Algebraic Expressions Class 7 Complete Guide
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Table of Contents
- Introduction to Algebraic Expressions
- What is Algebra?
- Variables and Constants
- Terms in an Expression
- Coefficients
- Types of Algebraic Expressions
- Like and Unlike Terms
- Addition and Subtraction of Expressions
- Real-Life Applications
- Key Points for Revision
- Important Abbreviations
- HOTS Questions
- Word Problems
- Practice Questions with Answers
- Viewer Challenge Questions
Introduction
Mathematics is not only about numbers. Sometimes we use letters along with numbers to represent unknown quantities. These mathematical statements are known as Algebraic Expressions.
गणित केवल संख्याओं का विषय नहीं है। कई बार हम अज्ञात राशियों को दर्शाने के लिए अक्षरों का उपयोग करते हैं। ऐसे गणितीय रूपों को Algebraic Expressions (बीजीय व्यंजक) कहा जाता है।
What is Algebra?
Algebra is a branch of mathematics that uses letters, symbols, and numbers to represent relationships.
Algebra गणित की वह शाखा है जिसमें अक्षरों, प्रतीकों और संख्याओं का उपयोग करके संबंधों को व्यक्त किया जाता है।
Example:
x + 5
Here x represents an unknown number.
यहाँ x एक अज्ञात संख्या को दर्शाता है।
Variables and Constants
Variable
A symbol whose value can change.
जिसका मान बदल सकता है उसे Variable कहते हैं।
Examples:
- x
- y
- a
- b
Constant
A fixed value that never changes.
जिसका मान निश्चित रहता है उसे Constant कहते हैं।
Examples:
- 5
- 10
- 25
Example:
3x + 7
Variable = x
Constant = 7
Terms in an Expression
Parts separated by + or – signs are called Terms.
जो भाग + या – द्वारा अलग किए जाते हैं उन्हें Terms कहते हैं।
Expression:
4x + 3y – 7
Terms:
- 4x
- 3y
- –7
Total Terms = 3
Coefficient
The numerical factor attached to a variable is called Coefficient.
Variable के साथ जुड़ी संख्या Coefficient कहलाती है।
Examples:
5x → Coefficient = 5
9a → Coefficient = 9
x → Coefficient = 1
Types of Algebraic Expressions
1. Monomial
Only one term.
केवल एक पद।
Examples:
- 5x
- 7a²
2. Binomial
Two terms.
दो पद।
Examples:
- x + 5
- 2a – 3
3. Trinomial
Three terms.
तीन पद।
Examples:
- x + y + 5
- a + b – 7
Like and Unlike Terms
Like Terms
Same variables with same powers.
जिन पदों में Variables और उनकी Powers समान हों।
Examples:
- 3x and 5x
- 7a² and 2a²
Unlike Terms
Different variables or powers.
Examples:
- 3x and 3y
- 5a and 5a²
Addition of Algebraic Expressions
Example:
(3x + 4) + (2x + 5)
= 3x + 2x + 4 + 5
= 5x + 9
Subtraction of Algebraic Expressions
Example:
(8x + 6) – (3x + 2)
= 8x + 6 – 3x – 2
= 5x + 4
Real-Life Applications
- Calculating age.
- Finding total cost.
- Measuring distances.
- Business profit calculations.
- Scientific formulas.
Important Abbreviations
| Abbreviation | Full Form |
|---|---|
| ALG | Algebra |
| VAR | Variable |
| CONST | Constant |
| EXP | Expression |
| COEF | Coefficient |
| LT | Like Terms |
| ULT | Unlike Terms |
Key Points for Quick Revision
| Variables are represented by letters. |
| Constants have fixed values. |
| Coefficient is the numerical part. |
| Terms are separated by + or – signs. |
| Like terms can be added or subtracted directly. |
| Unlike terms cannot be combined. |
| Algebra is widely used in daily life. |
HOTS (Higher Order Thinking Skills)
Q1.
If x = 4, find the value of:
3x + 7
Answer:
= 3(4) + 7 = 12 + 7 = 19
Q2.
Find the value of:
2a + 5 when a = 10
Answer:
= 2(10) + 5
= 25
Q3.
Which expression has more terms?
A) 3x + 2
B) x + y + z + 5
Answer:
B has 4 terms.
Word Problems
Problem 1
Rahul has x chocolates. His friend gives him 5 more chocolates.
How many chocolates does Rahul have now?
Answer:
x + 5
Problem 2
A pen costs ₹10. Riya buys x pens.
Find total cost.
Answer:
10x
Problem 3
A classroom has y boys and 15 girls.
Total students?
Answer:
y + 15
Additional NCERT Based Questions and Explanations
NCERT Example 1
Question
Identify the variables and constants in the following expression:
5x + 7
Solution
Variable = x
Constant = 7
Coefficient of x = 5
Explanation
The value of x can change, therefore it is a variable.
