NCERT Solutions for Class 6 Maths Chapter 2 Whole Numbers Exercise 2.3

Understanding the Magic of Patterns & Properties

Whole numbers are filled with beautiful rules and patterns that make calculations simple and elegant. In Exercise 2.3 of Class 6 NCERT Maths, we focus on three main mathematical keys: the behavior of Zero (0), the behavior of One (1), and visual number patterns. For instance, did you know that multiplying any whole number by 0 always results in 0, but dividing a number by 0 is completely undefined? Similarly, if the product of two whole numbers is 1, both numbers must be 1. We also use the distributive property of multiplication over addition to split numbers like 101 into (100 + 1) to multiply without doing painful long calculations. These are not just shortcuts; they form the foundation of algebraic thinking!

How to Use the Distributive Property for Fast Calculations

1. Identify the Friendly Number — Look for the number in the multiplication that is closest to a multiple of 10, 100, or 1000 (for example, 101, 1001, or 25).
2. Split the Number — Rewrite this friendly number as an addition or subtraction of simpler numbers. For example, rewrite 101 as (100 + 1) or 1001 as (1000 + 1).
3. Distribute the Multiplier — Apply the distributive property: a × (b + c) = (a × b) + (a × c). Multiply the outside number with both numbers inside the bracket separately.
4. Calculate and Combine — Solve the two simple multiplications and add (or subtract) the results to get your final answer instantly.

Crucial Exam Tip: Zero vs. One Rules

Many students make mistakes when working with zero and one. Remember these rules:

1. Division by Zero: Any number divided by zero (e.g., 5 ÷ 0) is not defined. However, zero divided by any non-zero number (e.g., 0 ÷ 5) is always 0.
2. Product of Zero: If a × b = 0, then either a = 0, b = 0, or both are 0.
3. Product of One: If a × b = 1, then both a and b must be equal to 1 (assuming they are whole numbers). One of them alone being 1 is not enough unless the other is also 1!

Practice Questions with Solutions

• Q: Which of the following will not represent zero? (a) 1 + 0 (b) 0 × 0 (c) 0 / 2 (d) (10 - 10) / 2 A: Step 1: Let us evaluate each option one by one. Step 2: (a) 1 + 0 = 1. This does not equal zero. Step 3: (b) 0 × 0 = 0. This equals zero. Step 4: (c) 0 / 2 = 0. This equals zero. Step 5: (d) (10 - 10) / 2 = 0 / 2 = 0. This equals zero. Final answer: Option (a) 1 + 0 does not represent zero.
• Q: If the product of two whole numbers is zero, can we say that one or both of them will be zero? Justify with examples. A: Step 1: Recall the multiplicative property of zero. If we multiply any number by zero, the result is zero. Step 2: Example of one number being zero: 5 × 0 = 0, or 0 × 12 = 0. Here, only one number is zero, and the product is zero. Step 3: Example of both numbers being zero: 0 × 0 = 0. Here, both numbers are zero. Step 4: Conclusion: Yes, if the product is zero, then at least one of the numbers, or both of them, must be zero. Final answer: Yes, either one or both numbers must be zero.
• Q: Find the value of 5437 × 1001 using the distributive property. A: Step 1: Write the expression: 5437 × 1001. Step 2: Split 1001 into friendly numbers: 1001 = (1000 + 1). Step 3: Apply the distributive law: 5437 × (1000 + 1) = (5437 × 1000) + (5437 × 1). Step 4: Calculate the individual products: 5437 × 1000 = 5437000, and 5437 × 1 = 5437. Step 5: Add the products: 5437000 + 5437 = 5442437. Final answer: 54,42,437
• Q: Study the pattern: 1 × 8 + 1 = 9 12 × 8 + 2 = 98 123 × 8 + 3 = 987 Write the next step. A: Step 1: Analyze the structure of the left side. The numbers being multiplied by 8 are increasing their digits: 1, then 12, then 123. The next number should be 1234. Step 2: Analyze the added number: 1, 2, 3. The next added number should be 4. Step 3: Form the left side of the next equation: 1234 × 8 + 4. Step 4: Analyze the right side (the answer): 9, 98, 987. The digits are decreasing sequentially. The next sequence should be 9876. Final answer: The next step is 1234 × 8 + 4 = 9876.

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