Multiplication and division fact families

Three numbers, four facts

A multiplication and division fact family uses the same three numbers. For 4, 6 and 24:

The biggest number (24) is the product. The two smaller numbers (4 and 6) are the factors. In the division facts, the product is always divided, and the answer, the quotient, is one of the factors.

Why it works

Multiplication and division are inverse operations: one undoes the other. An array shows the whole family at once:

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• 4 rows of 6 → 4 × 6 = 24
• 6 columns of 4 → 6 × 4 = 24
• 24 shared into 4 rows → 24 ÷ 4 = 6
• 24 shared into 6 columns → 24 ÷ 6 = 4

Fact triangles

A fact triangle puts the product at the top and the factors at the bottom corners. Cover one number:

• Cover the top → multiply the bottom two.
• Cover a bottom corner → divide the top by the other bottom number.

Using fact families to divide

If you know your times tables, you know your division facts too.

• 63 ÷ 7 = ? Think: 7 × ? = 63. Since 7 × 9 = 63, the answer is 9.

Families with square numbers

When both factors are the same, there are only two facts:

• 5 × 5 = 25
• 25 ÷ 5 = 5

Missing numbers

Worked examples

Example 1: Write the fact family for 3, 7 and 21.

3 × 7 = 21, 7 × 3 = 21, 21 ÷ 3 = 7, 21 ÷ 7 = 3.

Example 2: Use 9 × 8 = 72 to find 72 ÷ 9.

Same family: 8.

Example 3: Does 5 × 6 = 30 belong in the family of 6, 5 and 30?

Yes: it uses the same three numbers.

Common mistakes

• Dividing a factor by the product: 4 ÷ 24 is not in the family.
• Including a number from outside the family.
• Forgetting that order matters in division.

Try it yourself

1. Write the fact family for 6, 8 and 48.
2. You know 7 × 9 = 63. What is 63 ÷ 7?
3. Solve 4 × __ = 36.
4. Solve __ ÷ 5 = 8.

Answers: 1) 6 × 8 = 48, 8 × 6 = 48, 48 ÷ 6 = 8, 48 ÷ 8 = 6 2) 9 3) 9 4) 40

Quick recap

• A fact family links multiplication and division with three numbers.
• The product is divided; the quotient is a factor.
• Use known multiplication facts to divide.