Class 7 Maths Chapter 4 Expressions Using Letter Numbers | NCERT Ganita Prakash Solutions

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

1. Simplify:

4x + 7x

2. Write expression:

3 more than twice a number.

3. Find perimeter of a square if side = 9 cm.

4. Write algebraic expression:

Cost of y notebooks if price of one notebook = ₹25.

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