🔁 Using Expressions Again and Again
In the previous post, we learnt:
Letters can stand for numbers
Expressions help us write maths in short form
Now let us go a little deeper — step by step, no tension 🙂
✖️ Writing Multiplication Without “×”
In algebra, we usually do not write the multiplication sign.
Example:
4 × n is written as 4n
7 × k is written as 7k
👉 Number is written before the letter.
So:
5m means 5 times m
NOT 5 + m
This is very important.
⚠️ Common Mistake (Very Important)
❌ 5u and 5 + u are NOT the same
5u = 5 × u
5 + u = 5 added to u
Example:
If u = 2
5u = 10
5 + u = 7
Different answers → different meanings.
➕ Simplifying Expressions
Simplifying means making the expression shorter and cleaner, without changing its value.
Example:
l + b + l + b
We rearrange:l + l + b + b
This becomes:
2l + 2b
Both expressions give the same answer, but the second one is simpler.
🔁 Like Terms and Unlike Terms
✔ Like Terms
Terms with same letter.
Examples:
5c, 3c, 10c → all have c
So:
5c + 3c + 10c = 18c
❌ Unlike Terms
Terms with different letters.
Examples:
18c and 11d
They cannot be added.
So:
18c + 11d stays as it is.
🪑 Example: Chair and Table Rent
Rent paid:
Chair = ₹40
Table = ₹75
Refund given:
Chair = ₹6
Table = ₹10
Let:
x = number of chairs
y = number of tables
Money paid = 40x + 75y
Money returned = 6x + 10y
Final amount paid:
(40x + 75y) − (6x + 10y)
Open the brackets:
40x + 75y − 6x − 10y
Group same letters:
(40 − 6)x + (75 − 10)y
34x + 65y
📊 Patterns Using Algebra
Algebra is very useful for patterns.
Example: Matchstick Pattern
Number of matchsticks:
Step 1 → 3
Step 2 → 5
Step 3 → 7
Pattern:
Every step adds 2 matchsticks
Formula:
2y + 1
If y = step number,
this formula gives matchsticks for any step.
📅 Calendar Pattern (Interesting!)
In any 2 × 2 box of a calendar:
The sum of numbers on both diagonals is always equal.
We prove this using algebra by assuming:
Top left number = a
Then both diagonal sums become:
2a + 8
This shows the pattern works every time, not by chance.
🧠 Why This Chapter Is Important
✔ Helps understand patterns
✔ Saves time in calculations
✔ Useful in higher classes
✔ Trains logical thinking
This is the foundation of algebra.
📝 Final Takeaway
Letters represent numbers
Multiplication sign is usually not written
Like terms can be added
Unlike terms cannot be added
Algebra helps explain patterns clearly