# NCERT Class 7 Mathematics Chapter 6 Number Play: Summary, Concepts, and Revision Notes | SwaVid This chapter, 'Number Play', introduces students to the fascinating world of numbers beyond simple arithmetic. It explores the general form of numbers,... Canonical: https://swavid.com/maths/class/7/chapter/number-play Source: https://swavid.com/maths/class/7/chapter/number-play # Number Play ## Concepts in this chapter ## The ideas this chapter keeps returning to ## Where this chapter usually trips people up ## Find the gaps before this chapter finds them for you. ## Related chapters ### Numbers in General Form Chapter 6 · Class 7 Mathematics This chapter, 'Number Play', introduces students to the fascinating world of numbers beyond simple arithmetic. It explores the general form of numbers, using letters to represent digits, and delves into intriguing number games. A significant part of the chapter is dedicated to understanding and applying various divisibility rules, which are fundamental for number theory and mental mathematics. Your study route Key topics Any two-digit number 'ab' can be written as 10a + b, where 'a' is the tens digit and 'b' is the units digit. Similarly, a three-digit number 'abc' can be written as 100a + 10b + c. This algebraic representation helps in understanding number properties. Example 25 = 10 x 2 + 5, 132 = 100 x 1 + 10 x 3 + 2 Watch out Confusing 'ab' as a product (a multiplied by b) instead of a two-digit number (10a + b). Any two-digit number 'ab' can be written as 10a + b, where 'a' is the tens digit and 'b' is the units digit. Similarly, a three-digit number 'abc' can be written as 100a + 10b + c. This algebraic representation helps in understanding number properties. Tap the card for an example Example 25 = 10 x 2 + 5, 132 = 100 x 1 + 10 x 3 + 2 Why it matters This forms the basis for understanding number properties algebraically, which is crucial for solving number puzzles and proving divisibility rules. It connects arithmetic with algebra. Watch out Confusing 'ab' as a product (a multiplied by b) instead of a two-digit number (10a + b). Ask at home Ask the child to write a few two-digit and three-digit numbers in their general form, for example, 73 as 10x7+3 or 458 as 100x4+10x5+8. Chapter 6, 'Number Play', from NCERT Class 7 Ganita Prakash, focuses on understanding the structure and properties of numbers. It begins by expressing two-digit and three-digit numbers in their general form, like 10a + b or 100a + 10b + c, which helps in algebraic manipulation. The chapter then introduces engaging 'games with numbers', demonstrating patterns that emerge when digits are reversed and numbers are added or subtracted. These games reveal interesting properties related to divisibility. A key section involves solving puzzles where letters stand for digits, requiring logical reasoning and basic arithmetic. Finally, the chapter comprehensively covers divisibility tests for 2, 3, 5, 9, and 10, explaining the underlying principles. This knowledge enhances number sense and problem-solving skills. Chapter summary Chapter 6, 'Number Play', from NCERT Class 7 Ganita Prakash, focuses on understanding the structure and properties of numbers. It begins by expressing two-digit and three-digit numbers in their general form, like 10a + b or 100a + 10b + c, which helps in algebraic manipulation. The chapter then introduces engaging 'games with numbers', demonstrating patterns that emerge when digits are reversed and numbers are added or subtracted. These games reveal interesting properties related to divisibility. A key section involves solving puzzles where letters stand for digits, requiring logical reasoning and basic arithmetic. Finally, the chapter comprehensively covers divisibility tests for 2, 3, 5, 9, and 10, explaining the underlying principles. This knowledge enhances number sense and problem-solving skills. What you should learn Keep these close Numbers like 'ab' can be written in general form as 10a + b. Numbers like 'abc' can be written in general form as 100a + 10b + c. Adding a two-digit number and its reverse results in a sum divisible by 11. Subtracting a two-digit number and its reverse results in a difference divisible by 9. Subtracting a three-digit number and its reverse (first digit > last digit) results in a difference divisible by 99. The sum of three numbers formed