Written addition under each other

Add thousands under each other too

How much is 347 + 285? Hard from the head. But on paper you can do it in half a minute — by a method called written addition.

The trick is simple: write the numbers under each other so that the floors line up — ones under ones, tens under tens, hundreds under hundreds. Then you add by columns, from the back, as if you were adding three small questions instead of one big one.

Sometimes a column “overflows”: the ones give more than 9, say 12. Then in the place you write only two and the one moves a floor up — it goes on. That is called a carry and it is the only snag of the whole method.

Written addition is a machine: when you line up the floors and do not forget the carry, you add 347 + 285 just as well as five-digit numbers. Learn it once, it works for ever.

Filip is saving for Lego and counting how much two dream boxes cost: 347 Kč and 285 Kč. He tries it from the head, but he keeps getting something different. Dad hands him paper: “Under each other. Ones under ones.” Filip writes 347, under that 285, underlines with a line. Seven and five is twelve — he writes two, he notes the one tiny at the top. Four and eight and one is thirteen — he writes three, the one goes on. Three and two and one is six. Result: 632 Kč. At last a number he believes.

💡

Write the carried one tiny above the next column, do not hold it in your head. The head should calculate, the paper should remember.

Method: line up, add from the back, carry

I will show you on 347 + 285.

Step 1: write under each other, floors line up.

  347
+ 285
-----

Seven above five (ones), four above eight (tens), three above two (hundreds).

Step 2: add the ones. 7 + 5 = 12. That is more than 9 → in the ones place write 2, the one goes on (write it small above the tens column).

Step 3: add the tens + the carry. 4 + 8 = 12, plus the carried 1 = 13. Write 3, the one goes on above the hundreds.

Step 4: add the hundreds + the carry. 3 + 2 = 5, plus 1 = 6. Write 6.

Result: 632.

Step 5: check by swapping. Add the numbers in the other order (285 + 347) or at least by estimating: 347 is almost 350, 285 almost 300, together around 650. 632 came out — close to the estimate, I believe it.

Why do you add from the back, from the ones? Because of carries. The one always moves up to a higher floor — and that must still be uncalculated, so it can take it in.

Adding with one carry

Example: 426 + 137.

  426
+ 137
-----

Ones: 6 + 7 = 13 → I write 3, the one goes on.

Tens: 2 + 3 = 5, plus 1 = 6 → I write 6.

Hundreds: 4 + 1 = 5 → I write 5.

Result: 563.

Estimate as a check: 430 + 140 = 570. 563 came out, they fit together.

A carry in two columns

Example: 456 + 378.

Ones: 6 + 8 = 14 → I write 4, one goes on.

Tens: 5 + 7 = 12, plus 1 = 13 → I write 3, one goes on.

Hundreds: 4 + 3 = 7, plus 1 = 8 → I write 8.

Result: 834.

Two carries in a row — and the method handled them as calmly as one. That is why it is a machine: the step repeats until the columns run out.

Numbers of different lengths

Example: 508 + 46.

Watch the write-up! The six belongs under the eight (ones under ones), the four under the zero (tens under tens). There are no hundreds in 46.

  508
+  46
-----

Ones: 8 + 6 = 14 → I write 4, one goes on.

Tens: 0 + 4 = 4, plus 1 = 5 → I write 5.

Hundreds: 5 and nothing → I write 5.

Result: 554.

⚠️

Most mistakes do not come from calculating, but from a crooked write-up. When you write 46 under 508 to the left (the four under the five), you add hundreds with tens and nonsense comes out. Always line up from the back: ones under ones. Squared paper is a friend.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. スタート with ten. When it goes well, add more.

Write under each other on paper, mark carries with a tiny one. Here only the result.

Practise the questions

On paper

Squared paper, one digit in one square.

Work out under each other: 235 + 143, 367 + 254, 489 + 178.
Work out under each other with a short number: 605 + 87, 730 + 96.
For each question from steps 1 and 2 first write an estimate (round in your head to hundreds) and after calculating compare.
Find the mistake in someone else’s calculation: 256 + 167 = 313. Recalculate under each other and write in which column the mistake happened. (Hint: watch the carry from the ones.)

Now you 💪

You write 508 + 46 under each other correctly — the six under the eight.
You can explain what “the one goes on” means and exactly where it goes.
You add 456 + 378 with two carries and get 834.

✅

Done when: You add any three-digit numbers under each other, you mark carries on paper and you compare the result with an estimate.

What to take from this lesson

Written addition: numbers under each other, ones under ones.
You add from the back, by columns.
Column over 9? Write the ones, the one goes on to the higher floor.
Write the carry tiny above the column — do not hold it in your head.
Check by estimating: round the addends and compare with the result.