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💡 A Variable Is a Placeholder
In math, a variable is a letter (like n, x, or a) that stands for a number. It's like a blank box — you can put different numbers into it!
When someone writes n + 3, they mean:
"Pick any number, call it n, and add 3 to it."
Example: What Does n + 3 Mean?
Every time you replace n with a number, you get a new answer!
1 Plug In the Number 🔌
Replace the letter with the given number and calculate the result.
n + 5 when n = 2
Replace n with 2:
2 + 5 =
n + 5 when n = 10
Replace n with 10:
+ 5 =
n − 1 when n = 7
Replace n with 7:
− 1 =
n − 1 when n = 20
Replace n with 20:
− 1 =
✖️ Multiplying with Variables
When you see 2 × n (or just 2n), it means "double the number."
When you see 3 × n (or 3n), it means "triple the number."
The number next to the letter tells you how many times to multiply!
2 Multiply It Out ✖️
Replace n with the given number, then multiply.
2 × n when n = 3
2 × 3 =
2 × n when n = 7
2 × =
3 × n when n = 4
3 × =
5 × n when n = 6
× =
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🧩 Two Steps: Multiply, Then Add or Subtract
Sometimes a formula has two operations. For example:
2 × n + 1 means "double n, then add 1."
2 × n − 1 means "double n, then subtract 1."
Always do the multiplication first, then the addition or subtraction.
Example: 2 × n − 1
| n | Step 1: 2 × n | Step 2: subtract 1 | Result |
|---|
| 1 | 2 × 1 = 2 | 2 − 1 | 1 |
| 2 | 2 × 2 = 4 | 4 − 1 | 3 |
| 3 | 2 × 3 = 6 | 6 − 1 | 5 |
The results are 1, 3, 5 — odd numbers! Keep going: n=4→7, n=5→9.
The formula 2n − 1 gives you the nth odd number.
3 Two-Step Formulas 🪜
Follow the steps: multiply first, then add or subtract.
2 × n + 1 when n = 3
Step 1: 2 × 3 =
Step 2: + 1 =
2 × n + 1 when n = 5
Step 1: 2 × =
Step 2: + 1 =
2 × n − 1 when n = 6
Step 1: 2 × 6 =
Step 2: − 1 =
2 × n − 1 when n = 10
Step 1: 2 × =
Step 2: − 1 =
4 Fill In the Table 📋
Use the formula 2 × n − 1 to fill in the missing values.
| n | 2 × n | 2 × n − 1 |
|---|
| 1 | | |
| 2 | | |
| 3 | | |
| 4 | | |
| 5 | | |
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5 What's the 50th Odd Number? 🤔
Use the formula 2 × n − 1 to find the answer without listing all the odd numbers!
The 50th odd number:
n = 50 → 2 × 50 − 1 =
The 100th odd number:
n = 100 → 2 × − 1 =
6 Mixed Practice 🎯
Use the given formula and value to find the answer.
n + 7 when n = 15
+ 7 =
4 × n when n = 8
4 × =
2 × n + 1 when n = 12
Step 1: 2 × 12 =
Step 2: + 1 =
2 × n − 1 when n = 25
Step 1: 2 × =
Step 2: − 1 =
🌟 Why Formulas Are Powerful
A formula like 2 × n − 1 lets you jump straight to any answer — even a huge one like the 1000th odd number — without writing out every number before it. Formulas also show up outside of math class: shops, recipes, and trips all use them!
7 Real-World Formulas 🌍
Use each formula to solve the real-world problem.
Cost = 3 × tickets
If tickets = 6:
3 × =
Distance = 5 × hours
If hours = 4:
5 × =
Total = n + 2 free books
If n = 9:
+ 2 =
Brother's age = n − 4
If n = 13:
− 4 =
8 Create Your Own Formula ✏️
Each sticker costs $2. Write a formula for the total cost, then use it.
My formula:
Cost = × stickers
Use your formula for 6 stickers:
Cost = × 6 =
Answer Key:
1) 7, 15, 6, 19 —
2) 6, 14, 12, 30 —
3) 6→7, 10→11, 12→11, 20→19 —
4) 2→1, 4→3, 6→5, 8→7, 10→9 —
5) 99, 199 —
6) 22, 32, 24→25, 50→49 —
7) 6→18, 4→20, 9→11, 13→9 —
8) Cost = 2 × stickers; 2 × 6 = 12.