GSEB Class 7 Maths Notes Chapter 12 Algebraic Expressions

   

This GSEB Class 7 Maths Notes Chapter 12 Algebraic Expressions covers all the important topics and concepts as mentioned in the chapter.

Algebraic Expressions Class 7 GSEB Notes

We know already about simple algebraic expressions like x + 7, 2x – y, 3x + 8y, 2y -9 etc and use of such expressions in forming words problems and simple equations.

In this chapter, we shall learn more about algebraic expressions and “How are Algebraic expressions formed”, Factors of a term, coefficient of a term, like and unlike terms types of polynomials. Also we shall learn to find the value of an expression for a particular value of the variable.

Let us revise some definition related as algebraic expressions.
1. Constant: Constant is a term that has a fixed value. Some examples of a constant are 2, 3, 5, 0, \(\frac{-2}{5}\), \(\sqrt{3}\) etc.
Infact every number is a constant.

2. Variable: Variable is a term that does not have a fixed value. Letters of english alphabets are used for variables. For example x, y, z, s, t etc.
Let us assume any number less than 5. It may be – 10, – 7, – 6, – 3, – 1, 0, 1, 2, 3 and many more.

Therefore, when we think any number less than 5. We observe that we do not have single fixed number less than 5 we will write x < 5.
Where x may have varying value. Which is less than 5 ∴ x is variable.

3. Term: A term is a number or constant, a variable or a combination (Product or quotient) of numbers and variables. For example:
5, y, 7b, xy, \(\frac{-3 x}{2 y}, \frac{7 m}{9}\), 5 etc

4. Algebraic expressions: A combination of one or more terms, which are separated by addition, subtraction is called on Algebraic expression. For example 2 + 10x, 3x – 7y, 7a + 3b, ax + by + cz etc.
Note that only (-) minus and (+) plus signs separate the terms. Where as the division and product do not separate the terms.

5. Factors: The terms are made of the product of factors. For example the term 3xy of expression 3xy +7z has three factors 3, x and y and the term 7z has 7 and ‘z’ two factors and expression 3xy + 7z has two terms.

6. Coefficient: Any of the factors of a term is called the coefficient of the product of all the remaining factors. In particular, the constant part is called the “numerical coefficient” and the remaining part is called the ‘Literal coefficient” of term.

For example: Consider the expression. 2x2y + 5xy – 1
In the term 3x2y
Numerical coefficient = 2
Coefficient of y = 2x2
Coefficient of x2 = 2y
Coefficient of x = 2xy

Similarly: In the term 7xy
Numerical coefficient = 5
Coefficient of x = 5y
Coefficient of y = 5x

7. Like Terms: The terms having same variable factors are called like terms. For example 5x2y and – 3x2y. 2xyz and 7xyz, – 3x2yz2 and 2x2yz2 etc.
Note. Like term may have different numerical coefficient, but same literal coefficient.

Unlike terms: The terms having ditlerent variable factors are called unlike terms. For example xy2 and xyz, x2y2z and yz2, 3x2 and 3y2 etc.

GSEB Class 7 Maths Notes Chapter 12 Algebraic Expressions

Types of Algebraic Expressions

Number of Terms Name of Expression Examples
One Monomial x, 3x, \( \frac{5 z}{2},- \frac{7 x^{2}}{11} \) etc
Two Binomial x + 7, 3x – 5y 2x2 – z2
Three Trinomial x + y + z, p2 + q2 + r2, rsq + p + t2
Two or more than two terms Polynomial x, 2x + 3 y, p + q + z, x2 + y2 + zx

Every binomial, every trinomial, is a polynomial.

Tree diagram: It is a diagramatic way of representing terms and factors of an algebraic expression. The terms and the factors of each terms of an algebraic expression is shown by a tree diagram.

Addition and Subtraction of Algebraic Expressions
Imagine, you have 12 apples and your brother has 15 apples, then how many Apples do you both have together? The answer is simple 15 + 12 = 27 Apples.
If we denote an apple by x then you have 12x and your brother has 15x which can be added as 12x + 15x = 27x.

Addition of like terms. The sum of two or more like terms is again the like terms whose numerical coefficient is the sum of the numerical coefficient of the given terms.
For example: 3y + 2y = (3 + 2) y = 5y
3x + 7y + 8x = (3 + 7 + 8)
x = 18x
2ab + 7ab + 5ab = (2 + 7 + 5) ab = 14ab

Addition of Algebraic Expressions: For adding algebraic expressions, we have to group like terms and then carry out addition on them. This can be done by two methods.

  • Horizontal Method. In this method, all expressions are written in a horizontal line and then the terms are arranged in the group of like terms and then like terms are added.
  • Column method. In this method each expression is written in a separate row such that there like terms are arranged one below the other in a column. Then the addition of terms is done column wise. Subtraction of like terms. Subtraction of like terms is done in a manner exactly similar to that of integers. In other words change the sign of each term to be subtracted and then add.

Subtraction of algebraic expression: Subtraction of algebraic expressions can be done by two methods.

  • Horizontal method. Change the sign of each term of the expression to be subtracted and then add.
  • Column Method. Write both expressions one below the other such that the expression to be subtracted comes in the second row and the like terms come one below the other. Change the sign of every term of the expression in the second row and then add.

Value of an Algebraic Expression

  • The value of Algebraic expression changes with the change in the value of variable forming the expression.
  • The process of finding the value of an algebraic expression by replacing the variable by their particular value is called substitution.

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