Class 7 Maths Chapter 4 Expressions Using Letters NCERT Solutions (Step-by-Step Answers, Examples & Complete Guide | Ganita Prakash)
Class 7 Maths Chapter 4 Expressions Using Letters NCERT Solutions (Step-by-Step Answers, Examples & Complete Guide | Ganita Prakash)
Class 7 Ganita Prakash Navigation
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Introduction
In mathematics, numbers are often represented using letters.
These letters help us write general rules and formulas that work for many numbers.
Example:
Instead of writing
2 + 3 = 5
3 + 3 = 6
4 + 3 = 7
we can write a general expression:
x + 3
Here x can represent any number.
Using letters in mathematics is called algebra.
In this chapter students learn:
• Variables
• Algebraic expressions
• Writing formulas
• Simplifying expressions
• Like and unlike terms
• Patterns using algebra
1. Letter-Numbers in Mathematics 
Letters used in mathematics are called letter-numbers or variables.
Examples:
x
y
n
a
b
These letters represent numbers whose values may change.
Example:
Age of Aftab = a
Age of Shabnam = a + 3
If Aftab is 23 years old
Shabnam’s age =
a + 3
= 23 + 3
= 26 years
Algebra allows us to describe relationships using expressions.
2. Algebraic Expressions
An algebraic expression is a mathematical expression that contains:
• numbers
• variables
• operations
Example expressions:
5x
3a + 2
4y − 7
2m + 5n
Example
Cost of coconuts = 35 × c
Cost of jaggery = 60 × j
Total cost:
35c + 60j
ch4class7EXPRESSIONS
Here
c = number of coconuts
j = kg of jaggery
Example Problem
If
c = 8
j = 9
Find total cost.
Expression:
35c + 60j
Substitute values
= 35 × 8 + 60 × 9
= 280 + 540
= ₹820
3. Writing Formulas Using Expressions
Algebra is often used to write formulas.
Example: Perimeter of shapes.
Perimeter of square:
Side length = q
Perimeter:
4 × q
= 4q
If q = 7 cm
Perimeter
= 4 × 7
= 28 cm
More Examples
Perimeter of triangle with equal sides:
Side length = a
Perimeter
= 3a
Regular pentagon
Perimeter
= 5a
Regular hexagon
Perimeter
= 6a
4. Simplifying Expressions
Sometimes expressions contain many terms.
Example
5c + 3c + 10c
Combine like terms
= (5 + 3 + 10)c
= 18c
Both expressions give the same value.
5. Like Terms and Unlike Terms
Like Terms
Terms with the same variable and power.
Examples:
5x
2x
9x
These can be added.
Example
5x + 3x = 8x
Unlike Terms
Terms with different variables.
Examples:
3x
5y
7a
These cannot be added.
6. Simplifying Expressions with Variables
Example
Money earned from selling pencils.
Day 1 → 5c
Day 2 → 3c
Day 3 → 10c
Total
5c + 3c + 10c
Simplify
= 18c
7. Expressions from Real Life Situations
Example
Renting furniture.
Cost per chair = ₹40
Cost per table = ₹75
Refund:
Chair = ₹6
Table = ₹10
If
x chairs and y tables are rented.
Amount paid
40x + 75y
Amount returned
6x + 10y
Total cost
(40x + 75y) − (6x + 10y)
Simplify
= 40x − 6x + 75y − 10y
= 34x + 65y
8. Patterns Using Algebra
Example sequence:
4, 8, 12, 16, 20…
These are multiples of 4.
The nth term can be written as:
4n
Example:
10th term
4 × 10 = 40
9. Expressions and Equality
Consider two expressions:
5u
5 + u
These expressions look similar but give different values for different numbers.
Example:
If u = 2
5u = 10
5 + u = 7
So the expressions are not equal.
Important Questions with Solutions
Question 1
Write expressions for the following.
a) 5 more than a number
Let number = x
Expression
x + 5
b) 4 less than a number
Let number = x
Expression
x − 4
c) 2 less than 13 times a number
13x − 2
d) 13 less than 2 times a number
2x − 13
Question 2
Munirathna has a pipe of 20 m. Another pipe of length k is joined.
Find the total length.
Expression
20 + k
Total pipe length
(20 + k) meters
Question 3
Find perimeter of rectangle.
Length = l
Breadth = b
Perimeter
l + b + l + b
Simplify
= 2l + 2b
Key Concepts of This Chapter
Students learned:
• Variables
• Algebraic expressions
• Writing formulas
• Simplifying expressions
• Like and unlike terms
• Using algebra for patterns
Algebra helps express mathematical ideas in a simple and general way.
Practice Questions
Simplify:
4x + 7x
Write expression:
3 more than twice a number.
Find perimeter of a square if side = 9 cm.
Write algebraic expression:
Cost of y notebooks if price of one notebook = ₹25.
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