PW Class 7 Maths Notes Chapter 2: Arithmetic Expressions

Arithmetic expressions introduce you to an important part of mathematics where numbers, variables, and mathematical operations are used together. In Chapter 2, you understand how expressions are formed, identify their different components, and distinguish between different types of expressions.

The PW Class 7 Maths Notes Chapter 2: Arithmetic Expressions cover concepts such as constants, variables, coefficients, like and unlike terms, monomials, binomials, trinomials, and polynomials. You also work with BODMAS, evaluation of expressions, and addition, subtraction, and multiplication of algebraic expressions.

What Is an Arithmetic Expression?

An arithmetic expression is a combination of numbers, variables, and mathematical operators such as addition, subtraction, multiplication, and division. An expression does not use an equal sign.

Examples include:

• 5+3

• X−7

• 3a+2b−5

An expression can represent a numerical value or a mathematical operation. Understanding how an expression is formed makes it easier to simplify and work with more complex expressions later.

Components of an Arithmetic Expression

An arithmetic expression can contain several components. You should be able to identify each one before performing operations on an expression.

1. Like Terms

Like terms have the same variables raised to the same powers.

For example:

4x2,  −5x2,  8x2,  11x2

Because the variable and exponent are the same, these terms can be combined.

2. Unlike Terms

Unlike terms contain different variables or have different powers.

For example:

3x2y,  5xy,  3x,  6y3

You cannot directly combine unlike terms through addition or subtraction.

Types of Expressions

Expressions can broadly be classified as numerical and algebraic expressions.

1. Numerical Expression

A numerical expression contains only numbers and mathematical operators.

Example:

10+3×210+3\times2

2. Algebraic Expression

An algebraic expression contains variables along with numbers and mathematical operators.

Example:

4x+3y−74x+3y-7

Types of Algebraic Expressions

Algebraic expressions can also be classified according to the number of terms they contain.

Knowing the type of expression can help you understand its structure before simplifying or performing operations on it.

BODMAS Rule in Arithmetic Expressions

When an expression contains several mathematical operations, you need to perform them in the correct order. The notes use the BODMAS/PEMDAS rule for this purpose.

• B – Brackets

• O – Orders or powers and roots

• D – Division

• M – Multiplication

• A – Addition

• S – Subtraction

For example:

6+2×(5−3)

First, solve the brackets:

5−3=2

Then perform multiplication:

2×2=4

Finally:

6+4=10

Therefore, the value of the expression is 10.

How to Form Algebraic Expressions

You can form an algebraic expression by representing an unknown number using a variable and then applying the operations given in the statement.

For example, suppose you need to write “twice a number added to 3.”

Let the unknown number be xx.

Then:

2x+3

Similarly, “5 more than thrice a number” becomes:

3x+5

While forming an expression, pay attention to words such as more than, less than, twice, and thrice because they tell you which mathematical operations to use.

How to Evaluate Algebraic Expressions

To evaluate an expression, substitute the given value of the variable and then simplify.

Suppose:

3x+4

and

x=2

Substitute 2 in place of x:

3(2)+4

=6+4

=10

Therefore, the value of the expression is 10.

Addition of Algebraic Expressions

When adding algebraic expressions, collect the like terms and add their coefficients.

For example:

(5x2−7x+3)+(−8x2+2x−5)+(7x2−x−2)

Collect the like terms:

(5−8+7)x2+(−7+2−1)x+(3−5−2)

Therefore:

4x2−6x−4

The variable part remains unchanged while you add or subtract the coefficients of like terms.

Subtraction of Algebraic Expressions

When subtracting an algebraic expression, change the sign of every term in the expression being subtracted and then combine the like terms.

For example:

(3x2+4x+6)−(2x2−5x+7)

Change the signs of the second expression:

3x2+4x+6−2x2+5x−7

Now combine the like terms:

X2+9x−1

Pay particular attention to negative signs because a sign error can change the complete answer.

Multiplication of Algebraic Expressions

The method of multiplication depends on the expressions being multiplied.

Multiplication of Two Monomials

Multiply the coefficients and add the exponents of like variables.

For example:

(3x2)(4x3) 

Multiply the coefficients:

3×4=12

Add the exponents:

x2+3=x5

Therefore:

(3x2)(4x3)=12x5

Multiplication of Two Polynomials

When multiplying two polynomials, multiply every term of one polynomial by every term of the other polynomial. Once the multiplication is complete, identify and combine the like terms.

Writing each multiplication separately can make it easier to keep track of coefficients, variables, powers, and signs.

PW Class 7 Maths Chapter 2 Arithmetic Expressions Notes PDF

The PW Class 7 Maths Chapter 2 Arithmetic Expressions Notes PDF can be useful when you want to revise the chapter without going through every concept in detail again. It brings together the main definitions, rules, classifications, and worked examples from the chapter, including BODMAS and operations on algebraic expressions.

You can use the PDF after completing the chapter to revise terms and coefficients, like and unlike terms, types of expressions, evaluation, and algebraic operations. While preparing for a test, first revise the rule and then try the related example without looking at its solution.

How Complete PW Resources Help You Prepare for Class 7 Maths

Once you understand Arithmetic Expressions, the next step is to practise the concepts in different ways. PW Class 7 Maths resources can help you move from revising a concept to solving textbook exercises, attempting additional questions, and finally checking your preparation with paper-level practice.

You can use the resources in the following way:

1. CBSE Class 7 Syllabus – Check the complete subject-wise syllabus and keep track of the chapters and topics you need to cover. 

2. PW Class 7 Maths Notes – Revise chapter-wise concepts, formulas, rules, and examples when you need to refresh a topic. PW Class 7 Maths Notes 

3. PW Class 7 Maths Solutions – Work through textbook exercises and check the steps used to solve different types of questions. PW Class 7 Maths Solutions 

4. Class 7 Maths Important Questions – Practise additional questions after completing the chapter to check whether you can apply the concepts independently. Class 7 Maths Important Questions 

5. Class 7 Maths Sample Papers – Use sample papers after covering multiple chapters to practise bringing different Maths concepts together under exam-style conditions.

PW Class 7 Maths Notes Chapter 2: Arithmetic Expressions can help you revise the basic language of algebra before moving to more advanced concepts. Make sure you can identify terms, variables, constants and coefficients, distinguish like and unlike terms, apply BODMAS, and perform operations on expressions. After revising the notes and PDF, use PW solutions, important questions, and sample papers to practise the chapter and check how confidently you can apply each concept.