Expressions Using Letter-Numbers
Class 7 Mathematics · Ganita Prakash Part 1 · Chapter 4
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- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
Summary
This chapter introduces algebra by using letters to stand for numbers. A letter such as \(a\) or \(s\) used to represent a number is called a letter-number (a variable). For example, if Aftab's age is \(a\) and Shabnam is 3 years older, then Shabnam's age is \(s = a + 3\); substituting \(a = 23\) gives \(s = 26\). Expressions containing letter-numbers, like \(a + 3\) or \(2n - 1\), are called algebraic expressions, and replacing the letter by a number to compute a value is called substitution. You learn to translate word relationships into expressions, to read patterns in sequences (the \(n\)th multiple of 4 is \(4n\); the \(n\)th even number is \(2n\); the \(n\)th odd number is \(2n-1\)), and to use these generalisations to explain why a pattern holds. The power of letter-numbers is that one short expression captures infinitely many cases at once, making it possible both to predict values and to justify mathematical claims — a major step beyond arithmetic.