Class 7 Notes - Algebraic Expressions

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Algebraic Expressions

Algebraic expressions are mathematical phrases that include numbers, variables (like x or y), and operations (such as addition, subtraction, multiplication, and division). They do not have an equals sign.

1. What is an Algebraic Expression?

  • An algebraic expression is a combination of constants, variables, and mathematical operations.
  • Examples: 2x + 3, 5y - 7, a + b + c, 4m - 2n + 8

2. Terms, Coefficients, and Constants

  • Term: Each part of an expression separated by + or - signs. Example: In 3x + 5y - 7, the terms are 3x, 5y, and -7.
  • Coefficient: The number multiplied by a variable. In 4x, 4 is the coefficient.
  • Constant: A number without a variable. In 2x + 5, 5 is the constant.

3. Types of Algebraic Expressions

  • Monomial: An expression with one term (e.g., 7x).
  • Binomial: An expression with two terms (e.g., 3x + 4).
  • Trinomial: An expression with three terms (e.g., x + 2y + 3).
  • Polynomial: An expression with one or more terms.

4. Like and Unlike Terms

  • Like Terms: Terms that have the same variable(s) raised to the same power. Example: 2x and 5x are like terms.
  • Unlike Terms: Terms with different variables or powers. Example: 3x and 4y are unlike terms.

5. Addition and Subtraction of Algebraic Expressions

  • Add or subtract like terms only.
  • Example: (3x + 4y) + (2x - y) = (3x + 2x) + (4y - y) = 5x + 3y

6. Value of an Expression

  • To find the value, substitute the given values for the variables.
  • Example: If x = 2, then 5x + 3 = 5×2 + 3 = 10 + 3 = 13

7. Word Problems

  1. Problem: Write an expression for "5 more than twice a number x".
    Solution: 2x + 5
  2. Problem: If y = 4, what is the value of 3y - 2?
    Solution: 3×4 - 2 = 12 - 2 = 10

8. Practice Exercises

  1. Identify the terms, coefficients, and constants in: 7x + 3y - 5
  2. Simplify: 4a + 3a - 2a
  3. Find the value of 2x + 3 when x = 5
  4. Write an algebraic expression for "the sum of a number y and 9"

Summary

  • Algebraic expressions use variables, numbers, and operations.
  • They can be simplified by combining like terms.
  • Values can be found by substituting numbers for variables.