NCERT Solutions for Class 8th Maths Chapter 6 Algebra Play
Updated on 2026-09-19
About this chapter
A letter-number stands for every possible starting value at once . That is why one line of algebra settles a trick that no amount of trying out numbers can ever settle — testing 100 starting numbers only tests 100 of them. Solving an equation means doing the same thing to both sides — adding, subtracting, multiplying or dividing by the same amount. The two sides name one number, so an operation applied to both keeps them naming one number. That is the whole justification for every step. Modelling a word situation means naming the unknown, then translating each sentence into an equation about it. “The mother is 5 times her daughter’s age” becomes m = 5d; “in 6 years” becomes d + 6 and m + 6. In a number pyramid each box is the sum of the two below it. Read forwards it is addition; read back
- .2 Thinking about ‘Think of a Number’ Tricks
- .3 Number Pyramids
- .4 Fun with Grids
- .5 The Largest Product
- .6 Decoding Divisibility Tricks
Quick revision
| Idea | What the algebra shows | Key expression | Where it appears |
|---|---|---|---|
| ‘Think of a Number’ trick | Every step acts on x, so the x-terms cancel and a constant survives | 2x + 4, halved, minus x = 2 | Page 135 |
| Date trick | ×5, ×4, ×5 multiplies the month by 100, so month and day sit in separate place-value slots | Answer = 100M + 165 + D | Pages 136 – 137 |
| Number pyramid | Each box is the sum of the two below; read backwards, a missing box is a subtraction | 10 – 4 = 6, 4 – 1 = 3 | Page 138 |
| Pyramid in letter-numbers | When no box has both neighbours known, name the unknowns and solve | 20 + 2c = 60 → c = 20 | Pages 138 – 139 |
| Top of a pyramid | A bottom entry is counted once for each path up to the top | 3 rows: a + 2b + c; 4 rows: a + 3b + 3c + d | Page 140 |
| Virahāṅka-Fibonacci pyramid | Fj + Fj+1 = Fj+2, so each row up starts two places later in the sequence | Top of n rows = the (2n – 1)th V-F number | Page 140 |
| Calendar 2 × 2 grid | A week is 7 days, so the box below a date holds 7 more | a + (a+1) + (a+7) + (a+8) = 4a + 16 | Page 141 |
| Algebra grid | Each row is one equation; combining rows removes a shape | 2■ + ● = 27, 2● + ■ = 21 → ■ = 11, ● = 5 | Page 142 |
| Largest product | Largest digit as multiplier, other two in decreasing order | For p < q < r the winner is (10q + p) × r | Pages 142 – 144 |
| Reversing two digits | 10b + a minus 10a + b leaves nine of each digit | Difference = 9(b – a); Sum = 11(a + b) | Pages 144 – 145 |
| Cycling three digits | Each digit visits the hundreds, tens and units place exactly once | abc + bca + cab = 111(a + b + c) | Page 145 |
| Repeating a block | Writing abc twice multiplies it by 1001 | 1001 = 7 × 11 × 13 | Page 145 |
Exercises
- .1 Algebra Play / 6.2 Thinking about ‘Think of a Number’ Tricks — In-text Questions Page 1356
- .2 Thinking about ‘Think of a Number’ Tricks — In-text Questions Page 1366
- .2 Thinking about ‘Think of a Number’ Tricks — In-text Questions Page 1376
- .3 Number Pyramids — In-text Questions Page 1386
- .3 Number Pyramids — In-text Questions Page 1396
- .3 Number Pyramids — In-text Question Page 1406
- .3 Number Pyramids — Figure it Out Page 1406
- .4 Fun with Grids — In-text Questions Page 1416
- .4 Fun with Grids — In-text Questions Page 1426
- .5 The Largest Product — In-text Questions Page 142 – 1436
- .5 The Largest Product — Figure it Out Page 1446
- .6 Decoding Divisibility Tricks — In-text Questions Page 1456
- .6 Decoding Divisibility Tricks — Figure it Out Page 145 – 1476