Learn · Mathematics · Class 4

Addition & Subtraction to 10,000

Adding and subtracting big numbers by keeping the columns lined up.

8 parts
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📘 DefinitionPlace value goes furtherPart 1 of 8
Line up the columnsThHTO34582127+568518 + 7 = 15 → write 5, carry 1Always start from the ones column on the right
Ones under ones, tens under tens. Start from the right.
🧮 EquationsCarrying and borrowingPart 3 of 8
✏️ Worked exampleA full worked subtractionPart 4 of 8
🌍 In the real worldWhere big numbers turn upPart 5 of 8
⚠️ Common mistakesWhere it usually goes wrongPart 6 of 8
✅ SummaryWhat to rememberPart 7 of 8
Shelves of books, the kind of quantity that needs four-digit arithmetic to keep track of. Photo: 1904.CC, CC BY 4.0, via Wikimedia Commons.
Shelves of books, the kind of quantity that needs four-digit arithmetic to keep track of. Photo: 1904.CC, CC BY 4.0, via Wikimedia Commons.
1📘 DefinitionPart 1 / 8

Place value goes further

A four-digit number is made of thousands, hundreds, tens and ones.

3458 = 3000 + 400 + 50 + 8

The position of a digit decides its value. In 3458 the 4 is worth 400, not 4. Move it one place left and it would be worth 4000.

Everything in this lesson follows from that one idea.

2🧩 The partsPart 2 / 8

Lining up the columns

When you add or subtract, write the numbers so that ones sit under ones, tens under tens, and so on.

Then work from the right, one column at a time.

Getting the columns straight is most of the job. Most wrong answers come from a digit in the wrong place, not from a wrong sum.

3🧮 EquationsPart 3 / 8

Carrying and borrowing

Carrying: when a column adds to 10 or more, the extra ten belongs in the next column left.

8 + 7 = 15 → write 5, carry 1

Borrowing: when the top digit is too small, take one from the column to its left. That one is worth ten here.

4 − 7 will not work
borrow: 14 − 7 = 7

Remember the column you borrowed from is now one smaller.

4✏️ Worked examplePart 4 / 8

A full worked subtraction

Question. 5203 − 1476

Ones: 3 − 6 will not work. Borrow from the tens, but the tens digit is 0, so borrow from the hundreds first.

Result: 13 − 6 = 7

Tens: 9 − 7 = 2   Hundreds: 1 − 4 → borrow → 11 − 4 = 7   Thousands: 4 − 1 = 3

5203 − 1476 = 3727

Check it: add your answer back. 3727 + 1476 = 5203. It matches, so the answer is right.

5🌍 In the real worldPart 5 / 8

Where big numbers turn up

Money. A bicycle costs Rs 8,500 and you have Rs 6,750. How much more do you need? That is a four-digit subtraction.

Distances. Karachi to Lahore is about 1,200 km; Lahore to Peshawar about 500 km. Adding journeys is the same skill.

Populations and scores. Newspapers, cricket totals and school registers all use numbers in the thousands.

Estimating first is the habit worth building: 5203 − 1476 is roughly 5200 − 1500 = 3700, so an answer of 3727 looks right and an answer of 6727 clearly does not.

6⚠️ Common mistakesPart 6 / 8

Where it usually goes wrong

  • Columns not lined up. Write neatly, or use squared paper.
  • Starting from the left. Always begin with the ones.
  • Forgetting the carried 1 in the next column.
  • Borrowing without reducing the column you borrowed from.
  • Not checking. Adding the answer back catches almost every slip.
7✅ SummaryPart 7 / 8

What to remember

  • Position decides value.
  • Line up the columns; start from the right.
  • Carry when over 10, borrow when too small.
  • Estimate first, check afterwards.
8✏️ Worked examplePart 8 / 8

Watch one worked through

Here is one done slowly, with the reason for every move. Then one for you.

Let me show you

A school has 4206 books. It gives 1478 away. How many are left?

  1. 4206 − 1478
    Write it as 4206 - 1478, lining the columns up by place value.
    Ones under ones, tens under tens. Lining numbers up by their right-hand edge works here only because both have four digits; line up by place value and it works every time.
  2. 16 − 8 = 8
    Ones: 6 - 8 will not go, so borrow a ten. 16 - 8 = 8.
    Borrowing moves one ten into the ones column as ten ones. Nothing is created, the number is only written differently.
  3. 9 − 7 = 2
    Tens: the 0 became 9 after the borrow travelled through. 9 - 7 = 2.
    When you borrow across a zero the zero becomes 9, because you took one from the hundreds and gave ten to the ones.
  4. 11 − 4 = 7
    Hundreds: 1 left after lending. 1 - 4 will not go, so borrow again. 11 - 4 = 7.
    A second borrow is normal. Check each column in turn rather than trying to see the whole sum at once.
  5. 4206 − 1478 = 2728
    Thousands: 3 - 1 = 2. The answer is 2728.
    Estimate to check: 4200 - 1500 is about 2700, so 2728 is believable. An estimate catches a slipped digit in seconds.

Answer: 2728

Now you try

Work out 5003 - 2647.

Show the answer

2356

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