Dividing Whole Numbers

Standard 5.NBT.6

Master the art of division with visual grids and step-by-step solutions

5.NBT.6: Fluently divide multi-digit numbers

By the end of this lesson, you will be able to:

  • Divide 4-digit numbers by 1-digit divisors using the standard algorithm
  • Divide multi-digit numbers by 2-digit divisors
  • Use partial quotients as an alternative division method
  • Check division using multiplication and addition
  • Solve word problems involving division

How do you share 2,634 stickers equally among 5 friends?

Each friend gets the same number of stickers. Let's use division to find out how many!

2,634 ÷ 5 = ?

Key Terms

Dividend: The number being divided (2,634 in 2,634 ÷ 5)
Divisor: The number we divide by (5 in 2,634 ÷ 5)
Quotient: The answer to a division problem (526 in 2,634 ÷ 5 = 526 R4)
Remainder: What's left over after dividing (R4 in 2,634 ÷ 5 = 526 R4)

The 5-Step Process

D — Divide: How many times does the divisor go into the digits?

M — Multiply: Multiply the quotient digit by the divisor

S — Subtract: Subtract to find what's left

B — Bring Down: Bring down the next digit

R — Repeat: Do it all again until no digits are left

Watch how the grid shows every step

In the next two problems, I'll show you:

  • The visual grid that shows all the work
  • DMSBR labels so you know what's happening at each step
  • How to fill in the grid as you divide

2,634 ÷ 5 = 526 R4

I Do
5
2
6
5
2
6
3
4
−
0
2
↓6
−
2
5
0
1
↓3
−
1
0
0
3
↓3
−
3
0
0
4
R4
D Divide
M Multiply
S Subtract
B Bring Down
R Repeat
Step 1 of 4

4,587 ÷ 7 = 655 R2

I Do
6
5
5
7
4
5
8
7
−
0
4
↓5
−
4
2
0
3
↓8
−
3
5
0
3
↓8
−
3
5
0
2
R2
D Divide
M Multiply
S Subtract
B Bring Down
R Repeat
Step 1 of 4

9,137 ÷ 4 = 2,284 R1

We Do
2
2
8
4
4
9
1
3
7
−
8
1
↓1
−
0
8
0
3
↓3
−
3
2
0
1
↓3
−
1
6
0
1
R1
Step 1 of 5

8,025 ÷ 6 = 1,337 R3

We Do
1
3
3
7
6
8
0
2
5
−
6
2
↓0
−
1
8
0
2
↓2
−
1
8
0
4
↓2
−
4
2
0
3
R3
Step 1 of 5

5,672 ÷ 8 = 709

You Do
7
0
9
8
5
6
7
2
−
0
5
↓6
−
5
6
0
0
↓7
−
0
7
↓6
−
7
2
0
0
Step 1 of 4

7,841 ÷ 3 = 2,613 R2

You Do
2
6
1
3
3
7
8
4
1
−
6
1
↓8
−
1
8
0
0
↓4
−
3
1
↓8
−
0
9
0
2
R2
Step 1 of 5

Use Multiplication and Addition

To check: (Quotient × Divisor) + Remainder = Dividend

For 2,634 ÷ 5 = 526 R4:

(526 × 5) + 4 = 2,630 + 4 = 2,634 ✓

Discuss with a partner:

Why do we check our division answers?

What does the remainder tell us in a real-world situation?

How do you know if your first digit in the quotient should be a 1-digit number or larger?

New Challenge!

Dividing by 2-digit numbers is trickier. You need to estimate first.

Tip: Round the divisor to the nearest 10, then estimate how many times it goes in.

Example: For 2,554 ÷ 43, round 43 to 40 and estimate!

