Grade by Grade
B. Number · Operations: Numbers to 10 000, Decimal Tenths, Multiplying and Dividing

Subtracting Whole Numbers within 10 000

B2.4 B2.1About 40 minutes
Learning goals
  • I can subtract 4-digit numbers using the column method.
  • I can regroup across zeros.
  • I can count up to subtract.
  • I can check a subtraction with addition.

Words to know

difference
The answer when you subtract.
regroup
Trade 1 of a place for 10 of the place to its right, like 1 thousand for 10 hundreds.
count up
Start at the smaller number and jump to the bigger one. The total of the jumps is the difference.
inverse operation
The operation that undoes another. Addition undoes subtraction.

Remember from Grade 3

In Grade 3 you subtracted 3-digit numbers. When the top digit was too small, you regrouped: you traded 1 ten for 10 ones, or 1 hundred for 10 tens. In Grade 4 you can also trade 1 thousand for 10 hundreds.

Let's start with a story

A library has 4752 books. 1386 are borrowed. How many books are still on the shelves?

Estimate first: 4800 − 1400 = 3400. Our answer should be close to that.

The column method for subtracting

  1. Estimate first.
  2. Line up the places. The bigger number goes on top.
  3. Start with the ones. If the top digit is smaller than the bottom digit, regroup from the next place to the left.
  4. Then do the tens, the hundreds and the thousands.
  5. Check with addition: difference + number you took away = starting number.
Worked example

Example 1: Regrouping two times

Solve 4752 − 1386.

  1. Ones: 2 − 6? Not enough. Regroup 1 ten: now 4 tens and 12 ones. 12 − 6 = 6.
  2. Tens: 4 − 8? Not enough. Regroup 1 hundred: now 6 hundreds and 14 tens. 14 − 8 = 6.
  3. Hundreds: 6 − 3 = 3.
  4. Thousands: 4 − 1 = 3.
  5. Check: 3366 + 1386 = 4752. ✓

4752 − 1386 = 3366 books. Close to our estimate of 3400. ✓

Worked example

Example 2: Regrouping in every place

Solve 6352 − 2786.

  1. Estimate: 6400 − 2800 = 3600.
  2. Ones: 2 − 6? Regroup a ten: 12 − 6 = 6. (Tens: 5 becomes 4.)
  3. Tens: 4 − 8? Regroup a hundred: 14 − 8 = 6. (Hundreds: 3 becomes 2.)
  4. Hundreds: 2 − 7? Regroup a thousand: 12 − 7 = 5. (Thousands: 6 becomes 5.)
  5. Thousands: 5 − 2 = 3.
  6. Check: 3566 + 2786 = 6352. ✓

6352 − 2786 = 3566

OTHTh121412525366872−6653
6352 − 2786 with regrouping. The crossed-out digits were regrouped; the small numbers above show what each place had after trading.

Subtracting from numbers with zeros

Numbers like 5000 have no ones, tens or hundreds to trade. Here are two good ways.

Worked example

Example 3: Take 1 from both numbers

Solve 5000 − 2347.

  1. Subtracting from 5000 is tricky. Take 1 away from both numbers. The difference stays the same.
  2. 5000 − 1 = 4999 and 2347 − 1 = 2346.
  3. Now 4999 − 2346 needs no regrouping: 9 − 6 = 3, 9 − 4 = 5, 9 − 3 = 6, 4 − 2 = 2.

5000 − 2347 = 2653. Check: 2653 + 2347 = 5000. ✓

Worked example

Example 4: Count up

Solve 4000 − 2675.

  1. Start at 2675. Jump 25 to 2700.
  2. Jump 300 to 3000.
  3. Jump 1000 to 4000.
  4. Add the jumps: 25 + 300 + 1000 = 1325.

4000 − 2675 = 1325

26002800300032003400360038004000+25+300+1000
Count up from 2675: +25 to 2700, +300 to 3000, +1000 to 4000. 25 + 300 + 1000 = 1325.

Always check

Every subtraction has an addition partner. When you finish, add your answer to the number you took away. If you get the top number, you're right!

Just for fun

Q: What did the 0 in the tens place say when the ones asked to borrow a ten?

A: "Sorry, I've got nothing! Go ask the hundreds next door."

Hands-on activity

Countdown from 10 000

You need: a deck of playing cards (take out the face cards and the 10s; Ace = 1), paper, a pencil and a partner.

  1. Each player writes 10 000 at the top of their paper.
  2. On your turn, flip 3 cards to make a 3-digit number, like 7, 2, 5 = 725.
  3. Subtract it from your number using the column method or counting up. Your partner checks it with addition.
  4. Keep taking turns. The first player to get below 1000 wins.

Math talk: "Which way was easier when your number had zeros: regrouping or counting up?"

Your turn

1

4876 − 2543 = ?

2

7352 − 4128 = ?

3

6215 − 3487 = ?

4

8000 − 3456 = ?

5

3002 − 1998 = ? Count up.

6

A concert hall has 2500 seats. 1875 tickets are sold. How many seats are left?

7

Estimate 7920 − 3080.

More practice: warm-up

1

5000 − 2000 = ?

2

6800 − 500 = ?

3

9999 − 4444 = ?

4

3450 − 1000 = ?

5

7000 − 1 = ?

More practice: on your own

1

9143 − 5678 = ?

2

6000 − 2785 = ?

3

4520 − 2999 = ?

4

A road trip is 3200 km. The family has driven 1765 km. How far is left?

5

Mia says 5302 − 1847 = 4545. Check with addition.

Challenge

1

Find the missing number: □ − 2468 = 3532

2

How much more is 10 000 than 6347?

3

A school wants to raise $5000 for a new playground. It raised $2375 in the fall and $1890 in the winter. How much more does it need?

Check your understanding

Quiz

1.

What is 5786 − 2341?

2.

What is 4000 − 1250?

3.

What is 6421 − 3758?

4.

Which addition checks 7400 − 2650 = 4750?

5.

What is the best estimate for 8125 − 2980?

6.

What is 4005 − 3998?

For parents and teachers

Big idea: The curriculum (B2.4) asks Grade 4 students to solve subtraction problems with whole numbers up to 10 000 using tools, strategies and algorithms. Your child should have more than one way: the column algorithm with regrouping, counting up, and adjusting numbers (like 5000 − 2347 = 4999 − 2346).

Common difficulties:

  • Taking the smaller digit from the bigger one in each column (6421 − 3758 = 3337). Ask: "Is the top digit big enough?"
  • Regrouping across zeros (6000 − 2785). Show the "take 1 from both" trick or counting up.
  • Forgetting to change the digit you regrouped from. Have your child cross it out and write the new digit above.

How to help: Ask "How much more?" questions: "The trip is 1200 km and we've driven 785. How far is left?" Always ask your child to check with addition.