Too big for key facts

Liri wanted to know how many squares there are altogether in 25 map sections if each section has 243 squares.

Liri: “243 × 25? I can’t work that out from key facts any more, like 6×7.”
Erklärus: “With numbers as big as these you split the problem up in writing – into two smaller multiplications that you add together at the end.”

✍️ Write them side by side, two rows, then add

We write both numbers side by side with a times sign between them – not one under the other. Then you split the second number into tens and ones, e.g. 37 = 30 + 7. First you multiply by the tens digit (the 3, which really stands for 30), then by the ones digit (the 7). At the end both rows are added.

At the end of the first row a red zero is added – it shows that we really multiplied by 30 (not just 3).

🔍 An example – step by step

We write both numbers side by side, not one under the other. Click on a digit to see the explanation:

4
2
×37
1
2
6
0
← × 3 × 10
+
2
9
4
← × 7
1
5
5
4
← Click on a digit!

The red zero shows: because we are multiplying by the tens digit of 37 (so really by 30), the answer shifts one place to the left. In the second row (times 7, ones digit) this zero isn’t needed – nothing shifts here.

Liri: “42 × 37 = 1554! And now I also know why the second row always starts one place further to the right.”

📝 Now you

For 132 days, a satellite sends 24 photos every day. How many photos altogether? Work it out in writing – fill in both rows and the answer yourself:

1
3
2
×24
← × 2 × 10
+
← × 4
🌌 Big numbers in the universe

The Hubble Space Telescope orbits the Earth 15 times a day – in a year that is over 5000 orbits.
Multiplication helps to work out, from small daily numbers (like photos or orbits), the huge totals for a whole year.

❌ Common mistake

The zero at the end of the first row is often forgotten!

Because you are really multiplying by the tens digit (20, not just 2), the answer has to shift one place to the left – the free place on the far right is filled with a 0.

Tip: before you calculate, write the zero straight down as a placeholder, then it can’t be forgotten!

Two rows, one answer

Liri had learned that even huge multiplications are made of smaller building blocks.

Liri: “I split the big problem up – and at the end I put it back together.”
Erklärus: “That is exactly the art of mathematics: splitting big problems into small, familiar steps.”
“Long multiplication: first multiply by the tens digit (add a zero!), then by the ones digit, and finally add both rows.”
What you learned today
243 × 25 = 6075
Tens digit first (add a zero!) · then ones digit · finally add
🌟

Chapter 21 mastered!

Liri can now solve even huge multiplications in writing.

Erklärus’s notebook – page 21:
“Long multiplication: split the second number into tens + ones. First multiply by the tens digit (shift the answer one place, add a zero), then by the ones digit. Add both rows at the end.”
← Back to overview 21 – Long Multiplication