Class 7 : Maths – Lesson 4. Expressions using Letter-Numbers

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On December 11, 2025

EXPLANATION AND ANALYSIS

🔵 Introduction: When Numbers Are Not Fixed

🧠 In earlier lessons, we worked with numbers whose values were known and fixed. However, in many situations, we do not know the exact value of a quantity. For example, the cost of one pen may vary, the number of students in a class may change, or the length of a side of a shape may not be given.

🌿 To represent such changing or unknown quantities, we use letters along with numbers. These combinations are called expressions using letter-numbers. This chapter introduces us to the idea of using letters to represent numbers and forming meaningful mathematical expressions.

🟢 Meaning of Letter-Numbers

🧠 A letter-number is a letter used to represent a number whose value is not fixed or is unknown.

🔹 Letters like x, y, a, b, p, q are commonly used
🔹 These letters stand for numbers

📌 Example
If x represents a number, then x + 5 is an expression using a letter-number.

💡 Concept:
Letter-numbers help us write rules and relationships in a general form.

🔵 Expressions Using Letter-Numbers

🧠 An expression using letter-numbers is formed when letters and numbers are combined using arithmetic operations.

🔹 It does not contain an equal sign
🔹 It represents a value that depends on the value of the letter

📌 Examples
🔹 x + 7
🔹 3a
🔹 5y − 2

✏️ Note:
The value of such an expression changes when the value of the letter changes.

🟢 Why Do We Use Letters in Mathematics?

🧠 Letters make mathematics more powerful and flexible.

🔹 They help represent unknown values
🔹 They help write general rules
🔹 They make formulas easy to remember
🔹 They reduce lengthy calculations

📌 Example
The perimeter of a square with side length a is written as
4a

💡 Concept:
Using letters allows us to describe many cases using one expression.

🔵 Forming Simple Algebraic Expressions

🧠 We can form expressions using letter-numbers by combining letters with numbers and operations.

🔹 Addition: x + 4
🔹 Subtraction: y − 3
🔹 Multiplication: 5a
🔹 Division: b ÷ 2

📌 Example
If the cost of one book is p rupees, then the cost of 3 books is
3p

✏️ Note:
Multiplication of a number and a letter is written without using the multiplication sign.

🟢 Terms in an Expression

🧠 An expression using letter-numbers is made up of terms.

🔹 A term may be a number
🔹 A term may be a letter
🔹 A term may be a product of numbers and letters

📌 Example
In the expression 3x + 5
🔹 3x is one term
🔹 5 is another term

💡 Concept:
Terms are separated by addition or subtraction signs.

🔵 Like and Unlike Terms

🧠 Terms that have the same letters raised to the same power are called like terms.

🔹 Like terms can be added or subtracted
🔹 Unlike terms cannot be combined

📌 Examples
🔹 3x and 7x are like terms
🔹 4a and 4b are unlike terms

✏️ Note:
Only like terms can be combined in an expression.

🟢 Evaluating Expressions Using Letter-Numbers

🧠 Evaluating an expression means finding its value when the value of the letter is given.

🔹 Substitute the given value of the letter
🔹 Perform the operations step by step

📌 Example
Evaluate 2x + 5 when x = 3

🔹 Substitute x = 3
🔹 2 × 3 + 5 = 6 + 5
🔹 Value = 11

💡 Concept:
Evaluation helps us find numerical results from expressions.

🟡 Using Expressions in Daily Life

🧠 Expressions using letter-numbers are useful in many real-life situations.

🔹 Calculating total cost when price per item is unknown
🔹 Finding perimeter and area of shapes
🔹 Writing rules in science and commerce
🔹 Representing patterns

📌 Example
If the length of a rectangle is l and breadth is b, then
Perimeter = 2(l + b)

🔴 Common Mistakes to Avoid

🔴 Using multiplication sign between number and letter
🔴 Adding unlike terms
🔴 Forgetting to substitute correct value while evaluating
🔴 Mixing up letters

✏️ Note:
Always check whether terms are like or unlike before combining them.

🟢 Importance of Expressions Using Letter-Numbers

🧠 Learning this chapter helps students to:

🔹 Understand the basics of algebra
🔹 Solve problems with unknown quantities
🔹 Write mathematical rules clearly
🔹 Prepare for higher classes

This chapter is the first step towards algebra, which is a very important branch of mathematics.

