Class 8 Maths - GUJARAT
Number Play
The chapter 'Number Play' in Class 8 Mathematics for Gujarat (GSEB) introduces students to fascinating patterns and puzzles involving numbers. It focuses on writing numbers in generalized forms using letters to represent digits, understanding divisibility tests for 2, 3, 5, 9, and 10, and solving engaging cryptarithms where letters stand for unknown digits. This chapter helps build a strong foundation in algebraic thinking and logical reasoning, which are essential for solving higher-level mathematical problems. It frequently appears in board exams through short objective questions, puzzles, and 2-to-3-mark application-based problems.
Start Learning FreeKey Concepts
Generalized Form of a 2-digit Number
Any 2-digit number consisting of digits 'a' (tens place) and 'b' (units place) can be written in generalized form as 10a + b.
Generalized Form of a 3-digit Number
A 3-digit number with digits 'a', 'b', and 'c' at the hundreds, tens, and units places respectively is written as 100a + 10b + c.
Reversing Digits of a Number
When the digits of a 2-digit number 10a + b are reversed, the new number becomes 10b + a, and the sum or difference of these numbers shows interesting mathematical properties.
Divisibility by 9 and 3
A number is divisible by 9 (or 3) if the sum of its digits is a multiple of 9 (or 3).
Cryptarithms (Number Puzzles)
Puzzles where arithmetic operations are performed using letters instead of digits, solved using logic and properties of addition and multiplication.
Important Formulas
Board Exam Info
In the Gujarat (GSEB) Class 8 Mathematics examinations, 'Number Play' typically carries around 3 to 5 marks. Questions usually include fill-in-the-blanks, true or false, finding unknown values in divisibility rules, and solving letter-arithmetic puzzles (cryptarithms).
Frequently Asked Questions
What is the difference between normal notation and generalized form?
Normal notation writes a number directly like 45, while generalized form shows its place value breakdown like (10 x 4) + 5.
How do we solve letter puzzles or cryptarithms?
You solve them by testing single-digit values from 0 to 9 for each letter, keeping basic addition and multiplication carry-over rules in mind.
Why is the sum of a 2-digit number and its reverse always divisible by 11?
Because the sum simplifies to 11(a + b), which contains 11 as a direct factor regardless of the digits 'a' and 'b'.
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