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Class 8 Algebra Play: cheat sheet
CBSE Mathematics. Use letters to explain number tricks and patterns: the 1089 trick, reversed digits, calendar squares and the nth term of a pattern.
Key ideas
- Write the unknown number as a letter and follow every step of the trick; what is left shows why it works.
- A two-digit number with digits a and b is 10a + b, not ab.
- The 1089 trick: take a three-digit number whose first and last digits differ by at least 2, subtract its reverse, then add the result to its own reverse: the answer is always 1089.
- In a 3 × 3 square of calendar dates with middle date m, the dates are m ± 1, m ± 6, m ± 7 and m ± 8.
- A pattern that grows by the same amount each step has nth term an + b.
Remember
| Two-digit number | 10a + b |
| Number and its reverse | (10a + b) + (10b + a) = 11(a + b); difference = 9(a − b) |
| Calendar 3 × 3 square | sum of all nine = 9m; each diagonal = 3m |
| Growing pattern | nth term = (step) × n + (first term − step) |
Watch out
- Writing a two-digit number as a × b or ab.
- Testing a trick with one example and calling it proved.
- Losing a minus sign when subtracting the reversed number.
Worked example
In a 3 × 3 square of dates on a calendar the middle date is 17. Find the sum of each diagonal and explain why they are equal.
Working: (m − 8) + m + (m + 8) = 3m and (m − 6) + m + (m + 6) = 3m
Answer: 51 each
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