Check every column before you start. Any of them might be short.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Unbundling can chain
To subtract from 5,003 you may need to break a thousand, then a hundred, then a ten.
The number never changes
5,003 becomes 4 thousands, 9 hundreds, 9 tens and 13 ones. Still 5,003.
Check by adding
Add your answer to what you took away. It should return the number you started with.
Step 2: Try It Yourself
Tap and try it out.
Start with
Taken away
What is left
Hundreds
2
Tens
5
Ones
6
503 − 247 = 256
Take 247 away from 503. The faded blocks are the ones that left.
Hundreds
5
Tens
0
Ones
3
5 hundreds, 0 tens and 3 ones is 503.
5003−2467
5,003, take away 2,467
Step 0 of 5
5,003 − 2,467 = …
Step 3: In Real Life
A car’s mileage
A car shows 40,000 miles. Last year it showed 27,458. 40,000 − 27,458 = 12,542 miles driven. The zeros on top mean unbundling across several places.
Step 4: Watch an Example
One step at a time.
Watch Leo Cross Two Zeros
Leo works out 5,003 − 2,467.
- Step 1
He checks the ones: 3, and 7 have to go. Not enough.
Step 5: Your Turn
Practice makes it stick.
The Target
Problem 1 of 2
A target of 8,000 has 3,465 done. How many are left?
left
The Collection
Problem 2 of 2
A collection of 6,240 loses 1,875. How many are left?
left
Subtract and Check
1 of 3
4,532 − 1,876 = ?
2 of 3
7,000 − 2,345 = ?
3 of 3
Check it: 4,655 + 2,345 = ?
Build the Answer
Build it, then check.
What is 503 take away 247? Build the answer.
Nothing.
You need ten ones before you can bundle.
Hundreds
0
Tens
0
Ones
0
0 hundreds, 0 tens and 0 ones is 0.
Step 6: Quick Check
Show what you know.
Question 1 of 2
6,004 − 2,738 = ?
Question 2 of 2
Does unbundling change the number?
What You Learned
- Check every column before you start.
- Unbundling can chain across several places.
- Check the answer by adding it back.
For the grown-up
This lesson is where the child subtracts multi-digit whole numbers fluently, including across zeros. Each place is ten times the one to its right, and that single rule generates the whole system all the way to a million and, later, all the way down past the decimal point.
Watch for large numbers read digit by digit. "Four hundred and seven thousand" is a structure; "four zero seven" is a phone number.
Have them say the number aloud before working with it. Most errors with big numbers are reading errors that the arithmetic then faithfully preserves.
Unbundling, several columns at once — When a column has too little to subtract from, open one unit from the column to its left: a thousand becomes ten hundreds, a hundred becomes ten tens. The value of the number is unchanged — only its packaging. This is the whole of multi-digit subtraction.
Unbundling across zeros — In 5,003 - 2,478 the tens and hundreds are both empty, so you must go left to the thousands and cascade: 5,003 becomes 4 thousands, 9 hundreds, 9 tens and 13 ones. Do the whole cascade first, writing every change down, and only then start subtracting.
Check by adding back — If 5,003 - 2,478 = 2,525, then 2,525 + 2,478 should return 5,003. It does. This check uses a different operation, so it is genuinely independent of the work you just did — unlike re-reading your own subtraction, which tends to repeat the same mistake.
When counting up is easier — For 5,003 - 4,987 the numbers are close, so counting up beats unbundling: 4,987 to 5,000 is 13, then 3 more is 16. Recognizing when the algorithm is the wrong tool is part of being genuinely fluent rather than merely trained.
Break open the next unit along — 50,000 − 23,456. Ones: 0 − 6. Nothing to break next door, so keep going left until you find something. Break the 5 ten-thousands into 4 ten-thousands and 10 thousands, then cascade down. Now every column has enough. 26,544. Check it: 26,544 + 23,456 = 50,000.