2,554 ÷ 43 = 59 R17

I Do
5
9
43
2
5
5
4
−
0
2
↓5
−
0
0
2
5
↓5
−
2
1
5
0
4
0
↓4
−
3
8
7
0
1
7
R17
D Divide
M Multiply
S Subtract
B Bring Down
R Repeat
Step 1 of 3

628 ÷ 24 = 26 R4

I Do
2
6
24
6
2
8
−
0
6
↓2
−
4
8
1
4
↓8
−
1
4
4
0
0
4
R4
D Divide
M Multiply
S Subtract
B Bring Down
R Repeat
Step 1 of 2

2,170 ÷ 29 = 74 R24

We Do
7
4
29
2
1
7
0
−
0
2
↓1
−
0
0
2
1
↓7
−
2
0
3
0
1
4
↓0
−
1
1
6
0
2
4
R24
Step 1 of 3

3,109 ÷ 35 = 88 R29

We Do
8
8
35
3
1
0
9
−
0
3
↓1
−
0
0
3
1
↓0
−
2
8
0
0
3
0
↓9
−
2
8
0
0
2
9
R29
Step 1 of 3

1,836 ÷ 27 = 68

You Do
6
8
27
1
8
3
6
−
0
1
↓8
−
0
0
1
8
↓3
−
1
6
2
0
2
1
↓6
−
2
1
6
0
0
0
Step 1 of 2

4,297 ÷ 53 = 81 R4

You Do
8
1
53
4
2
9
7
−
0
4
↓2
−
0
0
4
2
↓9
−
4
2
4
0
0
5
↓7
−
5
3
0
4
R4
Step 1 of 2

Turn & Talk

What's easier for you — dividing by 1-digit or 2-digit divisors?

When you estimate the first quotient digit, what strategy do you use?

How do the grids help you see the math clearly?

Another Way to Divide!

Subtract friendly chunks until you reach the remainder.

Advantage: You don't need to estimate perfectly. You can use any multiple that works!

Example: 4,587 ÷ 7
Subtract 3,500 (7 × 500), then 700 (7 × 100), then 350 (7 × 50), then 35 (7 × 5)

4,587 ÷ 7 = 655 R2

I Do — Partial Quotients
4587
− 4,200
(7 × 600)
387
→ 600
− 350
(7 × 50)
37
→ 50
− 35
(7 × 5)
2
→ 5
R = 2
───
= 655

3,826 ÷ 7 = 546 R4

I Do — Partial Quotients
3826
− 3,500
(7 × 500)
326
→ 500
− 280
(7 × 40)
46
→ 40
− 42
(7 × 6)
4
→ 6
R = 4
───
= 546

5,423 ÷ 6 = 903 R5

We Do — Partial Quotients
5423
− 5,400
(6 × 900)
23
→ 900
− 18
(6 × 3)
5
→ 3
R = 5
───
= 903

2,819 ÷ 32 = 88 R3

We Do — Partial Quotients
2819
− 2,560
(32 × 80)
259
→ 80
− 256
(32 × 8)
3
→ 8
R = 3
───
= 88

3,748 ÷ 5 = 749 R3

You Do — Partial Quotients
3748
− 3,500
(5 × 700)
248
→ 700
− 200
(5 × 40)
48
→ 40
− 45
(5 × 9)
3
→ 9
R = 3
───
= 749

1,973 ÷ 24 = 82 R5

You Do — Partial Quotients
1973
− 1,920
(24 × 80)
53
→ 80
− 48
(24 × 2)
5
→ 2
R = 5
───
= 82

9,577 ÷ 47 = 203 R36

Challenge
2
0
3
47
9
5
7
7
−
0
9
↓5
−
9
4
0
1
↓7
−
0
0
1
7
↓7
−
1
4
1
0
3
6
R36
Step 1 of 3

Real-World Division

Problem: A teacher has $2,528 to spend on supplies over 8 months.

How much can she spend each month?

Solution: 2,528 ÷ 8 = $316 per month

Show the grid
3
1
6
8
2
5
2
8
−
0
2
↓5
−
2
4
0
1
↓2
−
0
8
0
4
↓2
−
4
8
0
0
Step 1 of 4

Division Methods

Standard Algorithm: DMSBR — Divide, Multiply, Subtract, Bring Down, Repeat

Partial Quotients: Subtract friendly chunks until you get to the remainder

Checking: Use (Quotient × Divisor) + Remainder = Dividend

Both methods work! Choose the one that makes sense to you.

Solve these three problems:

1. 6,453 ÷ 9 = ?

2. 1,748 ÷ 23 = ?

3. 4,235 ÷ 8 = ?

Use either the standard algorithm or partial quotients. Show your work!

Which method do you prefer?

Standard Algorithm or Partial Quotients?

Explain your reasoning to a partner.

What makes one method easier for you than the other?

You can divide like a pro! 🚀

Keep practicing and you'll master division in no time.

Great work today!

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