When adding large numbers, align digits by place value — ones under ones, tens under tens, hundreds under hundreds. Add from right to left. When a column total reaches 10 or more, carry the extra ten to the next column.
Example 1 — Calculate \(3456 + 2789\)
Step 1
Write the numbers in columns, ones aligned under ones.
Subtract right to left. If a top digit is smaller than the bottom digit, borrow (exchange) from the next column to the left — take 1 ten and convert it to 10 ones in the current column. When you borrow from a zero, you must chain-borrow.
Example 3 — Calculate \(5002 - 1487\)
Step 1
Ones: \(2 - 7\) — can't do it. Tens is 0, so chain-borrow from hundreds (also 0), then thousands.
Common mistake: Writing 0 when you try to subtract from 0 without borrowing. Always chain-borrow left until you find a non-zero digit.
✓ Quick Check 2 — Column Subtraction with Borrowing
Question 1 of 10
Real-Life Problems — Budgeting, Distance and Shopping
Many real-life problems require more than one step. Read carefully to decide whether to add or subtract (or both). Always check your answer makes sense.
Example 5 — Monthly budget (multi-step)
Step 1
Add all income: \(£1850 + £230 = £2080\)
Step 2
Add all expenses: \(£750 + £320 = £1070\), then \(£1070 + £415 = £1485\)
Step 3
Remaining: \(£2080 - £1485 = \mathbf{£595}\)
Example 6 — Shopping with change (multi-step)
Step 1
A shopper has £500. Items cost £127, £89, £214 and £36.
Step 2
Total spent: \(127 + 89 = 216\), then \(216 + 214 = 430\), then \(430 + 36 = £466\).
Step 3
Change: \(£500 - £466 = \mathbf{£34}\)
Try it: Distance Challenge
A route has three legs: 347 km, 528 km and 215 km. A driver has completed the first two legs. How far have they driven, and how far remains?
Total route: \(347 + 528 + 215 = 1090\) km. Driven: \(347 + 528 = 875\) km. Remaining: \(1090 - 875 = \mathbf{215}\) km.
✓ Quick Check 3 — Real-Life Addition and Subtraction
Question 1 of 10
Practice: Adding and Subtracting Whole Numbers
Enter your answers as numbers.
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Question
Answer
Result
1
4,582 + 3,976
2
12,340 − 7,865
3
A shop has 3,250 items in stock and sells 1,486. How many remain?
4
A school has 890 pupils. 215 more join. What is the new total?
5
£2,400 + £1,875 − £960
6
6,745 + 2,389
7
15,600 − 8,742
8
A warehouse has 5,400 boxes and receives 1,275 more. What is the new total?
9
A concert had 4,820 attendees; 1,340 left early. How many remained?
10
£3,200 − £1,150 + £480
⚠ Things to Watch Out For
Not aligning place values: Always line up digits by place value in column addition/subtraction — units under units, tens under tens. Misalignment is the most common error.
Forgetting to carry: When digits in a column add to 10 or more, write the units digit and carry the tens digit to the next column. A forgotten carry changes the entire answer.
Borrowing from zero: When subtracting 5,002 − 1,487, you must borrow across multiple columns. Work carefully through each column, updating the digits as you go.
Subtraction order: Always subtract the smaller number FROM the larger in each column (after borrowing). Never reverse the order within a column.
Not checking with the inverse: Always check your subtraction by adding the answer back to the number you subtracted: if 500 − 187 = 313, check 313 + 187 = 500.