📘 Summary

🔵 Letters are used to represent unknown numbers
🟢 Expressions using letter-numbers combine letters and numbers
🟡 Such expressions do not have an equal sign
🔴 Letters help write general rules
🔵 Like terms can be combined
🟢 Expressions can be evaluated by substitution
🟡 Letter-number expressions are widely used in daily life

📝 Quick Recap

📝 Quick Recap
🔵 Letters represent unknown values
🟢 Letter-numbers form algebraic expressions
🟡 Expressions change with the value of letters
🔴 Like terms can be added or subtracted
🔵 These expressions are the foundation of algebra

——————————————————————————————————————————————————————————————————————————–

TEXTBOOK QUESTIONS

🔵 THE NOTION OF LETTER-NUMBERS

🔒 ❓ 1. Write formulas for the perimeter of:

🔒 ❓ (a) a triangle with all sides equal

📌 ✅ Answer:

🔹 Let the length of one side be a
🔹 All three sides are equal

✔️ Final:
Perimeter = 3 × a

🔒 ❓ (b) a regular pentagon

📌 ✅ Answer:

🔹 A regular pentagon has 5 equal sides
🔹 Let the length of one side be a

✔️ Final:
Perimeter = 5 × a

🔒 ❓ (c) a regular hexagon

📌 ✅ Answer:

🔹 A regular hexagon has 6 equal sides
🔹 Let the length of one side be a

✔️ Final:
Perimeter = 6 × a

🔒 ❓ 2. Munirathna has a 20 m long pipe. He joins another pipe of length ‘k’. Write an expression for the combined length.

📌 ✅ Answer (Teacher-like explanation):

🔹 First pipe length = 20 m
🔹 Second pipe length = k m

✔️ Final:
Combined length = 20 + k meters

🔒 ❓ 3. Find the total amount Krithika has. Complete the table.

📌 ✅ Answer (row-wise):

🔹 Row 1:
3 ₹100 notes, 5 ₹20 notes, 6 ₹5 notes

🔸 Expression:
3 × 100 + 5 × 20 + 6 × 5
= 300 + 100 + 30

✔️ Final:
₹430

🔹 Row 2 (given example):
✔️ ₹695 (already correct)

🔹 Row 3:
8 ₹100 notes, 4 ₹20 notes, z ₹5 notes

🔸 Expression:
8 × 100 + 4 × 20 + z × 5

✔️ Final:
800 + 80 + 5z = 880 + 5z

🔹 Row 4:
x ₹100 notes, y ₹20 notes, z ₹5 notes

✔️ Final Expression:
100x + 20y + 5z

🔒 ❓ 4. Which expression shows the time to grind ‘y’ kg of grain?

📌 ✅ Answer (Teacher-like explanation):

🔹 Time to start machine = 10 seconds
🔹 Time to grind 1 kg = 8 seconds
🔹 Time for y kg = 8 × y seconds

🔹 Total time = starting time + grinding time

✔️ Final:
📌 ✅ 10 + 8 × y
(correct option d)

🔒 ❓ 5. Write algebraic expressions using letters of your choice:

🔒 ❓ (a) 5 more than a number

📌 ✅ Answer:

🔹 Let the number be x

✔️ Final:
x + 5

🔒 ❓ (b) 4 less than a number

📌 ✅ Answer:

✔️ Final:
x − 4

🔒 ❓ (c) 2 less than 13 times a number

📌 ✅ Answer:

🔹 13 times a number = 13x
🔹 2 less than that = subtract 2

✔️ Final:
13x − 2

🔒 ❓ (d) 13 less than 2 times a number

📌 ✅ Answer:

🔹 2 times a number = 2x
🔹 13 less than that = subtract 13

✔️ Final:
2x − 13

🔒 ❓ 6. Describe situations for the expressions:

🔒 ❓ (a) 8 × x + 3 × y

📌 ✅ Answer:

🔹 Suppose one notebook costs ₹8 and one pen costs ₹3
🔹 x notebooks and y pens are bought

✔️ Final:
Total cost = 8x + 3y

🔒 ❓ (b) 15 × j − 2 × k

📌 ✅ Answer:

🔹 Suppose j tickets cost ₹15 each
🔹 A discount of ₹2 is given on each of k tickets

✔️ Final:
Total cost after discount = 15j − 2k

🔒 ❓ 7. In a 2 × 3 calendar grid, the bottom middle cell has date ‘w’. Write expressions for the other dates.

