Place value & the four operations

1Summary 重點摘要

Each digit has a different value depending on its position; for the four operations there is an order: brackets first, then multiply/divide, then add/subtract.

2Vocabulary cards Vocabulary

3Step by step Steps

1. 1. What is place value?Example: 365.
   
   
   
   　　3　6　5
   
   　　↑　↑　↑
   
   　　Hundreds　Tens　Ones
   
   
   
   5 in ones place = 5.
   
   6 in tens place = 60.
   
   3 in hundreds place = 300.
   
   
   
   So 365 = 300 + 60 + 5.
2. 2. Place orderRight to left, each step × 10:
   
   
   
   Ones → Tens → Hundreds → Thousands
   
   　　↓　　↓　　↓　　↓
   
   　　1　　10　100　1000
   
   
   
   Example: 4567 = 4000 + 500 + 60 + 7.
3. 3. Four operationsAdd: combine. 3 + 5 = 8.
   
   Subtract: take away. 8 − 3 = 5.
   
   Multiply: fast addition. 3 × 5 = 15.
   
   Divide: share equally. 15 ÷ 3 = 5.
4. 4. Order: multiply/divide firstExample: 2 + 3 × 4 = ?
   
   
   
   Wrong (left to right): 2 + 3 = 5, 5 × 4 = 20.
   
   Right (multiply first): 3 × 4 = 12, + 2 = 14.
   
   
   
   So 2 + 3 × 4 = 14, not 20.
5. 5. Brackets firstExample: (2 + 3) × 4 = ?
   
   
   
   Brackets first: 2 + 3 = 5.
   
   Then multiply: 5 × 4 = 20.
   
   
   
   Compare:
   
   　No brackets: 2 + 3 × 4 = 14
   
   　With brackets: (2 + 3) × 4 = 20
   
   
   
   Brackets change the answer!
6. 6. EstimateExample: 198 + 205 = ?
   
   
   
   Exact: 198 + 205 = 403.
   
   Estimate: 198 ≈ 200, 205 ≈ 200, 200 + 200 = 400.
   
   
   
   If you get 4000, you know it is wrong (estimate is 400).
   
   Estimate = quick check.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Brackets first → multiply/divide → add/subtract
• Place value changes with position
• Ones, tens, hundreds... each step × 10
• Estimate to catch big errors
• Choose the right operation for each problem