How much is still missing?

Liri now knew the total distance to a far-off point on her map: 732 squares. She also knew how many she had already covered: 456.

Liri: “But how much is still missing before I reach my goal?”
Erklärus: “That is a subtraction – but with big numbers you do it differently from in your head. At every place you ask: how much is missing from the bottom number up to the top one? That is called the adding-on method.”

✍️ The adding-on method

In column subtraction you write the numbers one under the other, place by place, just like in addition. But you calculate differently: in every column you ask, from the bottom up: “How much is missing from the bottom digit to the top one?”

🔍 Example without a carry

Click on a digit to see the explanation:

6
5
8
−
2
3
4
4
2
4
← Click on a digit!

658 − 234 = 424 – no carry needed, because in every column the bottom digit is smaller.

🔥 Example with a carry – the biggest difficulty

With 732 − 456 it doesn’t work out in the ones column: adding on from 6 to 2 would need a negative number. So we borrow a 10.

1
1
7
3
2
−
4
5
6
2
7
6
← Click on a digit!
Liri: “732 − 456 = 276. I still have 276 squares to go to reach my goal!”

📝 Now you – without a carry

Liri has 869 squares to travel in total. She has already covered 345. How much is still missing? Fill in the columns yourself:

HTO
8
6
9
−
3
4
5

📝 Now you – with two carries

Another stretch of the route: 613 squares in total, 258 already covered. Careful, here you have to borrow twice!

HTO
6
1
3
−
2
5
8
🌌 Big numbers in the universe

Halley’s Comet takes 76 years to go once around the Sun.
A day on Venus lasts longer than its whole year: 243 Earth days!
Without column subtraction, astronomers couldn’t work out how many years are left until a comet next returns.

❌ Common mistake

In the adding-on method the carry is added to the bottom number of the next column – not to the top one!

Example: 732 − 456 → in the tens column you work out 5 + 1 (carry) = 6 at the bottom, not 3+1 at the top.

Tip: the little carry always goes to the number that is being subtracted (bottom), not to the number it is subtracted from (top)!

The rest of the way

Liri had now worked out three missing distances: 424, 276, 524. Every number brought her closer to her goal.

Liri: “Now I always know exactly how much I still have to go.”
Erklärus: “That is the power of subtraction. It doesn’t only show what is left – it also shows how far the way to the goal still is.”
“Column subtraction: the adding-on method asks column by column: how much is missing from the bottom up to the top? When borrowing, the carry moves to the bottom number of the next column.”
What you learned today
732 − 456 = 276
Adding-on method: add on from the bottom to the top  ·  the carry goes to the bottom number
🌟

Chapter 16 mastered!

Liri can now work out how much of the way she still has to go – with the written adding-on method up to 1,000.

Erklärus’s notebook – page 16:
“Column subtraction: adding-on method. Ask column by column: how much is missing from the bottom up to the top? With a carry: add the borrowed 10, then add the carry to the bottom number of the next column.”
← Back to overview 16 – Column Subtraction