Class 8 Maths - UP
Number Play
The chapter 'Number Play' in Class 8 Mathematics introduces students to fascinating patterns and puzzles involving numbers. It builds a strong foundation in algebraic thinking by exploring how numbers can be represented in generalized forms using letters. Students learn the logic behind divisibility tests for 2, 3, 5, 9, and 10, and how to solve fascinating number puzzles and cryptarithms. This chapter is essential for UP Board exams as it sharpens logical reasoning, enhances mental math capabilities, and frequently features in short and long-answer sections, carrying around 4 to 6 marks.
Start Learning FreeKey Concepts
Generalized Form of Numbers
Any two-digit number like 'ab' can be written in expanded algebraic 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 10a + b are reversed, the new number becomes 10b + a, and their sum or difference follows interesting mathematical patterns.
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 11
A number is divisible by 11 if the difference between the sum of its digits at odd places and even places is either 0 or a multiple of 11.
Cryptarithms (Letter Puzzles)
Puzzles where digits are replaced by letters of the alphabet, and students must find which digit each letter represents using basic arithmetic rules.
Important Formulas
Board Exam Info
In the UP Board Class 8 Mathematics examinations, this chapter typically carries about 4 to 6 marks. Common question types include finding unknown digits in addition or multiplication puzzles (cryptarithms), proving divisibility rules using generalized forms, and solving word problems based on reversing the digits of a two-digit number.
Frequently Asked Questions
Why do we write numbers like 10a + b in this chapter?
Writing numbers in generalized form helps us understand their algebraic structure, making it easier to solve puzzles and prove divisibility rules for any unknown number.
What is a cryptarithm?
A cryptarithm is a mathematical puzzle where letters or symbols are used in place of digits, and you have to deduce the original digits based on arithmetic operations.
How can I easily solve questions where digits are reversed?
Always start by writing the original number as 10a + b and the reversed number as 10b + a, then apply the given condition of their sum or difference to form a simple linear equation.
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