# NCERT Class 8 Mathematics Chapter 5 Number Play: Summary, Concepts, and Revision Notes | SwaVid

Chapter 5, "Number Play," from the NCERT Class 8 Mathematics textbook "Ganita Prakash" introduces students to the fascinating world of numbers beyond ba...

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# 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 5 · Class 8 Mathematics

Chapter 5, "Number Play," from the NCERT Class 8 Mathematics textbook "Ganita Prakash" introduces students to the fascinating world of numbers beyond basic arithmetic. It encourages a deeper understanding of number properties by representing them in a general form, exploring mathematical games, solving digit puzzles, and mastering various divisibility rules. This chapter builds a strong foundation for algebraic thinking and logical reasoning.

Your study route

Key topics

This section teaches how to represent two-digit and three-digit numbers using variables for their digits. For example, a two-digit number 'ab' is written as 10a + b, where 'a' is the tens digit and 'b' is the units digit. Similarly, a three-digit number 'abc' is 100a + 10b + c.

Example

A two-digit number can be written as 10a + b, where 'a' is the tens digit and 'b' is the units digit. For example, 52 = 10 × 5 + 2.

Watch out

Students often confuse 'ab' as a product (a multiplied by b) instead of representing a two-digit number (10a + b).

This section teaches how to represent two-digit and three-digit numbers using variables for their digits. For example, a two-digit number 'ab' is written as 10a + b, where 'a' is the tens digit and 'b' is the units digit. Similarly, a three-digit number 'abc' is 100a + 10b + c.

Tap the card for an example

Example

A two-digit number can be written as 10a + b, where 'a' is the tens digit and 'b' is the units digit. For example, 52 = 10 × 5 + 2.

Why it matters

Understanding the general form is crucial as it allows us to analyze number properties algebraically, which is the foundation for solving number puzzles and proving divisibility rules.

Watch out

Students often confuse 'ab' as a product (a multiplied by b) instead of representing a two-digit number (10a + b).

Ask at home

Ask your child to write numbers like 67 or 245 in their general form and explain what each variable (a, b, c) represents in terms of place value.

This chapter delves into the structure of numbers, starting with their general form (e.g., 10a+b for a two-digit number). It then explores intriguing number games, such as those involving reversing digits of two-digit and three-digit numbers, revealing consistent patterns of divisibility by 9, 11, and 99. Students learn to solve puzzles where letters represent unique digits, applying logical deduction and arithmetic principles. A significant portion of the chapter is dedicated to understanding and applying divisibility rules for 2, 3, 4, 5, 8, 9, 10, and 11. These rules provide quick methods to determine if a number is divisible by another without performing long division, enhancing number sense and problem-solving skills. The chapter emphasizes the power of algebraic representation in uncovering numerical properties.

Chapter summary

This chapter delves into the structure of numbers, starting with their general form (e.g., 10a+b for a two-digit number). It then explores intriguing number games, such as those involving reversing digits of two-digit and three-digit numbers, revealing consistent patterns of divisibility by 9, 11, and 99. Students learn to solve puzzles where letters represent unique digits, applying logical deduction and arithmetic principles. A significant portion of the chapter is dedicated to understanding and applying divisibility rules for 2, 3, 4, 5, 8, 9, 10, and 11. These rules provide quick methods to determine if a number is divisible by another without performing long division, enhancing number sense and problem-solving skills. The chapter emphasizes the power of algebraic representation in uncovering numerical properties.

What you should learn

Keep these close

A two-digit number 'ab' is represented as 10a + b.

A three-digit number 'abc' is represented as 100a + 10b + c.

The sum of a two-digit number and its reverse is always divisible by 11.

The difference between a two-digit number and its reverse is always divisible by 9.

The difference between a three-digit number and its reverse is always divisible by 99.

In letter puzzles, each letter represents a unique digit (0-9), and the first digit of a number cannot be 0.

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 3 or 9 if the sum of its digits is divisible by 3 or 9 respectively.

A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

A number is divisible by 11 if the difference between the sum of digits at odd places (from the right) and the sum of digits at even places (from the right) is 0 or a multiple of 11.

Common confusions

It is easy to think

The letters in a number puzzle (e.g., A in 'A + A = BA') can represent any digit, even if they are the same letter in different places or different letters representing the same digit.

The clearer idea

Each letter in a number puzzle represents a unique digit from 0 to 9. Also, the first digit of any number (like A in AB) cannot be 0. For example, if A=5, then A must be 5 everywhere it appears in that puzzle.

It is easy to think

To check divisibility by 3 or 9, I just need to look at the last digit, similar to rules for 2, 5, or 10.

The clearer idea

Divisibility by 3 or 9 requires summing all the digits of the number. If this sum is divisible by 3 (or 9), then the original number is divisible by 3 (or 9). The unit digit alone is not sufficient for these rules.

It is easy to think

For the divisibility rule of 11, I can sum digits from left to right, or just sum alternate digits without considering their position (odd/even place from right).

The clearer idea

For divisibility by 11, you must find the difference between the sum of digits at odd places (1st, 3rd, 5th from the RIGHT) and the sum of digits at even places (2nd, 4th, 6th from the RIGHT). The order and alternating nature are crucial for the rule to work correctly.

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 8

Source

- Express two-digit and three-digit numbers in their general form using variables.
- Understand and explain the mathematical basis behind number games involving reversing digits.
- Solve puzzles where letters represent digits by applying logical reasoning and arithmetic rules.
- Apply divisibility rules for 2, 3, 4, 5, 8, 9, 10, and 11 to check if a number is divisible by another.
- Use divisibility rules to find unknown digits in numbers and solve related problems.
- Express two-digit and three-digit numbers in their general form using variables.
- Understand and explain the mathematical basis behind number games involving reversing digits.
- Solve puzzles where letters represent digits by applying logical reasoning and arithmetic rules.
- Apply divisibility rules for 2, 3, 4, 5, 8, 9, 10, and 11 to check if a number is divisible by another.
- Use divisibility rules to find unknown digits in numbers and solve related problems.
- NCERT Class 8 Mathematics textbook: Ganita Prakash : Chapter 5: Number Play

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- [4 Quadrilaterals Elements of a Quadrilateral · Angle Sum Property of a Quadrilateral Open chapter](https://swavid.com/maths/class/8/chapter/quadrilaterals)
- [6 We Distribute, yet Things Multiply What are Expressions? · Terms, Factors, and Coefficients Open chapter](https://swavid.com/maths/class/8/chapter/we-distribute-yet-things-multiply)
- [3 A Story of Numbers Recalling Number Systems · Properties of Rational Numbers: Closure Open chapter](https://swavid.com/maths/class/8/chapter/a-story-of-numbers)
- [NCERT Class 8 Mathematics textbook: Ganita Prakash](https://ncert.nic.in/textbook/pdf/hegp105.pdf)