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Math · Grade 4 Math

Chapter 1: Place Value to a Million

Four-Digit Column Subtraction, Written Out

Borrow across as many zeros as it takes.

Lesson
8
Time
About 14 minutes
WorksheetAnswer key
0 of 8 done
Part 1 of 7Let's Learn

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Watch the idea first — 59 seconds. Then read on, and try it yourself in the next step.

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.

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.

5,000 − 2,637, one move at a time. Then try 8,204 − 3,678.
Step 0 of 5

5,000 − 2,637 = …

Finished. Two borrows, one of them across a zero.

8,204 − 3,678 = 4,526

  1. 1Ones: 4 is less than 8, so borrow from the hundreds. 2 becomes 1, the 0 in between becomes 9, and 4 becomes 14.
  2. 2Ones: 14 − 8 = 6. Write 6.
  3. 3Tens: 9 − 7 = 2. Write 2.
  4. 4Hundreds: 1 is less than 6, so borrow from the thousands. 8 becomes 7, and 1 becomes 11.
  5. 5Hundreds: 11 − 6 = 5. Write 5.
  6. 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 Tom Subtract 4,987 from 6,013

Tom writes 6,013 above 4,987.

  1. Step 1

    Ones: 3 is less than 7. He borrows a ten: 1 becomes 0, 3 becomes 13. 13 − 7 = 6.

Step 5: Your Turn

Practice makes it stick.

The Mileage

Problem 1 of 2

A plan allows 5,000 miles. 2,637 are used. Miles left?

miles

The Stadium

Problem 2 of 2

8,204 seats and 3,678 sold. Seats left?

seats

Four Columns Down

1 of 4

5,000 − 2,637

2 of 4

8,204 − 3,678

3 of 4

6,013 − 4,987

4 of 4

9,105 − 9,047

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?

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.