NCERT Solutions for Class 8 Mathematics Ganita Prakash Part 1 Chapter 6
NCERT solutions for Class 8 Mathematics Chapter We Distribute, Yet Things Multiply – complete answers & explanations
In this chapter of Class 8 Mathematics, titled "We Distribute, Yet Things Multiply," students are introduced to the distributive property of multiplication over addition. The chapter explores various multiplication patterns and how algebraic expressions can be simplified using this property. It emphasizes the importance of understanding distributivity, which helps in solving complex problems more efficiently. By grasping these concepts, students can simplify algebraic expressions, make faster calculations, and apply these techniques to real-world problems. Download the worksheet and practice alongside solutions for better clarity. Book a free trial now to get expert guidance.
What this NCERT chapter covers?
1. Introduction to the distributive property
of multiplication over addition.
2. Use of distributive property to find how products change when one or both numbers in a product are increased or decreased by a certain value.
3. Special cases like the square of the sum/difference of two numbers and the use of distributive property to simplify complex expressions.
4. Investigating patterns in mathematics, including sum of squares and differences of squares, using algebraic methods.
5. Fast multiplication techniques using distributive properties, especially when multiplying by numbers like 11, 101, and 1001.
How to use these NCERT solutions?
1. Students should attempt each question
in the worksheet first before checking the solutions.
2. After attempting, use the answers to verify their solutions and understand the correct approach.
3. Parents and teachers can guide students by explaining concepts such as distributivity and helping them simplify algebraic expressions.
4. The solutions follow the order of the worksheet exactly, making it easy for students to cross-check their work.
Important tips & tricks for students
1. Avoid common mistakes like misapplying the distributive property or forgetting to expand all terms in an expression.
2. Focus on the correct order of operations when using the distributive property for expansion.
3. When multiplying expressions, ensure that you distribute each term in the first set of parentheses to every term in the second set.
4. Pay attention to the signs when expanding expressions with both positive and negative terms.
5. For multiplication involving large numbers, break down the numbers using distributive properties for easier calculation.
NCERT solutions – complete answer key
6.1 Some Properties of Multiplication
1. How much does the product increase if the first number (23) is increased by 1?
Answer: The product increases by 27.
2. What if the second number (27) is increased by 1?
Answer: The product increases by 23.
3. How about when both numbers are increased by 1?
Answer: The product increases by 51.
6.2 Special Cases of the Distributive Property
1. Expand (60 + 5)² using the distributive property.
Answer: (60 + 5)² = 60² + 2×60×5 + 5² = 3600 + 600 + 25 = 4225.
2. Use distributive property to expand (a + b)².
Answer: (a + b)² = a² + 2ab + b².
6.3 Mind the Mistake, Mend the Mistake
1. (–3p) × (–5p + 2q) = 3p² – 6pq.
2. 2 × (x – 1) + 3(x + 4) = 2x – 2 + 3x + 12 = 5x + 10.
6.4 This Way or That Way, All Ways Lead to the Bay
1. For the number of circles in Step 15, use the formula k² + 2k where k = 15.
Answer: The number of circles in Step 15 is 15² + 2×15 = 225 + 30 = 255.
Why NCERT solutions help students?
NCERT solutions provide students with clear and reliable answers that are perfectly aligned with the prescribed textbook. These solutions help students prepare for exams by building concept clarity and reinforcing key mathematical principles. Using these solutions, students gain confidence in their problem-solving abilities.
Help your child build strong Mathematics fundamentals with expert-guided learning support.