Revision Notes for Class 8 Maths Chapter 13: Algebra Play

Condensed revision notes for Class 8 Maths Chapter 13: Algebra Play – Ganita Prakash textbook. These Class 8 Mathematics Chapter 13 notes are ideal for quick revision just before exams.

Last Updated: September 23, 2026

• “Think of a number” tricks: represent the chosen number as x; after multiply/add/divide steps, the x-terms cancel out, leaving a fixed constant — this is why the trick always “works” regardless of the starting number.
• Number pyramid rule: each cell = sum of the two cells directly below it (same rule as Pascal’s triangle).
• 3-row pyramid with bottom a,b,c: top = a+2b+c. 4-row pyramid with bottom a,b,c,d: top = a+3b+3c+d (coefficients 1,3,3,1 from Pascal’s triangle).
• Virahanka-Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, … (each term = sum of previous two). If the first n terms form the bottom row of an n-row pyramid, the top is always the (2n−1)th term of the same sequence.
• Grid sums: for a 3×3 block of consecutive-style numbers, the total = 9 × the centre value. For a straight 1×3 strip, the total = 3 × the middle value.
• Largest product (3 digits, one 2-digit number and one 1-digit multiplier): put the single largest digit as the multiplier, and arrange the remaining two digits in descending order for the 2-digit number.
• Divisibility tricks: two-digit number minus its reverse is always divisible by 9; two-digit number plus its reverse is always divisible by 11; a 3-digit number plus its two cyclic rotations is always divisible by 37 (and by 3); a 3-digit number repeated to form a 6-digit number is always divisible by 1001 = 7 × 11 × 13.
• Word problems: assign letters to unknowns, translate each sentence into an equation, and solve simultaneously when there are two unknowns (ages, cows, horses/hens, shop profit problems).

More on this chapter: NCERT Solutions for Class 8 Maths Chapter 13 | Extra Questions for Class 8 Maths Chapter 13 | Class 8 Maths Book | Formulas Handbook

Frequently Asked Questions

What is the difference between an algebraic expression and an algebraic equation?
An algebraic expression is a combination of variables, constants, and operations without an equals sign, such as 2x plus 3, while an algebraic equation states that two expressions are equal, such as 2x plus 3 equals 7.

Why are algebraic identities useful for simplifying calculations?
Algebraic identities are equations that hold true for all values of the variables, so recognising a standard pattern, such as the square of a sum, allows expressions to be expanded or factorised quickly without repeating full multiplication.

Written by Satish

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