📌 ✅ Answer (Teacher-like explanation):

🔹 Dates in a calendar increase by 1 each day
🔹 The bottom row is consecutive dates

✔️ Final:

🔹 Bottom left cell = w − 1
🔹 Bottom middle cell = w
🔹 Bottom right cell = w + 1

🔹 Top left cell = w − 8
🔹 Top middle cell = w − 7
🔹 Top right cell = w − 6

🔵 SIMPLIFICATION OF ALGEBRAIC EXPRESSIONS

🔒 ❓ 1. Add the numbers in each picture below. Write their corresponding expressions and simplify them.

📌 ✅ Answer (Picture-wise):

🔹 Picture 1

Numbers shown:
5y, −6, x, x, 2, 5y

Corresponding expression:
5y + (−6) + x + x + 2 + 5y

Simplifying:
🔹 5y + 5y = 10y
🔹 x + x = 2x
🔹 −6 + 2 = −4

✔️ Final:
📌 ✅ 10y + 2x − 4

🔹 Picture 2

Numbers shown:
2p, 3q, −2, 3,
3q, 2p, 3, −2,
2p, 3q,
3q, 2p

Corresponding expression:
(2p + 2p + 2p + 2p) + (3q + 3q + 3q + 3q) + (−2 + 3 + 3 − 2)

Simplifying:
🔹 2p × 4 = 8p
🔹 3q × 4 = 12q
🔹 −2 + 3 + 3 − 2 = 2

✔️ Final:
📌 ✅ 8p + 12q + 2

🔹 Picture 3

Numbers shown:
Four −5g circles at the corners
Twelve 5k circles inside

Corresponding expression:
(−5g − 5g − 5g − 5g) + (5k × 12)

Simplifying:
🔹 −5g × 4 = −20g
🔹 5k × 12 = 60k

✔️ Final:
📌 ✅ 60k − 20g

🔒 ❓ 2. Simplify each of the following expressions:

🔒 ❓ (a)
p + p + p + p,
p + p + p + q,
p + q + p − q

📌 ✅ Answers:
🔹 p + p + p + p = 4p
🔹 p + p + p + q = 3p + q
🔹 p + q + p − q = 2p

🔒 ❓ (b)
p − q + p − q,
p + q − p + q

📌 ✅ Answers:
🔹 p − q + p − q = 2p − 2q
🔹 p + q − p + q = 2q

🔒 ❓ (c)
p + q − (p + q),
p − q − p − q

📌 ✅ Answers:
🔹 p + q − (p + q) = 0
🔹 p − q − p − q = −2q

🔒 ❓ (d)
2d − d − d − d,
2d − d − d − c

📌 ✅ Answers:
🔹 2d − d − d − d = −d
🔹 2d − d − d − c = −c

🔒 ❓ (e)
2d − d − (d − c),
2d − (d − d) − c

📌 ✅ Answers:
🔹 2d − d − (d − c) = c
🔹 2d − (d − d) − c = 2d − c

🔒 ❓ (f)
2d − d − c − c

📌 ✅ Answer:
🔹 2d − d − c − c = d − 2c

🔵 FIGURE IT OUT ?

🔒 ❓ 1. One plate of Jowar roti costs ₹30 and one plate of Pulao costs ₹20. If x plates of Jowar roti and y plates of pulao were ordered in a day, which expression(s) describe the total amount in rupees earned that day?

🟢1️⃣ 30x + 20y
🔵2️⃣ (30 + 20) × (x + y)
🟡3️⃣ 20x + 30y
🟣4️⃣ (30 + 20) × x + y
🔹 (Option (e) is also printed, but MCQ format here uses 4 slots; we answer by correct expression.)

📌 ✅ Answer (Teacher-like explanation):
🔹 Amount from x plates of Jowar roti = 30 × x = 30x
🔹 Amount from y plates of pulao = 20 × y = 20y
🔹 Total amount earned = 30x + 20y

✔️ Answer: 🟢1️⃣

🔒 ❓ 2. Pushpita sells two types of flowers on Independence day: champak and marigold. ‘p’ customers only bought champak, ‘q’ customers only bought marigold, and ‘r’ customers bought both. On the same day, she gave away a tiny national flag to every customer. How many flags did she give away that day?

🟢1️⃣ p + q + r
🔵2️⃣ p + q + 2r
🟡3️⃣ 2 × (p + q + r)
🟣4️⃣ p + q + r + 2
🔹 (Options (e) and (f) are also printed in the book line, but the correct expression is clear.)