by cyclically permuting three distinct digits is always divisible by 3, 37, and 111. In letter puzzles, each letter represents a unique digit, and the first digit of a number cannot be zero. A number is divisible by 10 if its unit digit is 0. A number is divisible by 5 if its unit digit is 0 or 5. A number is divisible by 2 if its unit digit is 0, 2, 4, 6, or 8. A number is divisible by 9 if the sum of its digits is divisible by 9. A number is divisible by 3 if the sum of its digits is divisible by 3. Common confusions It is easy to think "ab" means "a multiplied by b" in the context of number play. The clearer idea In this chapter, when 'ab' represents a number, it means 10a + b, where 'a' and 'b' are digits. The product is written as a x b or ab with a dot. It is easy to think The first digit of a number in letter puzzles can be zero (e.g., A=0 in 'AB'). The clearer idea The first digit of any number (like A in AB or ABC) cannot be zero, as it would change the number of digits. For example, 05 is not a two-digit number; it's 5. It is easy to think If a number is divisible by 3, it must also be divisible by 9. The clearer idea Divisibility by 3 only requires the sum of digits to be divisible by 3. Divisibility by 9 requires the sum of digits to be divisible by 9. For example, 12 (sum=3) is divisible by 3 but not by 9. It is easy to think Divisibility rules are just tricks without mathematical reasoning. The clearer idea The chapter explains the algebraic basis for each divisibility rule, showing they are derived from the general form of numbers and place value, not arbitrary tricks. Before you push ahead Most stuck chapters trace back to one earlier idea. Check the prerequisites first, or let SwaVid adapt this chapter to the way your child learns. Keep exploring Class 7 Source - Express two-digit and three-digit numbers in their general form using variables. - Identify and explain patterns arising from reversing digits of numbers. - Solve number puzzles where letters represent unknown digits. - Apply divisibility rules for 2, 3, 5, 9, and 10 to determine if a number is divisible without actual division. - Develop logical reasoning and problem-solving skills through number-based activities. - Express two-digit and three-digit numbers in their general form using variables. - Identify and explain patterns arising from reversing digits of numbers. - Solve number puzzles where letters represent unknown digits. - Apply divisibility rules for 2, 3, 5, 9, and 10 to determine if a number is divisible without actual division. - Develop logical reasoning and problem-solving skills through number-based activities. - NCERT Class 7 Mathematics textbook: Ganita Prakash : Chapter 6: Number Play ## Key Links - [NCERT Mathematics](https://swavid.com/maths) - [Class 7](https://swavid.com/maths/class/7) - [Start with concepts](https://swavid.com/maths/class/7/chapter/number-play) - [Check a prerequisite](https://swavid.com/learning-debt-identifier) - [Concepts](https://swavid.com/maths/class/7/chapter/number-play) - [Practice](https://swavid.com/maths/class/7/chapter/number-play/practice-questions) - [NCERT Solutions](https://swavid.com/maths/class/7/chapter/number-play/ncert-solutions) - [Find the gaps before this chapter](https://swavid.com/learning-debt-identifier) - [Learn this chapter adapted to you](https://swavid.com/learning-style-test) - [Previous chapter 5 . Parallel and Intersecting Lines](https://swavid.com/maths/class/7/chapter/parallel-and-intersecting-lines) - [Next chapter 7 . A Tale of Three Intersecting Lines](https://swavid.com/maths/class/7/chapter/a-tale-of-three-intersecting-lines) - [All Class 7 chapters](https://swavid.com/maths/class/7) - [5 Parallel and Intersecting Lines Intersecting Lines and Angles Formed · Transversal and its Angles Open chapter](https://swavid.com/maths/class/7/chapter/parallel-and-intersecting-lines) - [7 A Tale of Three Intersecting Lines Complementary and Supplementary Angles · Adjacent Angles and Linear Pair Open chapter](https://swavid.com/maths/class/7/chapter/a-tale-of-three-intersecting-lines) - [4 Expressions using Letter-Numbers Variables and Constants · What is an Expression? Open chapter](https://swavid.com/maths/class/7/chapter/expressions-using-letter-numbers) - [NCERT Class 7 Mathematics textbook: Ganita Prakash](https://ncert.nic.in/textbook/pdf/gegp106.pdf)