Day 13: Algebraic Expressions
Middle Stage Mathematics | Apex Institute of Maths and Sciences
🚀 Level 1: The Quest (Concept)
Welcome, Math Explorer! Today we are learning how to combine Algebraic Expressions. Think of an expression like a basket of fruit. You can only add apples to apples and oranges to oranges. In Algebra, we call these “Like Terms”!
Understanding Like Terms
| Term Type | Examples | Status |
|---|---|---|
| Like Terms | 3x, 5x, -2x | ✅ Can Combine |
| Unlike Terms | 4x, 4y, 4x² | ❌ Cannot Combine |
⚡ Level 2: Power-Ups (Tools/Methods)
Example: Simplify (5x + 3) + (2x – 1)
- Group like terms: (5x + 2x) + (3 – 1)
- Add/Subtract: 7x + 2
Secret Tip: If there is a minus sign before parentheses, change the sign of every term inside!
👾 Level 3: Mini-Boss Battles (Applications)
You buy x notebooks for $5 each and y pens for $2 each. Your friend buys 3x notebooks and 4y pens. What is the total expression for the cost?
Solution: (5x + 2y) + (15x + 8y) = 20x + 10y
A rectangular garden has a length of (2x + 5) and a width of (x – 2). What is the perimeter?
Solution: 2[(2x + 5) + (x – 2)] = 2[3x + 3] = 6x + 6
🏠 Level 4: Home Quests (Activities)
Count the spoons (s) and forks (f) in your kitchen. Write an expression for the total (s + f). Now, imagine you buy 3 more spoons and lose 2 forks. Write the simplified new expression: (s + 3) + (f – 2) = s + f + 1.
Go for a walk. Let t be the number of trees you see and c be the number of cars. Create an expression (t + c). If you walk the same path back, you double it: 2(t + c) = 2t + 2c.
Nice
I got 10 out of 10 super 👌 👍 😍