Class 7 Maths - UP
Number Play
The chapter 'Number Play' in Class 7 Mathematics helps students explore the fascinating world of numbers through puzzles, patterns, and mathematical games. It focuses on general forms of two-digit and three-digit numbers, number puzzles, and divisibility tests by 2, 3, 5, 9, and 10. For UP Board students, this chapter is crucial as it builds strong mental math skills, logical reasoning, and foundation for algebra. Questions from this chapter frequently appear in board examinations as short-answer and puzzle-based problems, testing the student's ability to manipulate algebraic representations of numbers.
Start Learning FreeKey Concepts
General Form of Numbers
Any two-digit number 'ab' can be written in its expanded general form as 10a + b, where 'a' is the ten's digit and 'b' is the unit's 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 2, 5, and 10
A number is divisible by 2 if its unit digit is even, by 5 if its unit digit is 0 or 5, and by 10 if its unit digit is 0.
Divisibility by 3 and 9
A number is divisible by 3 or 9 if the sum of all its digits is a multiple of 3 or 9 respectively.
Number Puzzles
Logical puzzles where letters or symbols replace digits in arithmetic operations, solved using basic algebraic properties and number facts.
Important Formulas
Board Exam Info
In UP Board Class 7 Mathematics examinations, this chapter typically carries around 4 to 6 marks. Common question types include writing numbers in general form, proving divisibility rules, solving letter-number puzzles (cryptarithms), and finding the sum or difference of reversed numbers.
Frequently Asked Questions
Why do we write numbers like 10a + b instead of just 'ab'?
In algebra, writing 'ab' means 'a multiplied by b'. To represent a two-digit number where 'a' is the ten's digit and 'b' is the unit's digit, we must write it in expanded form as 10a + b.
How do I solve letter puzzles where letters represent unknown digits?
Look at the units column first to find clues about possible digit values, and use trial and method keeping in mind that each letter represents a single digit from 0 to 9.
Is the sum of a two-digit number and its reverse always divisible by 11?
Yes, because the sum equals 11(a + b), which is always a multiple of 11 for any digits 'a' and 'b'.
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