Written multiplying · البرمجة مع مارتن

Times a number under each other, digit by digit

How much is 234 × 3? The small times tables are not enough — 234 is not in them. But it is enough to use them three times in a row. That is called written multiplying.

The idea: split 234 into floors (200 + 30 + 4) and times each floor by three on its own: 4 × 3 = 12, 30 × 3 = 90, 200 × 3 = 600. Add: 702.

The written method under each other does exactly that, only more tightly — it times the floors from the back and passes carries straight away, like in adding. You go from the right: ones, tens, hundreds. What overflows past nine, you send on with a one (or a two!).

Everything you need you already know: the small times tables, zeros from the last lesson and carries from adding. Today we just join them together.

Tereza is getting a trip ready with the club. 156 children are going… wait — 156 sandwiches? The leader says it differently: “We need 4 sandwiches for each child and there are 156 children. How many to order?” Tereza takes paper: 156 × 4. Six times four is 24 — she writes 4, two goes on. Five times four is 20, and two is 22 — she writes 2, two goes on. One times four is 4, and two is 6. Order: 624 sandwiches. The leader checks by estimating: 150 × 4 is 600. It fits, they order.

💡

A carry in multiplying does not have to be only a one — easily a two or a three (from 6 × 4 = 24, 2 goes on). Write it tiny above the next column, like in adding.

Method: times from the back, carry, write

I will show you on 234 × 3.

Step 1: write under each other:

  234
×   3
-----

Step 2: ones. 4 × 3 = 12. I write 2, the one goes on.

Step 3: tens. 3 × 3 = 9, plus the carried 1 = 10. I write 0, the one goes on.

Step 4: hundreds. 2 × 3 = 6, plus 1 = 7. I write 7.

Result: 702.

Notice the rhythm of each column: times, add the carry, write the ones, send the rest on. Over and over, until the digits run out.

Step 5: check by estimating. 234 is about 200 to 250; times 3 gives 600 to 750. Result 702 is inside. I believe it.

One more check, a quick one: the last digit. The ones of the result must match the ones of the product of the last digits: 4 × 3 = 12, so the result must end in two. 702 ends in two. It fits.

Important: the carry is added only after multiplying. First 3 × 3 = 9, then + 1 = 10. Whoever adds the carry before multiplying (3 + 1 = 4, then × 3 = 12) gets nonsense.

One carry

Example: 123 × 4.

  123
×   4
-----

Ones: 3 × 4 = 12 → I write 2, one goes on.

Tens: 2 × 4 = 8, plus 1 = 9 → I write 9.

Hundreds: 1 × 4 = 4 → I write 4.

Result: 492.

Estimate: 123 is about 120, 120 × 4 = 480. إغلاق to 492, it fits.

A big carry — two goes on

Example: 156 × 4.

Ones: 6 × 4 = 24 → I write 4, two goes on.

Tens: 5 × 4 = 20, plus 2 = 22 → I write 2, two goes on.

Hundreds: 1 × 4 = 4, plus 2 = 6 → I write 6.

Result: 624.

Estimate: 150 × 4 = 600. It fits. A carry bigger than one is normal in multiplying — it happens whenever the product in a column goes over twenty.

A zero inside a number

Example: 408 × 5.

Ones: 8 × 5 = 40 → I write 0, four goes on.

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

Hundreds: 4 × 5 = 20 → I write 20 (last column, the carry has nowhere to go, you write the whole thing).

Result: 2 040.

A zero inside a number is not a problem — times it honestly (it gives zero) and add the carry. You must not skip it, it holds the floor.

⚠️

The order in a column is sacred: first times, then add the carry. 3 × 3 + 1 = 10, never (3 + 1) × 3 = 12. Whoever adds first gets a different — wrong — result.

Practice: now you do it 🎲

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

Calculate under each other on paper. Rhythm: times, add the carry, write, send on.

Practise the questions

On paper

For each calculation write an estimate too. The estimate is your nonsense detector.

Work out under each other: 213 × 3, 142 × 4, 325 × 2.
Work out with big carries: 156 × 6, 278 × 3, 449 × 5.
Work out with a zero inside: 306 × 4, 570 × 3.
Sandwich problem: for a party you need 3 canapés for each of 84 guests. Write the write-up, the estimate, the calculation under each other and the answer in a full sentence.

Now you 💪

You know the column rhythm: times, add the carry, write the ones, send the rest on.
You work out 156 × 4 with two-carries and get 624.
Before every calculation you say an estimate and after it you compare.

✅

Done when: You times a three-digit number by a one-digit number under each other, you handle carries even bigger than one, and you watch the result with an estimate.

What to take from this lesson

Written multiplying = the small times tables used on each floor on its own, from the back.
Column rhythm: times, add the carry, write, send on.
A carry can be 2 or 3 as well — it comes from big products.
First times, then add the carry. Never the other way.
An estimate before calculating (150 × 4 ≈ 600) catches big mistakes at once.