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

Division Facts and Fact Families

B2.2 B2.1About 35 minutes
Learning goals
  • I can use a multiplication fact to find a division fact.
  • I can write a fact family.
  • I can solve sharing and grouping problems with division facts.

Words to know

division
Splitting a total into equal groups. The sign is ÷.
dividend
The number being divided. In 42 ÷ 6 = 7, the dividend is 42.
divisor
The number you divide by. In 42 ÷ 6 = 7, the divisor is 6.
quotient
The answer when you divide. In 42 ÷ 6 = 7, the quotient is 7.
fact family
A group of related facts that use the same three numbers, like 4 × 7 = 28, 7 × 4 = 28, 28 ÷ 4 = 7 and 28 ÷ 7 = 4.

Remember from Grade 3

In Grade 3 you divided by sharing (how many in each group?) and by grouping (how many groups?). You learned division facts for 2, 5 and 10. Now that you are learning all the multiplication facts, you can find every division fact up to 100 ÷ 10.

The secret: think multiplication

Division and multiplication are partners. To solve a division, turn it into a missing-factor multiplication.

42 ÷ 6 = ? Think: 6 × ? = 42. You know 6 × 7 = 42. So 42 ÷ 6 = 7.

An array of 4 rows of 7 shows a whole fact family: 4 × 7 = 28, 7 × 4 = 28, 28 ÷ 4 = 7 and 28 ÷ 7 = 4.

Fact families

The array above has 28 dots in 4 rows of 7. One picture, four facts:

  • 4 × 7 = 28
  • 7 × 4 = 28
  • 28 ÷ 4 = 7 (28 dots in 4 rows: 7 in each row)
  • 28 ÷ 7 = 4 (28 dots in groups of 7: 4 groups)

In every fact family, the biggest number is the product. In the division facts, the biggest number comes first.

Worked example

Example 1: Use a multiplication fact

Solve 56 ÷ 8.

  1. Think: 8 × ? = 56.
  2. 8 × 7 = 56.
  3. So 56 ÷ 8 = 7.

56 ÷ 8 = 7

Worked example

Example 2: Write a fact family

Write the fact family for 6, 9 and 54.

  1. The biggest number, 54, is the product.
  2. Multiplication: 6 × 9 = 54 and 9 × 6 = 54.
  3. Division: 54 ÷ 6 = 9 and 54 ÷ 9 = 6.

6 × 9 = 54, 9 × 6 = 54, 54 ÷ 6 = 9, 54 ÷ 9 = 6

54product69× ÷6 × 9 = 549 × 6 = 5454 ÷ 6 = 954 ÷ 9 = 6One triangle, four facts:
A fact triangle for 6, 9 and 54. The product sits at the top. Cover any number and the other two tell you how to find it.
Worked example

Example 3: A sharing story

Ava has 36 hockey cards. She shares them equally among 4 friends. How many cards does each friend get?

  1. This is sharing: 36 shared into 4 equal groups. Write 36 ÷ 4.
  2. Think: 4 × ? = 36. 4 × 9 = 36.
  3. So 36 ÷ 4 = 9.

Each friend gets 9 cards.

Worked example

Example 4: A grouping story

45 children go to a snowshoe club. They make teams of 5. How many teams?

  1. This is grouping: how many groups of 5 are in 45? Write 45 ÷ 5.
  2. Think: 5 × ? = 45. 5 × 9 = 45.

There are 9 teams.

Division rules to remember

  • Divide by 1: the number stays the same. 8 ÷ 1 = 8.
  • Divide a number by itself: the answer is 1. 9 ÷ 9 = 1.
  • Zero divided by a number: the answer is 0. 0 ÷ 6 = 0 (nothing to share).
  • You cannot divide by zero. Sharing 6 cookies among 0 people makes no sense!

Stuck?

If you get stuck on a division fact, find the multiplication partner first. If you're stuck on that too, use a strategy from the last lesson: double, add a group or take away a group.

Just for fun

Q: Why can't you share 6 cookies among 0 friends?

A: There's nobody to share with, so the cookies just sit there wondering what the answer is. (That's why dividing by zero doesn't work!)

Hands-on activity

Fact family triangles

You need: paper, scissors (ask a grown-up), and a pencil.

  1. Cut out 6 paper triangles.
  2. On each one, write a product in the top corner and its two factors in the bottom corners. For example: 28 at the top, 4 and 7 at the bottom.
  3. Cover one corner with your thumb. Your partner says the hidden number and the fact that finds it.
  • Cover the 28: "4 × 7 = 28."
  • Cover the 7: "28 ÷ 4 = 7."
  1. Use your "working on it" facts from last lesson.

Math talk: "Which number is always at the top? Why?"

Your turn

1

35 ÷ 5 = ?

2

48 ÷ 6 = ?

3

63 ÷ 9 = ?

4

72 ÷ 8 = ?

5

49 ÷ 7 = ?

6

Write the fact family for 3, 8 and 24.

7

A bakery puts 40 muffins in boxes of 4. How many boxes?

More practice: warm-up

1

20 ÷ 2 = ?

2

30 ÷ 10 = ?

3

15 ÷ 5 = ?

4

9 ÷ 1 = ?

5

8 ÷ 8 = ?

More practice: on your own

1

54 ÷ 9 = ?

2

42 ÷ 7 = ?

3

0 ÷ 6 = ?

4

81 ÷ 9 = ?

5

32 children make 4 equal teams. How many on each team?

Challenge

1

Find the missing number: □ ÷ 7 = 8

2

Find 64 ÷ 8 and 64 ÷ 4. What do you notice?

3

The fact family for 6, 6 and 36 has only two facts. Why?

Check your understanding

Quiz

1.

What is 56 ÷ 7?

2.

Which fact belongs in the fact family of 5, 9 and 45?

3.

What is 27 ÷ 3?

4.

30 apples go into bags of 6. How many bags?

5.

What is 7 ÷ 7?

6.

Which multiplication fact helps you find 72 ÷ 9?

For parents and teachers

Big idea: Division facts are learned through their multiplication partners (B2.2). When your child knows 6 × 9 = 54, they also know 54 ÷ 6 and 54 ÷ 9. Fact families make this link visible.

Common difficulties:

  • Writing division backwards (6 ÷ 54). Remind your child that in division the total (the biggest number) comes first.
  • Confusing 0 ÷ 6 = 0 with 6 ÷ 0. Keep it practical: zero cookies shared by 6 people gives 0 each; you can't share 6 cookies among 0 people.
  • Counting by ones to divide. Ask: "What times 6 makes 48?"

How to help: Ask division questions in daily life: "There are 24 grapes for the 4 of us. How many each?" Use the fact family triangles for a few minutes each day.