📌 ✅ Answer (Teacher-like explanation):
🔹 Customers are counted person-wise, not flower-wise
🔹 p customers (only champak) get 1 flag each
🔹 q customers (only marigold) get 1 flag each
🔹 r customers (bought both) are still r people, so they also get 1 flag each
🔹 Total flags = total customers = p + q + r

✔️ Answer: 🟢1️⃣

🔒 ❓ 3. A snail is trying to climb along the wall of a deep well. During the day it climbs up ‘u’ cm and during the night it slowly slips down ‘d’ cm. This happens for 10 days and 10 nights.

🔒 ❓ (a) Write an expression describing how far away the snail is from its starting position.

📌 ✅ Answer (Teacher-like explanation):
🔹 In 1 day and 1 night, net movement = u − d
🔹 This repeats for 10 days and 10 nights
🔹 Net distance from start after 10 cycles = 10(u − d)

📌 ✅ Final: 10(u − d)

🔒 ❓ (b) What can we say about the snail’s movement if d > u?

📌 ✅ Answer (Teacher-like explanation):
🔹 If d > u, then u − d is negative
🔹 Negative net movement means slipping down is more than climbing up
📌 ✅ Final: The snail moves downward overall and ends up below its starting position after 10 days and 10 nights.

🔒 ❓ 4. Radha is preparing for a cycling race and practices daily. The first week she cycles 5 km every day. Every week she increases the daily distance cycled by ‘z’ km. How many kilometers would Radha have cycled after 3 weeks?

📌 ✅ Answer (Teacher-like explanation):
🔹 Week 1 daily distance = 5
🔹 Week 2 daily distance = 5 + z
🔹 Week 3 daily distance = 5 + 2z
🔹 Each week has 7 days

🔹 Total distance in 3 weeks
🔸 Week 1 total = 7 × 5
🔸 Week 2 total = 7 × (5 + z)
🔸 Week 3 total = 7 × (5 + 2z)

🔹 Add them
🔸 = 7×5 + 7(5 + z) + 7(5 + 2z)
🔸 = 35 + (35 + 7z) + (35 + 14z)
🔸 = 105 + 21z

📌 ✅ Final: 105 + 21z km

🔒 ❓ 5. In the following figure, observe how the expression w + 2 becomes 4w + 20 along one path. Fill in the missing blanks on the remaining paths. (The ovals contain expressions and the boxes contain operations.)

📌 ✅ Answer (Teacher-like explanation):
🔹 Start from the center oval: w + 2
🔹 Follow arrows exactly and apply the operation in each box

🔹 Top-left path (ends at a blank oval)
🔸 w + 2, then −5 gives: (w + 2) − 5 = w − 3 (this oval is already shown)
🔸 Then ×3 gives: 3(w − 3) = 3w − 9
📌 ✅ Blank top-left oval: 3w − 9

🔹 Bottom-left path (two blank ovals)
🔸 w + 2, then −8 gives: (w + 2) − 8 = w − 6
📌 ✅ Blank middle bottom oval: w − 6
🔸 Then −4 gives: (w − 6) − 4 = w − 10
📌 ✅ Blank left bottom oval: w − 10

🔹 Bottom-right path (one blank oval before ×4)
🔸 After ×4, result is 3w − 6
🔸 So the oval just before ×4 must be: (3w − 6)/4
📌 ✅ Blank bottom-right oval: (3w − 6)/4

🔒 ❓ Question 6
A local train from Yahapur to Vahapur stops at three stations at equal distances along the way.
The time taken (in minutes) to travel from one station to the next station is the same and is denoted by t.
The train stops for 2 minutes at each of the three stations.

(a) If t = 4, what is the time taken to travel from Yahapur to Vahapur?
(b) What is the algebraic expression for the time taken to travel from Yahapur to Vahapur?

📌 ✅ Answer:

🔹 First understand the journey structure
🔸 Yahapur → Station 1 → Station 2 → Station 3 → Vahapur
🔸 Total 4 travel segments, each taking t minutes

🔹 Travel time
🔸 Total travel time = 4 × t = 4t minutes

🔹 Stoppage time
🔸 Train stops at 3 stations
🔸 Each stop = 2 minutes
🔸 Total stoppage time = 3 × 2 = 6 minutes

🔹 (a) When t = 4
🔸 Travel time = 4 × 4 = 16 minutes
🔸 Total time = 16 + 6 = 22 minutes

🔹 (b) Algebraic expression
📌 Total time = 4t + 6

🔒 ❓ Question 7
Simplify the following expressions:

