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Mathematics Class 7 - Algebraic Expressions Notes

Comprehensive study notes for Class 7 - Algebraic Expressions olympiad preparation

Algebraic Expressions

Welcome to the chapter on Algebraic Expressions for Class 7. In this chapter, you will learn what algebraic expressions are, how to form them, and how to use them in math problems. By the end of this chapter, you will be able to write, simplify, and evaluate algebraic expressions confidently!

Introduction

Algebraic expressions are combinations of numbers, variables (letters like x, y), and mathematical operations (like +, -, ×, ÷). They help us write math problems in a simple way.

Parts of an Algebraic Expression

  • Variable: A letter that stands for a number (e.g., x, y).
  • Constant: A fixed number (e.g., 5, 12).
  • Coefficient: The number multiplied by the variable (e.g., in 3x, 3 is the coefficient).
  • Term: Each part of the expression separated by + or - (e.g., in 2x + 3, 2x and 3 are terms).

Forming Algebraic Expressions

You can form algebraic expressions using variables, constants, and operations.

  • Sum of a number and 5: x + 5
  • Twice a number minus 3: 2y - 3
  • Product of a number and 7: 7a

Types of Algebraic Expressions

  • Monomial: An expression with one term (e.g., 4x).
  • Binomial: An expression with two terms (e.g., x + 5).
  • Trinomial: An expression with three terms (e.g., x + y + 7).
  • Polynomial: An expression with many terms.

Simplifying Algebraic Expressions

Combine like terms to make expressions simpler.

  • Example: 2x + 3x = 5x
  • Example: 4y - 2y = 2y

Evaluating Algebraic Expressions

To evaluate an expression, substitute the value of the variable and solve.

  • If x = 2, then 3x + 4 = 3 × 2 + 4 = 6 + 4 = 10
  • If y = 5, then y - 3 = 5 - 3 = 2

Fun Activity: Make Your Own Expression!

Think of a math problem and write it as an algebraic expression. Share it with your friends and solve each other's expressions!

Summary

  • Algebraic expressions use variables, constants, and operations.
  • You can simplify and evaluate expressions.
  • Expressions can have one or more terms.

Practice Questions

  1. Write an expression for "a number increased by 7".
  2. Simplify: 5x + 2x
  3. Evaluate: 4y - 3 when y = 2
  4. What is a binomial? Give an example.
  5. Write an expression for "three times a number minus 4".

Challenge Yourself

  • Make a word problem and write its algebraic expression.
  • Simplify: 2a + 3b + 4a - b

Did You Know?

  • Algebra comes from an Arabic word meaning "reunion of broken parts".
  • Algebraic expressions are used in science, engineering, and daily life!

Glossary

  • Variable: A letter that stands for a number.
  • Constant: A fixed number.
  • Coefficient: The number multiplied by a variable.
  • Term: Each part of an expression separated by + or -.

Answers to Practice Questions

  1. x + 7
  2. 7x
  3. 4 × 2 - 3 = 8 - 3 = 5
  4. An expression with two terms, e.g., x + 5
  5. 3x - 4

Practice algebraic expressions to become a math expert!

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