Master Chapter 4 Class 7 - Expressions using Letter-Numbers (Ganita Prakash) with comprehensive NCERT Solutions, Practice Questions, MCQs, Sample Papers, Case Based Questions, and Video lessons.
Start Learning NowWelcome to Chapter 4, Expressions Using Letter-Numbers, from your Class 7 Maths book, Ganita Prakash.
In the last chapter, we learned the rules for "arithmetic expressions," which are mathematical phrases made of numbers and operations (like 30 + 5 × 4). In this chapter, we take a huge step forward by introducing one of the most powerful ideas in all of mathematics: using letters to represent numbers.
This is the beginning of Algebra.
We start with a simple, real-world idea. Imagine Shabnam is 3 years older than Aftab.
If Aftab is 10, Shabnam is 10 + 3 = 13.
If Aftab is 23, Shabnam is 23 + 3 = 26.
We can describe this relationship for any age by saying:
Shabnam's age = Aftab's age + 3
Instead of writing "Aftab's age" every time, we can use a letter-number as a placeholder. If we let the letter a stand for Aftab's age, the relationship becomes a simple, powerful expression:
a + 3
This is called an algebraic expression. The letter 'a' is a variable—its value can change depending on Aftab's current age.
This chapter will teach you how to create, read, and work with these new algebraic expressions.
Writing Expressions (Formulas)
You'll learn to translate word problems and patterns into concise algebraic expressions. For example:
Patterns: If one 'L' shape is made of 2 matchsticks, 'n' L-shapes will need 2 × n (or just 2n) matchsticks.
Formulas: The perimeter of a square can be written as 4q, where 'q' is the length of its side.
Evaluating Expressions
This means finding the value of an expression by replacing the letter-number with a specific number. For instance, if the expression for a quiz score is 7p - 3q, and you get p=4 points for a correct answer and q=1 point as a penalty, your score is (7 × 4) - (3 × 1) = 28 - 3 = 25.
Simplifying Expressions (Combining Like Terms)
This is a key skill. You'll learn that we can only add or subtract terms that have the same letter-number.
Like Terms: 5c + 3c + 10c can be simplified. Just as "5 coconuts + 3 coconuts + 10 coconuts" is "18 coconuts," this expression simplifies to 18c.
Unlike Terms: An expression like 18c + 11d (e.g., the cost of 'c' coconuts and 'd' erasers) cannot be simplified any further because 'c' and 'd' are different.
Simplifying with Brackets
We will use the same rules from arithmetic (like the distributive property) to simplify more complex expressions. For example:
(40x + 75y) - (6x + 10y)
= 40x + 75y - 6x - 10y
= (40x - 6x) + (75y - 10y)
= 34x + 65y
Using Algebra to Prove Patterns
Finally, you'll see the true power of algebra. We can use it to prove that a pattern will always be true. For example, by using 'a' for a date in a calendar, we can prove that in any 2x2 square, the sums of the diagonals are always equal.
Algebra is a new language that makes it easier to describe and solve complex problems. At Teachoo, we'll guide you through every step, from your first letter-number to simplifying long expressions, to make sure you become fluent.
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