The number 7 remains fixed, therefore it is a constant.
NCERT Example 2
Question
Write an algebraic expression for:
“A number increased by 8”
Solution
Let the number be x.
Required expression:
x + 8
Hindi Explanation
किसी संख्या में 8 जोड़ने पर प्राप्त व्यंजक x + 8 होगा।
NCERT Example 3
Question
Write an algebraic expression for:
“Seven times a number”
Solution
Let the number be y.
Expression:
7y
NCERT Example 4
Question
Write an expression for:
“The sum of a number and 15”
Solution
Let the number be a.
Expression:
a + 15
Common Mistakes Students Make
1. Writing 7 + x instead of x + 7 is not wrong mathematically but always understand the meaning carefully.
2. Confusing coefficient with constant.
3. Adding unlike terms such as:
3x + 2y = 5xy
This is incorrect.
Multiple Choice Questions (MCQs)
1. Which of the following is a variable?
A) 5
B) 10
C) x
D) 20
✅ Answer: C
2. The coefficient of x in 9x is:
A) x
B) 9
C) 1
D) 0
✅ Answer: B
3. Which of the following is a monomial?
A) x + y
B) x + 5
C) 7x
D) x + y + z
✅ Answer: C
4. Which pair contains like terms?
A) 5x and 4y
B) 3a and 2a
C) x and y
D) a² and a
✅ Answer: B
5. Number of terms in x + y + z + 10
A) 2
B) 3
C) 4
D) 5
✅ Answer: C
Fill in the Blanks
- The symbol whose value changes is called _______.
✅ Variable
- The numerical factor of a term is called _______.
✅ Coefficient
- x + 5 contains _______ terms.
✅ Two
- 5x and 3x are _______ terms.
✅ Like
- 7 is a _______.
✅ Constant
True or False
1.
5x and 7x are like terms.
✅ True
2.
3x and 3y are like terms.
❌ False
3.
The coefficient of x in x is 1.
✅ True
4.
Constants can change their value.
❌ False
5.
An algebraic expression may contain variables and numbers.
✅ True
Assertion and Reason Questions
Question 1
Assertion (A):
3x and 7x are like terms.
Reason (R):
Both have the same variable x.
✅ Answer:
Both A and R are true and R correctly explains A.
Question 2
Assertion (A):
5x and 5y are like terms.
Reason (R):
Their coefficients are equal.
✅ Answer:
Assertion is false.
Reason is true.
Case Study Based Questions
School Library Case
A school library has x story books and 25 science books.
Total books = x + 25
Questions
- Identify the variable.
Answer: x
- Identify the constant.
Answer: 25
- Number of terms?
Answer: 2
- Type of expression?
Answer: Binomial
Higher Order Thinking Skills (HOTS) ( Algebraic Expressions Class 7 )
Q1
Which is greater?
3x + 4 or 2x + 9 when x = 5
Solution
3(5)+4 = 19
2(5)+9 = 19
Both are equal.
Q2
Can 5x and 5 be added directly?
Answer:
No.
Because one contains a variable and the other is a constant.
Q3
Can 4a + 6b be simplified further?
Answer:
No.
Because they are unlike terms.
Long Answer Questions ( Algebraic Expressions Class 7 )
Q1.
Define algebraic expression with examples.
Q2.
Explain variable, constant and coefficient.
Q3.
Differentiate between monomial, binomial and trinomial.
Q4.
What are like and unlike terms?
Q5.
Write five algebraic expressions from daily life situations.
Daily Life Word Problems ( Algebraic Expressions Class 7 )
Problem 1
A notebook costs ₹25.
Ravi buys x notebooks.
Find total cost.
Answer:
25x
Problem 2
A bus contains x passengers.
15 more passengers enter.
Find total passengers.
Answer:
x + 15
Problem 3
A farmer has y mango trees.
He plants 20 more trees.
Total trees?
Answer:
y + 20
Problem 4
A shopkeeper earns ₹50 profit on each bag.
He sells x bags.
Find total profit.
Answer:
50x
Important Exam Questions (Repeated Pattern)
| Define algebraic expression. |
| What is a coefficient? |
| What are variables? |
| Explain monomial with examples |
| Explain binomial with examples. |
| Differentiate between like and unlike terms. |
| Find coefficient in given expressions. |
| Form algebraic expressions from statements. |
| Solve word problems based on algebraic expressions. |
| Identify terms, variables and constants. |
Mega Viewer Challenge Contest ( Algebraic Expressions Class 7 )
🎯 Send answers through Comment, WhatsApp or Message.
Question 1
Write an algebraic expression for:
“Five more than a number.”
Question 2
Identify coefficient and variable in:
8x + 12
Question 3
Find value of:
3x + 5
when x = 4
Question 4
Are 6a and 9a like terms?
Give reason.
Question 5
A pencil costs ₹7.
Write an algebraic expression for the cost of x pencils.
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