve for x:

   3(x + 4) = 27

3. Simplify:

   10(y – 2) + 5y

4. Factorize:

   14p + 21q

5. Solve using the distributive property:

   5(2x – 3) + 4(x + 1)

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The distributive property is a powerful mathematical tool that simplifies calculations and helps in problem-solving. It is widely used in algebra and everyday life. By practicing the questions provided students can gain a solid understanding of this property and perform well in their Class 7 math exams. Keep practicing and applying this concept to become more confident in mathematics!