(a) 3a + 9b − 6 + 8a − 4b − 7a + 16
📌 ✅ Answer:
🔹 Combine like terms
🔸 (3a + 8a − 7a) + (9b − 4b) + (−6 + 16)
🔸 = 4a + 5b + 10

(b) 3(3a − 3b) − 8a − 4b − 16
📌 ✅ Answer:
🔹 First multiply
🔸 9a − 9b − 8a − 4b − 16
🔸 = a − 13b − 16

(c) 2(2x − 3) + 8x + 12
📌 ✅ Answer:
🔹 Multiply first
🔸 4x − 6 + 8x + 12
🔸 = 12x + 6

(d) 8x − (2x − 3) + 12
📌 ✅ Answer:
🔹 Remove bracket carefully
🔸 8x − 2x + 3 + 12
🔸 = 6x + 15

(e) 8h − (5 + 7h) + 9
📌 ✅ Answer:
🔹 Distribute minus sign
🔸 8h − 5 − 7h + 9
🔸 = h + 4

(f) 23 + 4(6m − 3n) − 8n − 3m − 18
📌 ✅ Answer:
🔹 Multiply first
🔸 23 + 24m − 12n − 8n − 3m − 18
🔸 = 21m − 20n + 5

🔒 ❓ Question 8
Add the expressions given below:

(a) 4d − 7c + 9 and 8c − 11 + 9d
📌 ✅ Answer:
🔹 Add like terms
🔸 (4d + 9d) + (−7c + 8c) + (9 − 11)
🔸 = 13d + c − 2

(b) −6f + 19 − 8s and −23 + 13f + 12s
📌 ✅ Answer:
🔹 = 7f + 4s − 4

(c) 8d − 14c + 9 and 16c − (11 + 9d)
📌 ✅ Answer:
🔹 Simplify second expression
🔸 16c − 11 − 9d
🔸 = −d + 2c − 2

(d) 6f − 20 + 8s and 23 − 13f − 12s
📌 ✅ Answer:
🔹 = −7f − 4s + 3

(e) 13m − 12n and 12n − 13m
📌 ✅ Answer:
🔹 = 0

(f) −26m + 24n and 26m − 24n
📌 ✅ Answer:
🔹 = 0

🔒 ❓ Question 9
Subtract the expressions given below:

(a) 9a − 6b + 14 from 6a + 9b − 18
📌 ✅ Answer:
🔹 (6a + 9b − 18) − (9a − 6b + 14)
🔸 = −3a + 15b − 32

(b) −15x + 13 − 9y from 7y − 10 + 3x
📌 ✅ Answer:
🔹 = 18x + 16y − 23

(c) 17g + 9 − 7h from 11 − 10g + 3h
📌 ✅ Answer:
🔹 = −27g + 10h + 2

(d) 9a − 6b + 14 from 6a − (9b + 18)
📌 ✅ Answer:
🔹 = −3a − 32

(e) 10x + 2 + 10y from −3y + 8 − 3x
📌 ✅ Answer:
🔹 = −13x − 13y + 6

(f) 8g + 4h − 10 from 7h − 8g + 20
📌 ✅ Answer:
🔹 = −16g + 3h + 30

🔒 ❓ Question 10
Describe situations corresponding to:

(a) 8x + 3y
📌 ✅ Answer:
🔹 Cost of x items at ₹8 each and y items at ₹3 each

(b) 15x − 2x
📌 ✅ Answer:
🔹 Total of 15 groups reduced by 2 groups of x items

🔒 ❓ Question 11
A rope is cut once → 2 pieces
Fold once and cut → 3 pieces

🔹 Observe the pattern
🔸 Each fold increases pieces by 1

📌 ✅ Answer:
🔹 For 10 folds → 11 pieces
🔹 For r folds → r + 1 pieces

🔒 ❓ Q12. Look at the matchstick pattern below. Observe and identify the pattern.
How many matchsticks are required to make 10 such squares?
How many are required to make w squares?

📌 ✅ Answer:

🔹 Step 1: Observe the pattern

1 square needs 4 matchsticks
2 squares share one side → 7 matchsticks
3 squares → 10 matchsticks

🔹 Each new square adds 3 matchsticks.

🔹 General pattern

Matchsticks = 4 + 3 × (number of extra squares)

🔹 For w squares

Matchsticks = 4 + 3(w − 1)
= 3w + 1

🔹 For 10 squares

Matchsticks = 3 × 10 + 1
= 31 matchsticks

✔️ Final Answer:
🔹 10 squares → 31 matchsticks
🔹 w squares → 3w + 1

🔒 ❓ Q13. Traffic signal colour pattern is shown.
Find the colour at positions 90, 190, and 343.
Write expressions for the positions of each colour.

