NCERT Solutions Class 7 Maths Chapter 10 Algebraic Expressions

NCERT Solutions for Class 7 Maths Chapter 10: Algebraic Expressions is a valuable resource for students. It helps them master algebraic concepts, develop problem-solving skills, and build a strong foundation for future mathematical studies.

NCERT Solutions for Algebraic expressions are incredibly helpful for students in building a strong foundation, mastering algebraic operations, and enhancing problem-solving skills. NCERT Solutions offers a wide range of practice problems with varying difficulty levels, allowing students to apply their understanding and develop problem-solving skills.

1.0Key Concepts in Class 7 Maths Chapter 10: Algebraic Expressions

1. What is an Algebraic Expression?

A combination of variables (letters representing unknown quantities), constants (fixed numbers), and mathematical operations (addition, subtraction, multiplication, division).

Examples:

• 3x + 5
• 2a - b
• 4x²y

2. Terms of an Algebraic Expression:

Parts of an expression are separated by '+' or '-' signs.

Example: In 3x + 5y - 2, the terms are 3x, 5y, and -2.

3. Coefficients:

The numerical factor of a term.

Example: In 5x², the coefficient of x² is 5.

4. Variables:

Letters that represent unknown quantities.

Example: x, y, a, b in the above expressions.

5. Constants:

Numbers that have a fixed value.

Example: 3, 5, -2 in the above expressions.

6. Like and Unlike Terms:

Like Terms: Terms have the same variables and the same exponents.

Example: 3x and 7x, 2y² and -5y²

Unlike Terms: Terms have different variables or different exponents.

Example: 3x and 5y, 2x² and 3x

7. Addition and Subtraction of Algebraic Expressions:

Rule: Only like terms can be added or subtracted.

Example:

3x + 5x = 8x

7y² - 2y² = 5y²

8. Multiplication of Algebraic Expressions:

Use the distributive law: a(b + c) = ab + ac

Multiply monomials, binomials, and polynomials using appropriate rules.

9. Division of Algebraic Expressions:

Divide monomials by monomials using the laws of exponents.

Algebraic Identities:

• Formulas that hold true for all values of the variables involved.
• Some common identities:
• • (a + b)² = a² + 2ab + b²
  • (a - b)² = a² - 2ab + b²
  • (a + b)(a - b) = a² - b²

2.0Benefits of NCERT Solutions for Class 7 Maths Chapter 10

1. The chapter introduces core algebraic concepts like variables, constants, terms, coefficients, and expressions. These are building blocks for higher-level algebra and other branches of mathematics.
2. NCERT Solutions breaks down these concepts into easy-to-understand explanations, ensuring a solid foundation for students.
3. The solutions guide students through adding and subtracting algebraic expressions, including combining like terms and simplifying expressions.
4. Students learn how to multiply monomials, binomials, and polynomials and divide monomials by monomials.
5. Important algebraic identities are introduced and explained, providing valuable shortcuts for solving algebraic problems.
6. Algebraic expressions are used in various real-world situations. NCERT Solutions can help students understand how algebraic concepts are applied in everyday life, making learning more engaging.

3.0Why are NCERT Solutions for Class 7 Maths Chapter 10 important?

• Foundation for Higher Mathematics: These concepts are fundamental to understanding more advanced algebraic topics like equations, inequalities, and functions.
• Problem-Solving: They are essential for solving various mathematical problems in algebra and other areas of mathematics.
• Real-World Applications: Algebraic expressions are used to model and solve real-world problems in various fields, such as physics, engineering, and economics.