Schooling · Class 7 · Mathematics · Number Play · Chapter on a page
CBSE Class 7 · Mathematics · NCERT Ganita Prakash
Number Play: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Palindromic numbers
- Divisibility rules
- Place value
- Reversing digits and comparing the…
- Certain sums and products follow…
- Magic squares
- Number puzzles using missing digits…
- Formulas and facts
- Divisibility by 2
- Divisibility by 3
- Divisibility by 4
- Divisibility by 5
- Divisibility by 6
- Divisibility by 9
- Divisibility by 10
- Worked examples
- Testing divisibility by 9
- Creating a palindrome
- Testing divisibility by 11
- Watch out for
- Adding digits wrongly when testing…
- Forgetting that divisibility by 6…
- Confusing odd-place and even-place…
- Thinking every number becomes a…
- Mixing up "divisible by" and "divides"
What this chapter is about
This chapter is about exploring numbers in fun and interesting ways. You will discover patterns hidden inside numbers, learn tricks to check if a number can be divided by certain divisors, and play with how digits behave when you reverse or rearrange them.
Key ideas
- Palindromic numbers read the same forwards and backwards. Examples: 121, 4554, 78987. You can often create a palindrome by adding a number to its reverse.
- Divisibility rules let you check if a number divides evenly by 2, 3, 4, 5, 6, 9, 10 or 11 without long division. Each rule uses the digits or their sum in a quick test.
- Place value is the value a digit gets from its position. In 5824, the digit 5 stands for 5000 because it is in the thousands place.
- Reversing digits and comparing the original number with its reverse often reveals interesting patterns, especially when you add or subtract them.
- Certain sums and products follow patterns. For instance, the sum of the first few odd numbers is always a perfect square: 1 + 3 + 5 + 7 = 16 = 4².
- Magic squares are grids where every row, column and main diagonal add up to the same total, called the magic sum.
- Number puzzles using missing digits teach logical reasoning and help you practise mental maths.
Formulas and facts to remember
- Divisibility by 2: The number ends in 0, 2, 4, 6 or 8.
- Divisibility by 3: The sum of all digits is divisible by 3.
- Divisibility by 4: The last two digits form a number divisible by 4.
- Divisibility by 5: The number ends in 0 or 5.
- Divisibility by 6: The number is divisible by both 2 and 3.
- Divisibility by 9: The sum of all digits is divisible by 9.
- Divisibility by 10: The number ends in 0.
- Divisibility by 11: The difference between the sum of digits in odd places and the sum of digits in even places is 0 or a multiple of 11.
- Sum of first n odd numbers: 1 + 3 + 5 + … (n terms) = n².
Common mistakes
- Adding digits wrongly when testing divisibility → Work carefully; double-check the addition.
- Forgetting that divisibility by 6 needs both the 2-test and the 3-test → Always check both rules.
- Confusing odd-place and even-place digits for the 11-rule → Count positions from the right, starting at 1.
- Thinking every number becomes a palindrome in one step → Some need several reverse-and-add steps.
- Mixing up "divisible by" and "divides" → 12 is divisible by 3 means 3 goes into 12 evenly.
Quick revision
- A number is divisible by 9 when its digit-sum is divisible by 9.
- Palindromic numbers read the same forwards and backwards.
- Divisibility by 6 = divisible by 2 AND divisible by 3.
- Sum of first n odd numbers = n².
- Use the difference of alternate-position sums for the 11-rule.