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

Dividing 2- and 3-Digit Numbers by 1-Digit Numbers

B2.6 B2.1About 45 minutes
Learning goals
  • I can divide by sharing tens and ones, and trading when I need to.
  • I can divide using partial quotients (taking away friendly groups).
  • I can check a division with multiplication.
  • I can solve division story problems.

Words to know

quotient
The answer when you divide.
dividend
The number being divided.
divisor
The number you divide by.
partial quotients
A way to divide by taking away friendly groups (like 10 groups or 20 groups) and adding up how many groups you took.

Let's start with a story

Grandma made 84 perogies. She shares them equally among 4 families. How many perogies does each family get?

That's 84 ÷ 4. It's bigger than our division facts. Let's use place value.

Way 1: Share the tens, then the ones

84 is 8 tens and 4 ones.

  • Share the 8 tens among 4 groups: each gets 2 tens (20).
  • Share the 4 ones among 4 groups: each gets 1 one.
  • Each group gets 20 + 1 = 21.
21212121
84 shared into 4 equal groups. Each group has 2 tens and 1 one, which is 21.
Worked example

Example 1: Sharing with a trade

Solve 72 ÷ 3.

  1. 72 is 7 tens and 2 ones.
  2. Share 7 tens among 3 groups: each gets 2 tens. That uses 6 tens. 1 ten is left over.
  3. Trade the leftover ten for 10 ones. Now there are 10 + 2 = 12 ones.
  4. Share 12 ones among 3 groups: each gets 4 ones.
  5. Each group has 2 tens and 4 ones = 24.
  6. Check: 3 × 24 = 72. ✓

72 ÷ 3 = 24

Way 2: Partial quotients (take away friendly groups)

Think: How many groups of the divisor fit in the number? Take away big, friendly groups first, like 10 groups or 20 groups. Keep track of how many groups you took. Then add them up.

Worked example

Example 2: Partial quotients

Solve 156 ÷ 6.

  1. How many 6s are in 156? Start with a friendly amount: 20 groups of 6 = 120.
  2. 156 − 120 = 36 left.
  3. How many 6s are in 36? 6 groups of 6 = 36.
  4. 36 − 36 = 0 left.
  5. Add the groups: 20 + 6 = 26.
  6. Check: 6 × 26 = 120 + 36 = 156. ✓

156 ÷ 6 = 26

Take awayGroups of 6What's left
Start156
6 × 20 = 12020156 − 120 = 36
6 × 6 = 36636 − 36 = 0
Total26
Partial quotients for 156 ÷ 6. Add the groups: 20 + 6 = 26.
Worked example

Example 3: A 3-digit number

Solve 455 ÷ 5.

  1. Take away 90 groups of 5 = 450. (5 × 9 = 45, so 5 × 90 = 450.)
  2. 455 − 450 = 5 left.
  3. Take away 1 group of 5. 5 − 5 = 0.
  4. Add the groups: 90 + 1 = 91.
  5. Check: 5 × 91 = 450 + 5 = 455. ✓

455 ÷ 5 = 91

Worked example

Example 4: A story problem

336 stickers go equally into 8 albums. How many stickers in each album?

  1. We need 336 ÷ 8.
  2. Take away 40 groups of 8 = 320. 336 − 320 = 16 left.
  3. Take away 2 groups of 8 = 16. 16 − 16 = 0.
  4. 40 + 2 = 42.
  5. Check: 8 × 42 = 320 + 16 = 336. ✓

42 stickers in each album.

Division as a missing side

Division is the opposite of multiplication, so you can also think of an area model with a missing side. For 156 ÷ 6, ask: "6 times what makes 156?" The pieces 6 × 20 = 120 and 6 × 6 = 36 fill the rectangle, so the missing side is 20 + 6 = 26.

6 × 20 = 1206 × 6 = 362066missing side: 20 + 6 = 26120 + 36= 156
156 ÷ 6 as a rectangle with a missing side. The two parts, 120 and 36, fill an area of 156, so the missing side is 20 + 6 = 26.

There's no wrong first step

Any friendly group size works in partial quotients. If you take away 10 groups, then 10 more, then 6, you'll still get 26 for 156 ÷ 6. Bigger groups just make it faster.

Just for fun

Q: Why is the division sign so popular at parties?

A: It always makes sure everybody gets a fair share!

Hands-on activity

Share the bundles

You need: about 100 popsicle sticks, straws or toothpicks, some elastic bands (keep elastics away from little children), and 4 plates or bowls.

  1. Make 9 bundles of 10 with elastic bands, and keep 6 loose sticks. That's 96.
  2. Share the bundles equally among the 4 plates. Each plate gets 2 bundles. 1 bundle is left.
  3. Take the elastic off the leftover bundle. Now you have 10 + 6 = 16 loose sticks.
  4. Share the 16 loose sticks among the 4 plates.
  5. Count what's on one plate: 2 bundles and 4 sticks = 24. So 96 ÷ 4 = 24.
  6. Check: 4 × 24 = 96.

Try again with 78 sticks shared among 3 plates. (Answer: 26 each.)

Your turn

1

69 ÷ 3 = ?

2

86 ÷ 2 = ?

3

76 ÷ 4 = ?

4

95 ÷ 5 = ?

5

128 ÷ 4 = ?

6

252 ÷ 6 = ?

7

A bakery packs 144 muffins in boxes of 6. How many boxes?

More practice: warm-up

1

60 ÷ 3 = ?

2

80 ÷ 4 = ?

3

46 ÷ 2 = ?

4

99 ÷ 3 = ?

5

50 ÷ 5 = ?

More practice: on your own

1

84 ÷ 6 = ?

2

91 ÷ 7 = ?

3

384 ÷ 8 = ?

4

615 ÷ 5 = ?

5

196 children make 4 equal groups for a field trip. How many in each group?

Challenge

1

936 ÷ 9 = ?

2

Find the missing number: 7 × □ = 588

3

Three friends earn $261 shovelling snow and share it equally. How much does each get? Check your answer.

Check your understanding

Quiz

1.

What is 96 ÷ 3?

2.

What is 175 ÷ 5?

3.

What is 448 ÷ 4?

4.

Which multiplication checks 216 ÷ 8 = 27?

5.

What is 90 ÷ 6?

6.

What is 702 ÷ 6?

For parents and teachers

Big idea: The curriculum (B2.6) asks Grade 4 students to solve problems that divide 2- or 3-digit numbers by 1-digit numbers, using tools such as arrays. This lesson uses only questions that divide evenly; the next lesson handles remainders.

Common difficulties:

  • Not trading a leftover ten when sharing (72 ÷ 3). Use bundles of sticks so your child physically unbundles the extra ten.
  • Taking away tiny groups one at a time in partial quotients. Encourage friendly groups of 10, 20, 50 or 100.
  • Forgetting to add up the groups at the end, or adding the amounts taken away instead.

How to help: Divide in real life: sharing a bag of candies, splitting a bill among friends, putting photos into album pages. Always ask: "How can you check?" (Multiply.)