Class 4 — Mathematics
Addition and Subtraction of Large Numbers
Class 4
- ✓Add large numbers (up to 6 digits) accurately using the column method.
- ✓Subtract large numbers (up to 6 digits) accurately, including regrouping (borrowing) across multiple places.
- ✓Solve word problems involving addition of large numbers by identifying keywords and forming appropriate statements.
- ✓Solve word problems involving subtraction of large numbers by identifying keywords and forming appropriate statements.
- ✓Solve multi-step word problems involving both addition and subtraction of large numbers.
Key concepts
When adding large numbers, we write the numbers one below the other, aligning the digits according to their place values (ones, tens, hundreds, thousands, ten thousands, lakhs). We always start adding from the ones place. If the sum of digits in any column is 10 or more, we carry over the tens digit to the next higher place value column.
For subtracting large numbers, we also arrange the numbers in columns according to their place values. We begin subtracting from the ones place. If a digit in the top number (minuend) is smaller than the digit below it (subtrahend), we 'borrow' or 'regroup' 1 from the digit in the next higher place value. This borrowed 1 becomes 10 units in the current place value, allowing subtraction. The digit from which we borrowed decreases by 1.
Word problems require us to read carefully and understand the situation. We need to identify what information is given and what needs to be found. Look for keywords that suggest addition (e.g., 'total', 'sum', 'altogether', 'in all') or subtraction (e.g., 'difference', 'how many more/less', 'left', 'remaining'). After identifying the operation, write clear statements for each step of your calculation and present the final answer with appropriate units.
Key facts to remember
- 1Always arrange numbers in columns according to their place values before performing addition or subtraction.
- 2Start all calculations (addition and subtraction) from the ones place (the rightmost digit).
- 3In addition, if the sum of digits in a column is 10 or more, 'carry over' the tens digit to the next higher place value column.
- 4In subtraction, if a digit in the minuend is smaller than the digit in the subtrahend, 'borrow' 1 from the next higher place value. Remember that the borrowed 1 becomes 10 units in the current place.
- 5Keywords like 'total', 'sum', 'altogether', 'in all' usually indicate addition.
- 6Keywords like 'difference', 'how many more/less', 'left', 'remaining' usually indicate subtraction.
- 7Always double-check your calculations to avoid simple errors.
Worked examples
Example 1
Add 2,34,567 and 1,89,321.
Answer
4,23,888
Always start adding from the rightmost column (ones place).
Example 2
Subtract 3,45,678 from 5,00,000.
Answer
1,54,322
Be very careful when borrowing across multiple zeros. It is a common source of error.
Example 3
A library has 75,890 storybooks and 48,325 textbooks. If 12,500 books were issued last month, how many books are still in the library?
Answer
1,11,715 books are still in the library.
Break down word problems into smaller, manageable steps. Write clear statements for each step.
Common mistakes
- ✗Not aligning the numbers correctly by their place values, leading to incorrect sums or differences.
- ✗Forgetting to carry over digits in addition, especially when sums exceed 9.
- ✗Making errors while borrowing in subtraction, particularly when borrowing across multiple zeros.
- ✗Performing the wrong operation (addition instead of subtraction, or vice-versa) in word problems.
- ✗Not writing the final answer with appropriate units (e.g., 'books', 'rupees') in word problems.
Exam tips
- ★Read each word problem carefully at least twice to fully understand the question and identify the necessary operations.
- ★Show all your working steps clearly for both addition/subtraction and word problems. This helps in getting partial marks even if the final answer is incorrect.
- ★After completing a calculation, quickly re-check it, perhaps by adding/subtracting in the reverse order or using estimation.
- ★For word problems, write a concluding statement that answers the question asked in the problem.
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