Class 8 Maths Chapter 6 NCERT Solutions: We Distribute, Yet Things Multiply

Exercise Questions – NCERT Solutions Class 8 Maths Chapter 6 We Distribute, Yet Things Multiply (2025-26)

1. Multiple choice questions.

1. Which of the following statements is true for distributive property?

• (a) $a \times (b + c) = (a \times b) + (a \times c)$
• (b) $a + (b \times c) = (a + b) \times (a + c)$
• (c) $a \times (b - c) = (a - b) \times (a - c)$
• (d) $a \times (b \times c) = (a \times b) + (a \times c)$

Answer: (a) $a \times (b + c) = (a \times b) + (a \times c)$

2. Answer the following questions in about 30 words.

1. What is the distributive property of multiplication over addition? Explain with an example.

Answer: The distributive property of multiplication over addition states that multiplying a number by the sum of two numbers is the same as multiplying it by each addend and then adding the products. For example, $3 \times (2 + 4) = 3 \times 2 + 3 \times 4 = 6 + 12 = 18$.

2. Give one example each to show that multiplication distributes over subtraction also.

Answer: Yes, multiplication distributes over subtraction. For example, $5 \times (7 - 2) = 5 \times 7 - 5 \times 2 = 35 - 10 = 25$.

3. Why is the distributive property important in simplification of expressions?

Answer: The distributive property helps to break down complex expressions into simpler terms, making calculations easier and enabling us to solve problems efficiently, especially when dealing with variables and large numbers.

3. Answer the following questions in about 150 words.

1. Show how the distributive property can help in mental math for calculating $19 \times 57$.

Answer: Using the distributive property, $19 \times 57$ can be rewritten as $(20 - 1) \times 57 = (20 \times 57) - (1 \times 57)$. Now, $20 \times 57 = 1,140$ and $1 \times 57 = 57$. So, $1,140 - 57 = 1,083$. Thus, $19 \times 57 = 1,083$. This method makes calculations easier by breaking the number into simpler parts.

2. A vegetable vendor arranges his vegetables in 5 groups. Each group has 8 carrots, 6 beetroots, and 7 turnips. Write a multiplication expression for the total number of vegetables and solve it using the distributive property.

Answer: Total vegetables in each group are $8 + 6 + 7 = 21$. The expression is $5 \times (8 + 6 + 7)$. By the distributive property: $5 \times 8 + 5 \times 6 + 5 \times 7 = 40 + 30 + 35 = 105$. So, there are 105 vegetables in all.

4. Match the following.

5. Solve the following using the distributive property.

• (a) $13 \times 17$
• (b) $24 \times 99$
• (c) $8 \times 104$

Answer:

• (a) $13 \times 17 = 13 \times (10 + 7) = 130 + 91 = 221$
• (b) $24 \times 99 = 24 \times (100 - 1) = 2,400 - 24 = 2,376$
• (c) $8 \times 104 = 8 \times (100 + 4) = 800 + 32 = 832$

6. Fill in the blanks using the distributive property.

• (a) $12 \times (7 + 3) = (12 \times 7) + (12 \times 3) = 84 + 36 = $120
• (b) $9 \times (15 - 4) = (9 \times 15) - (9 \times 4) = 135 - 36 = $99
• (c) $6 \times (11 + 2 + 7) = (6 \times 11) + (6 \times 2) + (6 \times 7) = 66 + 12 + 42 = $120

Mastering Distributive Property: NCERT Class 8 Maths Chapter 6

Understanding the distributive property in maths is essential for solving complex problems quickly. In Class 8, Chapter 6 – “We Distribute, Yet Things Multiply,” you’ll regularly use this property for efficient calculations and clear conceptual learning.

Practicing NCERT solutions on distributive property boosts your speed and confidence. Focus on breaking down expressions and simplifying multiplication using addition and subtraction. These techniques are important for exams and for developing a strong maths foundation.

For the best results in Class 8 Maths, remember to apply the distributive law whenever you see grouped numbers. Keep practicing exercise-based solutions to sharpen your problem-solving skills and ensure exam success!