Bigger number on top, four columns, ones first. Where the top digit is smaller, borrow from the next column to the left and cross out.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Try it first
A yard had 3,562 bricks. 1,427 are used. How many are left?
bricks
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
One borrow
8,204 − 3,678. Ones: 4 is less than 8. The tens are 0, so borrow from the hundreds: 2 becomes 1, the 0 becomes 9, the 4 becomes 14. 14 − 8 = 6.
Keep going
Tens: 9 − 7 = 2. Hundreds: 1 is less than 6, borrow from the thousands: 8 becomes 7, 1 becomes 11. 11 − 6 = 5. Thousands: 7 − 3 = 4. The answer is 4,526.
Across two zeros
5,000 − 2,637. Ones: 0 is less than 7. Tens and hundreds are both 0. Borrow from the thousands: 5 becomes 4, both zeros become 9, and the last 0 becomes 10.
Across zeros means borrowing from the nearest column that has something, and every zero passed on the way becomes 9.
Then it is ordinary
10 − 7 = 3. 9 − 3 = 6. 9 − 6 = 3. 4 − 2 = 2. The answer is 2,363. Check: 2,363 + 2,637 = 5,000.
Why the zeros become 9
A thousand is ten hundreds. One of them is broken into ten tens, and one of those into ten ones. Nine hundreds and nine tens are left, which is what the two 9s say.
Step 2: Try It Yourself
Press Next step. Watch both zeros turn into 9s.
5000−2637
Step 0 of 5
5,000 − 2,637 = …
7119148204−36784526
8,204 − 3,678 = 4,526
- 1Ones: 4 is less than 8, so borrow from the hundreds. 2 becomes 1, the 0 in between becomes 9, and 4 becomes 14.
- 2Ones: 14 − 8 = 6. Write 6.
- 3Tens: 9 − 7 = 2. Write 2.
- 4Hundreds: 1 is less than 6, so borrow from the thousands. 8 becomes 7, and 1 becomes 11.
- 5Hundreds: 11 − 6 = 5. Write 5.
- 6Thousands: 7 − 3 = 4. Write 4. 8,204 − 3,678 = 4,526. Check: 4,526 + 3,678 = 8,204.
Step 3: In Real Life
A car’s mileage
The car had done 5,000 miles at the start of the year and 2,637 were done before the summer. 5,000 − 2,637: borrow across two zeros, and the working shows 2,363 miles left in the year’s plan.
Step 4: Watch an Example
One step at a time.
Watch Dev Borrow Past Two Zeros
Dev works out 7,006 − 3,428 on the board. Press Next step to watch each move.
7006−3428
Step 0 of 5
7,006 − 3,428 = …
Watch Priya Borrow Twice
Priya works out 4,103 − 1,856 on the board. Watch for her two borrows.
4103−1856
Step 0 of 6
4,103 − 1,856 = …
Step 5: Your Turn
Practice makes it stick.
The Theater
Problem 1 of 11
A theater has 3,000 seats. 1,846 tickets are sold. How many seats are left?
3000−1846
Borrow: 0 is less than 6. The thousands digit 3 gives one away. What does it become?
Square 1 of 8
3,000 − 1,846 = …
The Mileage Log
Problem 2 of 11
A van showed 4,687 miles in January. In May it showed 9,030 miles. How many miles did it go in between?
9030−4687
Borrow: 0 is less than 7. The tens digit 3 gives one away. What does it become?
Square 1 of 9
9,030 − 4,687 = …
Four Columns Down
Write the first two on the board. Type the last answer.
Problem 3 of 11
8,000 − 3,542 = ?
8000−3542
Borrow: 0 is less than 2. The thousands digit 8 gives one away. What does it become?
Square 1 of 8
8,000 − 3,542 = …
Problem 4 of 11
5,204 − 1,736 = ?
5204−1736
Borrow: 4 is less than 6. The hundreds digit 2 gives one away. What does it become?
Square 1 of 9
5,204 − 1,736 = …
Problem 5 of 11
7,031 − 6,984 = ?
Find the Mistake
One line on each page is a slip. Find it, then fix it.
Problem 6 of 11
Leo works out 5,008 − 2,349. One line is a slip. Which?
Leo’s answer for 5,008 − 2,349
- 15,008 − 2,349
- 2The 5 becomes 4, and both 0s become 10
- 3Ones 18 − 9 = 9, tens 10 − 4 = 6, hundreds 10 − 3 = 7
- AnswerThousands 4 − 2 = 2, so 2,769
Problem 7 of 11
What is 5,008 − 2,349? Write it out, and watch the zeros.
5008−2349
Borrow: 8 is less than 9. The thousands digit 5 gives one away. What does it become?
Square 1 of 8
5,008 − 2,349 = …
Problem 8 of 11
Noor works out 9,046 − 528. One line is a slip. Which?
Noor’s answer for 9,046 − 528
- 19,046 − 528
- 25 under the 9, 2 under the 0, 8 under the 4
- 3Ones 6 − 0 = 6, tens 14 − 8 = 6, hundreds 9 − 2 = 7
- AnswerThousands 8 − 5 = 3, so 3,766
Problem 9 of 11
What is 9,046 − 528? Write it out, ones under ones.
9046−528
Borrow: 6 is less than 8. The tens digit 4 gives one away. What does it become?
Square 1 of 8
9,046 − 528 = …
Which Way?
Pick the way that starts right.
Problem 10 of 11
In 3,204 − 1,568 the ones are short. The tens are 0. Which way?
Problem 11 of 11
To work out 8,479 − 3,256, which way starts right?
Step 6: Quick Check
Show what you know.
Question 1 of 2
5,000 − 2,637
Question 2 of 2
You borrow across two zeros. What do the two zeros become?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
A tank held 6,020 liters. 2,475 went out in June. 1,368 went out in July. How many liters are left?
liters
Stretch 2 of 2
A subtraction reads 7,004 − ? = 2,568. What number is missing?
What You Learned
- Ones first. Borrow where the top digit is smaller.
- Across zeros: borrow from the nearest non-zero column, and each zero passed becomes 9.
- Check by adding the answer back.
For the grown-up
This is lesson 1.6 written out. Borrowing across zeros is where most four-digit subtraction goes wrong; the widget shows every crossed-out digit and names the column it borrowed from.
The check by adding is the habit to keep: 2,363 + 2,637 = 5,000 proves the whole thing in one line.
The slip this lesson targets is a zero that becomes 10 instead of 9: Leo turns both zeros in 5,008 into tens and lands a hundred and a ten too high. Ask what a column has left after it has lent one on. The second slip is Noor's, and it is the four-digit classic: 528 lined up under the left-hand end of 9,046 instead of the right. Insist on squared paper, and on the ones digit sitting under the ones digit before a single column is subtracted.