Class 7 Maths - GUJARAT
Number Play
The Chapter 'Number Play' in Class 7 Mathematics under the Gujarat Secondary and Higher Secondary Education Board (GSEB) introduces students to the fascinating world of numbers through puzzles, riddles, and mathematical patterns. It helps students understand the properties of numbers, divisibility rules, and how numbers can be represented in generalized forms using digits like 'a' and 'b'. This chapter builds a strong foundation in logical reasoning and algebra, making it very important for board exam preparation as it forms the basis for higher-level problem-solving and puzzle-based questions.
Start Learning FreeKey Concepts
Generalized Form of Numbers
Writing a two-digit number like ab as (10 × a) + b, where 'a' is the tens digit and 'b' is the units digit.
Reversing Digits
When the digits of a two-digit number ab are reversed, the new number becomes ba, which is written as (10 × b) + 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 11
A number is divisible by 11 if the difference between the sum of its digits in odd places and even places is either 0 or a multiple of 11.
Number Puzzles and Cryptarithms
Puzzles where letters take the place of digits in arithmetic operations, requiring logical deduction to find the correct values.
Important Formulas
Board Exam Info
In the Gujarat (GSEB) Class 7 Mathematics examinations, this chapter typically carries around 4 to 6 marks. Common question types include short-answer questions based on divisibility tests, finding unknown digits in addition or multiplication puzzles (cryptarithms), and word problems involving the generalized form of two-digit and three-digit numbers.
Frequently Asked Questions
Why do we write numbers in generalized form like 10a + b?
Writing numbers in generalized form helps us understand their algebraic structure and makes it easier to solve number puzzles and prove divisibility rules.
How do I solve letter puzzles like A + B = C?
You solve them by testing single digits from 0 to 9 logically, keeping in mind rules like each letter must stand for a unique digit and the first digit of a number cannot be zero.
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.
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