Class 3 — Mathematics
Addition and Subtraction of 4-Digit Numbers with Regrouping
Class 3
- ✓By the end of this lesson students will be able to add two 4-digit numbers with regrouping (carrying over).
- ✓By the end of this lesson students will be able to subtract a 4-digit number from another 4-digit number with regrouping (borrowing).
- ✓By the end of this lesson students will be able to understand and apply the concept of regrouping in both addition and subtraction.
- ✓By the end of this lesson students will be able to solve simple word problems involving addition and subtraction of 4-digit numbers with regrouping.
Key concepts
Every digit in a number has a specific place value. For a 4-digit number, we have digits in the Ones, Tens, Hundreds, and Thousands places. Understanding place value is fundamental for correctly performing addition and subtraction, especially when regrouping.
When the sum of the digits in any place value column is 10 or more, we 'regroup' or 'carry over'. For example, if the sum of the Ones column is 15, we write 5 in the Ones place and carry over 1 Ten to the Tens column. We always start adding from the rightmost column (Ones place) and move towards the left.
When a digit in the top number is smaller than the digit below it in the same place value column, we 'regroup' or 'borrow'. We borrow 1 from the digit in the next higher place value column, which is equal to 10 units of the current place value. For example, if we need to subtract 7 from 3 in the Ones place, we borrow 1 Ten (which is 10 Ones) from the Tens place, making the 3 into 13. We always start subtracting from the rightmost column (Ones place) and move towards the left.
Key facts to remember
- 1Always start addition and subtraction from the Ones place (rightmost digit).
- 2In addition, when the sum of a column is 10 or more, we 'carry over' the Tens part to the next higher place value column.
- 3In subtraction, when a digit in the top number is smaller than the digit below it, we 'borrow' from the next higher place value column.
- 4When borrowing, 1 unit from the left becomes 10 units for the current column (e.g., 1 Ten becomes 10 Ones).
- 5Place value is crucial for correctly performing regrouping in both addition and subtraction.
- 6Addition and subtraction are inverse operations; one can be used to check the other.
Worked examples
Example 1
Add 3458 and 2765.
Answer
6223
Example 2
Subtract 1876 from 5342.
Answer
3466
Example 3
A library has 4567 storybooks and 3895 textbooks. How many books are there in total? If 1250 books were issued, how many books are left in the library?
Answer
There are 8462 books in total. 7212 books are left in the library.
Always read the word problem carefully to identify whether to add or subtract, or both.
Common mistakes
- ✗Not aligning numbers correctly according to their place values (Ones under Ones, Tens under Tens, etc.).
- ✗Forgetting to add the 'carried over' digit in addition to the next column.
- ✗Forgetting to reduce the digit from which 'borrowing' was done in subtraction.
- ✗Borrowing from the wrong place value or borrowing incorrectly (e.g., borrowing 1 instead of 10 units for the current column).
- ✗Starting calculations from the Thousands place instead of the Ones place.
Exam tips
- ★Always write numbers neatly in columns, aligning digits according to their place values.
- ★Show your regrouping (carry-over or borrow) clearly above the digits to avoid confusion and help with checking.
- ★After solving, quickly check your answer using the inverse operation (e.g., check subtraction with addition, or vice versa).
- ★Read word problems carefully to understand what operation(s) are required before starting to solve.
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