🎯 Number Fundamentals: Basic Arithmetic
The Kitchen Recipe Analogy 🍳
Imagine you’re a chef following a recipe. Just like cooking has a specific order (you can’t frost a cake before baking it!), math has rules about what to do first. Let’s learn these kitchen rules of math!
🔢 BODMAS and Simplification
What is BODMAS?
BODMAS is like a recipe card that tells you the ORDER of cooking steps in math.
| Letter | Stands For | Kitchen Meaning |
|---|---|---|
| B | Brackets | Open the ingredient box first |
| O | Orders (powers) | Prep your special sauces |
| D | Division | Cut things into pieces |
| M | Multiplication | Mix ingredients together |
| A | Addition | Add more stuff |
| S | Subtraction | Take some away |
🌟 The Golden Rule
Always work from LEFT to RIGHT when operations have the same priority!
Think of it like reading a book - you go left to right, page by page.
Simple Example: Solving 8 + 4 × 2
❌ Wrong way: 8 + 4 = 12, then 12 × 2 = 24
✅ Right way using BODMAS:
- Look for Brackets → None
- Look for Orders → None
- Look for Division/Multiplication → Found! 4 × 2 = 8
- Now do Addition → 8 + 8 = 16
Answer: 16 ✨
Example with Brackets: (5 + 3) × 2
Step 1: Solve inside brackets first
(5 + 3) = 8
Step 2: Now multiply
8 × 2 = 16
Answer: 16 ✨
The brackets are like a VIP room - deal with them first!
Harder Example: 20 ÷ 4 + 3²
Step 1: Orders first (3² means 3 × 3)
3² = 9
Step 2: Division next
20 ÷ 4 = 5
Step 3: Finally, add
5 + 9 = 14
Answer: 14 ✨
🥧 Fractions: Sharing the Pizza
What is a Fraction?
A fraction shows parts of a whole. Imagine cutting a pizza!
1 ← How many slices you get
---
4 ← Total slices in the pizza
1/4 means: You get 1 slice out of 4 total slices.
Types of Fractions
| Type | Example | What It Means |
|---|---|---|
| Proper | 3/4 | Top < Bottom (less than 1 pizza) |
| Improper | 5/4 | Top > Bottom (more than 1 pizza) |
| Mixed | 1¼ | A whole number + a fraction |
Adding Fractions (Same Bottom Number)
When pizzas have the same number of slices:
1 2 3
--- + --- = ---
5 5 5
Just add the top numbers!
Adding Fractions (Different Bottom Numbers)
When pizzas have different slice sizes:
1 1
--- + --- = ?
2 4
Step 1: Find a common bottom (4 works!)
Step 2: Convert 1/2 to 2/4
Step 3: Add: 2/4 + 1/4 = 3/4
Answer: 3/4 ✨
Multiplying Fractions
Super easy! Multiply tops, multiply bottoms:
2 3 6 3
--- × --- = --- = ---
4 5 20 10
(We can simplify 6/20 by dividing
both by 2 to get 3/10)
Dividing Fractions: The Flip Trick!
To divide fractions, FLIP the second one and MULTIPLY:
1 1
--- ÷ --- = ?
2 4
Flip 1/4 to get 4/1
1 4 4
--- × --- = --- = 2
2 1 2
Answer: 2 ✨
🔵 Decimals: The Point of Precision
What is a Decimal?
Decimals are fractions in disguise! The dot (.) separates whole numbers from parts.
3.25
↑ ↑↑
│ └┴─ Parts (25 hundredths)
└──── Whole number (3)
3.25 = 3 + 25/100 = 3¼
Place Values After the Decimal
| Position | Name | Value |
|---|---|---|
| .1 | Tenths | 1/10 |
| .01 | Hundredths | 1/100 |
| .001 | Thousandths | 1/1000 |
Example: 0.456 = 4 tenths + 5 hundredths + 6 thousandths
Converting Fractions to Decimals
Just divide the top by the bottom!
3
--- = 3 ÷ 4 = 0.75
4
1
--- = 1 ÷ 2 = 0.5
2
Adding and Subtracting Decimals
Key Rule: Line up the decimal points!
12.50
+ 3.75
-------
16.25
Always stack the dots on top of each other!
Multiplying Decimals
2.5 × 0.4 = ?
Step 1: Ignore decimals, multiply
25 × 4 = 100
Step 2: Count decimal places
2.5 has 1, 0.4 has 1
Total = 2 places
Step 3: Put decimal 2 places from right
100 → 1.00 = 1
Answer: 1 ✨
🎯 Approximation Techniques
What is Approximation?
Sometimes we don’t need the exact answer - just a close guess! Like estimating how many candies are in a jar.
Rounding Numbers
The 5 Rule: Look at the digit to the right.
- If it’s 5 or more → Round UP
- If it’s 4 or less → Round DOWN
| Number | Round to Nearest 10 |
|---|---|
| 43 | 40 (3 < 5, round down) |
| 78 | 80 (8 ≥ 5, round up) |
| 65 | 70 (5 = 5, round up) |
Estimating Calculations
Example: What’s approximately 48 × 21?
Step 1: Round each number
48 → 50
21 → 20
Step 2: Multiply the rounded numbers
50 × 20 = 1,000
Actual answer: 1,008
Our estimate: 1,000
Pretty close! ✨
Estimating with Decimals
Example: Estimate 4.89 + 3.12
Round each:
4.89 → 5
3.12 → 3
Estimate: 5 + 3 = 8
Actual: 8.01
Spot on! ✨
When to Use Approximation?
| Use Approximation When… | Use Exact When… |
|---|---|
| Shopping (total budget) | Paying the bill |
| Time to reach somewhere | Meeting time |
| Cooking for “about 10 people” | Medicine dosage |
🧠 Quick Memory Tricks
BODMAS Phrase
“Big Old Dragons Make Angry Sounds”
Brackets, Orders, Division, Multiplication, Addition, Subtraction
Fraction Division
“Keep, Change, Flip”
Keep first fraction, Change ÷ to ×, Flip second fraction
Decimal Addition
“Dots in a line, answer will be fine!”
Rounding
“5 or more, let it soar. 4 or less, let it rest.”
🎮 Summary Flow
graph TD A["See a Math Problem"] --> B{Any Brackets?} B -->|Yes| C["Solve brackets first"] B -->|No| D{Any Powers?} C --> D D -->|Yes| E["Calculate powers"] D -->|No| F{× or ÷ ?} E --> F F -->|Yes| G["Do left to right"] F -->|No| H{+ or − ?} G --> H H -->|Yes| I["Do left to right"] I --> J["✨ Done!"] H -->|No| J
🌟 You’ve Got This!
Remember:
- BODMAS is your recipe order
- Fractions are just pizza slices
- Decimals are fractions in disguise
- Approximation is smart guessing
Math isn’t scary - it’s just following simple rules, one step at a time! 🚀