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Column multiplication

Level 2 · Ages 8–11

Quick recall· Let's wake up what you already know before we start.

Recall: what is 8 + 8 + 8?

The whole lesson

Read it again any time, including while you work through the exercises.

You are packing cakes into boxes: 6 boxes of 47 cakes. You could compute 47 + 47 + 47 + 47 + 47 + 47... but what a waste of time! Multiplication does exactly that job: 47 × 6 means 6 times the number 47, all at once.

To multiply a big number, set it out in columns, just like addition. Multiply the units first: if the result goes past 9, write the units digit and carry the rest. For example 7 × 6 = 42: I write 2 and carry 4. Then multiply the tens and add the carry.

What if the second number also has two digits, like 34 × 26? We split the work: 34 × 6 first, then 34 × 20. Multiplying by 20 means multiplying by 2 and then by 10: that is why we shift the second line one place to the left (or write a 0 on the right). Finally, we add the two lines.

One last champion habit: before computing, estimate the size of the answer. 34 × 26 is close to 30 × 30 = 900. If you get 88 or 9000, you will instantly know something went wrong!

The worked example, step by step

Set out and compute 47 × 6.

  1. 7 × 6 = 42

    I multiply the units: 42 is 2 units and 4 tens. I write 2 and carry 4.

  2. 4 × 6 = 24, puis 24 + 4 = 28

    I multiply the tens and add the carry: 24 + 4 = 28. I write 28.

Result: 47 × 6 = 282

Set out and compute 34 × 26.

  1. 34 × 6 = 204

    First line: I multiply 34 by the units of 26. 4 × 6 = 24, write 4 and carry 2; 3 × 6 = 18, plus 2 makes 20.

  2. 34 × 20 = 680

    Second line: I multiply 34 by 2 tens. I shift one place (the tens 0), then 34 × 2 = 68.

  3. 204 + 680 = 884

    I add the two lines. Size check: close to 30 × 30 = 900, so it makes sense.

Result: 34 × 26 = 884