Class 7 Mathematics

Chapter 12: Algebraic Expressions

STAGE 0: Foundation

In algebra, we use letters along with numbers. These letters help us represent unknown values.

An algebraic expression is made using:

• Numbers
• Letters (variables)
• Mathematical signs (+, −, ×)

STAGE 1: Variables and Constants

• Variable: A letter used to represent a number (x, y, a, b)
• Constant: A fixed number (2, 5, −7)

Example:

In the expression 3x + 5
3 is a constant, x is a variable, and 5 is a constant.

STAGE 2: Terms of an Expression

Each part of an algebraic expression separated by + or − is called a term.

Example:

Expression: 4x + 3y − 7

• 4x → first term
• 3y → second term
• −7 → third term

STAGE 3: Coefficient

The number multiplied with a variable is called its coefficient.

Example:

In 5x, the coefficient of x is 5.

In −7y, the coefficient of y is −7.

STAGE 4: Like and Unlike Terms

• Like terms: Same variables with same powers
• Unlike terms: Different variables or powers

Examples:

• 3x and 5x → Like terms
• 4x and 4y → Unlike terms
• 2a² and 7a² → Like terms

STAGE 5: Simple Algebraic Expressions

• x + 3
• 2y − 5
• 4a + 7b

These expressions cannot be simplified further unless values are given.

STAGE 6: Forming Algebraic Expressions

Example 1:
5 more than a number x → x + 5

Example 2:
7 times a number y → 7y

Example 3:
10 less than twice a number a → 2a − 10

STAGE 7: Practice Questions

1. Identify variables and constants in 4x + 9.
2. Write the terms of 3a − 5b + 7.
3. Find the coefficient of x in −6x.
4. Write an expression for: “8 more than twice a number”.
5. Write two like terms of 5y.

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Shaktimatha CBSE Learning
Class 7 Mathematics – Chapter 12: Algebraic Expressions

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