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# Number facts: Multiplication and division

Multiplication and division facts are best learned through a process of noticing patterns and relationships.

Knowing the relationship between multiplication and division can help students.

For example, knowing that:

• 4 $$\times$$ 5 = 20 leads to 20 ÷ 4 = 5
• 5 $$\times$$ 4 = 20 leads to 20 ÷ 5 = 4.

The two-times and ten-times facts are the easiest to learn because the products are doubles and the numbers end in '-ty'. These facts can assist students to derive other facts using doubling and halving strategies.

Five-times facts are related to ten-times facts by doubling and halving.

Nine-times facts can be found by taking off one set of the tens-times facts. For example, 10 is 1 more than 9 so:

• 1 $$\times$$ 9 = 1 $$\times$$ 10 – 1
• 2 $$\times$$ 9 = 2 $$\times$$ 10 – 2
• 5 $$\times$$ 9 = 5 $$\times$$ 10 – 5.

The seven-times facts can be derived from the five-times facts using partitioning and the distributive property (e.g. 7 $$\times$$ 8 = 5 $$\times$$ 8 + 2 $$\times$$ 8).

Using halving and doubling can assist in working out 8 $$\times$$ 6 = ?

• Half of 8 is 4.
• 4 $$\times$$ 6 = 24
• Double the product (24) to get 48.

Students can be assisted to see patterns and relationships among the multiplication and division facts by using visual tools such as: