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CBSE Class 8 — Notes, Chapters & Practice Quizzes

Every Class 8 chapter, made friendly — notes with pictures, key words, and a quiz for each chapter.

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Mathematics · 14 chapters
Summary, key terms, extra questions with answers and a practice quiz with AI diagnosis for each.

Chapter 5: Algebra PlayClass 8 Mathematics — summary, notes, extra questions & MCQ quiz

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Why does doubling a number, adding \(4\), halving, then subtracting the original give \(2\)?

Summary

Algebra Play uses algebra to explain and invent number tricks and puzzles. Think-of-a-number tricks always land on a fixed value because the chosen number \(x\) cancels out — for example, doubling, adding \(4\), halving and subtracting \(x\) always gives \(2\). A date trick encodes month \(M\) and day \(D\) as \(100M + 165 + D\), so subtracting \(165\) recovers the date. Number pyramids, where each cell is the sum of the two below it, are decoded with letter-numbers: a three-row pyramid has top value \(a + 2b + c\). Algebra grids and calendar tricks (a \(2\times2\) calendar block sums to \(4a + 16\)) are solved by setting up and solving equations. The chapter shows how to make the largest product from given digits by using the largest as the multiplier, and proves divisibility tricks — the difference of a two-digit number and its reverse, \((10a+b)-(10b+a) = 9(b-a)\), is always divisible by \(9\); cycling the digits of \(abc\) yields a sum divisible by \(37\). Word problems on ages, animals and coins are modelled and solved with linear equations.

Think-of-a-number tricksNumber pyramidsAlgebra and calendar gridsLargest productsDivisibility tricks and word problems

Key terms

Think-of-a-number trick
A sequence of operations that always gives a fixed result because the unknown \(x\) cancels out.
Number pyramid
A triangular grid where each number equals the sum of the two directly below it.
Algebra grid
A grid where shapes stand for numbers and each row’s last cell is the sum of the others, solved by equations.
Calendar trick
Using algebra to recover entries of a calendar block from their sum, e.g. a \(2\times2\) block sums to \(4a + 16\).
Divisibility trick
A puzzle whose outcome is always divisible by a number, justified with algebra.
Linear equation
An equation modelling a word problem, solved to find an unknown quantity.

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A sequence of operations that always gives a fixed result because the unknown \(x\) cancels out.
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Practice quiz · Algebra Play

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Algebra Play

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