Constants, variables, coefficients, factors, and like and unlike terms are all covered in Chapter 12 of Algebraic Expressions, according to the NCERT syllabus. This chapter also covers the strategies for writing and solving algebraic expressions with one or two variables. Students with additional questions about the subject may always go to the official website and speak with one of our experts for a better grasp of NCERT Maths Class 7. On INFINITY learn, every NCERT Solution is offered to make the study simple and enjoyable. If you have access to NCERT Solutions for Class 7 Science, Maths solutions, and solutions for other topics, subjects like Science, Maths, and English will become easier to study.
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NCERT Solutions for Class 7 Maths Algebraic Expressions
Introduction
We deal with quantities in Arithmetic that are indicated by numbers with specific values, while we deal with quantities in Algebra that are denoted by symbols (in general, letters from the English Alphabet) that might have several values. Furthermore, the values of these symbols change depending on the circumstances. Variables are the names given to these symbols.
Algebra’s Fundamental Concepts
In algebra, there are two sorts of terms:
- A constant is a phrase with a predetermined numerical value. As a result, the values 3, -2, 4/9, and 0.2 are constant.
- A variable, often known as a literal, is a symbol that takes on various numerical values depending on the conditions.
The perimeter of a square, for example, can be calculated using the following formula:
P= 4 x s
As a result, 4 remains constant.
When s equals 6, P = 4 x 6 = 24.
When s equals 5, P = 4 x 5 = 20.
This indicates that the values of p and s are not set in stone. They differ. s and p are variables in the example above.
Facts
- A variable can have many different values, whereas a constant has only one.
- Basic operations on variables and constants can be used to create algebraic expressions.
- Any term in an algebraic expression has factored in general. Constant factors are numbers, while algebraic factors are variables.
- The coefficient of the remaining part of a word is any factor in the term.
- A monomial is the component of an algebraic expression that has only one term.
- Binomial refers to a polynomial with two terms, whereas trinomial refers to a polynomial with three terms.
- Like terms are those that have the same algebraic factors, and unlike terms are those that have distinct algebraic factors.
- The sum (or difference) of two similar terms is equivalent to a term with a coefficient equal to the sum (or difference) of the two similar terms’ coefficients.
- Algebraic expressions allow us to write rules and formulas in a concise and broad manner in mathematics.
What is the Process of Creating Algebraic Expressions?
A combination of constants and variables, or solely variables, are combined by the symbols +, —, x, and y to produce an algebraic expression.
Example:
- By multiplying the variable x by itself, the expression [Equation] is obtained.
[Equation]
- By multiplying the variable x by itself twice and multiplying the product [Equation] by the constant 3, the expression [Equation]is formed.
Expression Definitions
To make an algebraic expression, we must first separate the pieces and then combine them. Terms are the pieces of an expression that are produced individually and then combined.
Factors of a Term
When two or more quantities (numbers and literals) are multiplied, each is referred to as a product factor.
Coefficients
The coefficient of the product of all the remaining factors is any of the term’s factors.
Like and Unlike Terms
Like terms (or similar terms) have the same literal characteristics, whereas unlike terms do not have the same literal factors (or dissimilar terms).
Monomials, Binomials, Trinomials, and Polynomials:
A single-term phrase is known as a monomial.
A binomial expression is one that contains two terms.
A trinomial expression is one that has three terms.
An algebraic expression with two or more terms is called a polynomial.
FAQ:
What distinguishes NCERT Solutions for Class 7 Maths Chapter 12 from others?
NCERT Solutions for Class 7 Maths Chapter 12 includes answers to all of the NCERT Class 7 Maths Chapter 12 practice questions. Make a practice of difficult questions to help you comprehend the themes better.
What are the primary themes covered in Chapter 12 of NCERT Solutions for Class 7 Maths?
Introduction to how expressions are formed, terms of an expression, like and unlike terms, monomials, binomials, trinomials, and polynomials, addition, and subtraction of algebraic expressions, finding the value of an expression, and using algebraic expressions – formulas and rules are the main topics covered in NCERT Solutions for Class 7 Maths Chapter 12.
Is it required to memorize all of the questions in Chapter 12 of NCERT Solutions for Class 7 Maths?
Yes, all of the questions in NCERT Solutions for Class 7 Maths Chapter 12 must be memorized. These questions may appear on both board exams and class tests. Students will be prepared for their future exams if they learn these questions.