📌 ✅ Answer:

🔹 Observed colour sequence (repeats every 4):
1 → Red
2 → Yellow
3 → Green
4 → Yellow

🔹 Cycle length = 4

🔹 Position 90

90 ÷ 4 = remainder 2
Position 2 → Yellow

🔹 Position 190

190 ÷ 4 = remainder 2
Position 2 → Yellow

🔹 Position 343

343 ÷ 4 = remainder 3
Position 3 → Green

🔹 General expressions

Red positions → 4n − 3
Yellow positions → 4n − 2 and 4n
Green positions → 4n − 1

✔️ Final Answer:
🔹 90 → Yellow
🔹 190 → Yellow
🔹 343 → Green

🔒 ❓ Q14. Observe the pattern below.
How many squares will be there in Step 4, Step 10, Step 50?
Write a general formula.
How would the formula change if we want to count the number of vertices of all the squares?

📌 ✅ Answer:

🔹 Understanding the pattern
🔸 Step 1 has 5 squares
🔸 Step 2 has 9 squares
🔸 Step 3 has 13 squares

🔹 Observation
🔸 Each step increases by 4 squares

🔹 General formula
🔸 Number of squares in Step n = 4n + 1

🔹 Applying the formula
🔸 Step 4: 4 × 4 + 1 = 17 squares
🔸 Step 10: 4 × 10 + 1 = 41 squares
🔸 Step 50: 4 × 50 + 1 = 201 squares

🔹 Counting vertices
🔸 Each square has 4 vertices
🔸 Total vertices = 4 × (number of squares)

🔹 General formula for vertices
🔸 Vertices = 4 × (4n + 1)
🔸 = 16n + 4

✔️ Final:
🔹 Squares in Step n = 4n + 1
🔹 Vertices in Step n = 16n + 4

🔒 ❓ Q15. Numbers are written in a particular sequence in this endless 4-column grid.

📌 ✅ Answer:

🔹 (a) Expressions for each column

🔸 Column 1 numbers: 1, 5, 9, 13, …
🔸 Expression → 4n − 3

🔸 Column 2 numbers: 2, 6, 10, 14, …
🔸 Expression → 4n − 2

🔸 Column 3 numbers: 3, 7, 11, 15, …
🔸 Expression → 4n − 1

🔸 Column 4 numbers: 4, 8, 12, 16, …
🔸 Expression → 4n

🔹 (b) Row and column of given numbers

🔸 124
🔹 124 ÷ 4 = 31 remainder 0
🔸 Row = 31, Column = 4

🔸 147
🔹 147 ÷ 4 = 36 remainder 3
🔸 Row = 37, Column = 3

🔸 201
🔹 201 ÷ 4 = 50 remainder 1
🔸 Row = 51, Column = 1

🔹 (c) Number in row r and column c
🔸 Number = 4(r − 1) + c

🔹 (d) Pattern of multiples of 3
🔸 Multiples of 3 occur at regular intervals
🔸 Their positions repeat because numbers increase by 4 in each new row
🔸 Column positions follow a repeating cycle

✔️ Final:
🔹 General number at row r, column c = 4(r − 1) + c

Class 7 : Maths – Lesson 4. Expressions using Letter-Numbers

EXPLANATION AND ANALYSIS

🔵 Introduction: When Numbers Are Not Fixed

🟢 Meaning of Letter-Numbers

🔵 Expressions Using Letter-Numbers

🟢 Why Do We Use Letters in Mathematics?

🔵 Forming Simple Algebraic Expressions

🟢 Terms in an Expression

🔵 Like and Unlike Terms

🟢 Evaluating Expressions Using Letter-Numbers

🟡 Using Expressions in Daily Life

🔴 Common Mistakes to Avoid

🟢 Importance of Expressions Using Letter-Numbers

📘 Summary

📝 Quick Recap

TEXTBOOK QUESTIONS

OTHER IMPORTANT QUESTIONS

🔵 Section A – Very Short Answer (1 × 6 = 6 marks)

🟢 Section B – Short Answer I (2 × 6 = 12 marks)

🟡 Section C – Short Answer II (3 × 10 = 30 marks)

🔴 Section D – Long Answer (4 × 8 = 32 marks)

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