Class 8 Maths - PUNJAB
Number Play
The Chapter 'Number Play' in Class 8 Mathematics under the Punjab School Education Board (PSEB) introduces students to fascinating patterns and puzzles involving numbers. It focuses on writing numbers in generalized form using digits and variables, understanding divisibility tests for 2, 3, 5, 9, and 10, and solving stimulating cryptarithmetic puzzles where letters replace digits in arithmetic operations. This chapter strengthens logical reasoning, mental math skills, and algebraic thinking, laying a strong foundation for higher classes. Scoring well in this chapter is crucial for board exam success as it frequently features in conceptual and short-answer problem sections.
Start Learning FreeKey Concepts
Generalized Form of Numbers
A two-digit number like ab can be expressed in expanded or generalized form as 10a + b, where a is the tens digit and b is the units digit.
Reversing Digits
When the digits of a two-digit number ab (10a + b) are reversed, the new number becomes ba, which is expressed algebraically as 10b + a.
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 respectively.
Divisibility by 10, 5, and 2
A number is divisible by 10 if its units digit is 0, by 5 if its units digit is 0 or 5, and by 2 if it is an even number.
Puzzles with Digits (Cryptarithms)
These are addition or multiplication puzzles where letters represent hidden digits, solved by applying basic arithmetic rules and logical deduction.
Important Formulas
Board Exam Info
In the Punjab (PSEB) Class 8 Mathematics examination, 'Number Play' typically carries around 4 to 6 marks. Common question types include writing numbers in generalized form, finding the sum or difference of reversed numbers, proving divisibility rules, and solving letter-digit puzzle problems.
Frequently Asked Questions
What is the difference between a normal number and its generalized form?
A normal number is written with its face value (e.g., 45), while its generalized form shows the place value of each digit algebraically (e.g., 10(4) + 5).
How do I solve letter puzzles like A + B = C in Number Play?
Look at the units column first to find possible values for single digits (0 to 9) that satisfy the addition or multiplication rule, then test them in the tens column.
Why is the sum of any two-digit number and its reverse always divisible by 11?
Because the algebraic sum simplifies to 11(a + b), which contains 11 as a direct factor regardless of the digits a and b.
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