# Understand and apply the distributive property of multiplication (2)

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## Description

The first place that pupils will have encountered the distributive law is within the multiplication tables themselves. Pupils have seen, for example, that adjacent multiples in the 6 times table have a difference of 6. Number lines and arrays can be used to illustrate this.

Pupils should be able to represent such relationships using mixed operation equations, for example: 5 × 6 = 4 × 6 + 6 or 5 × 6 = 4 × 6 + 1 × 6  4 × 6 = 5 × 6 – 6 or 4 × 6 = 5 × 6 – 1 ×6

Pupils should learn that multiplication takes precedence over addition. They should then extend this understanding beyond the multiplication tables, for example, if they are given the equation  20 × 6 = 120, they should be able to determine that  21 × 6 = 126, or vice versa. Pupils also need to be able to apply the distributive property to non-adjacent multiples. The array chart used to show the connection between  4 × 6 and  5 × 6 can be adapted to show the connection between 5 × 6,  3 × 6 and  2 × 6.

As for adjacent multiples, pupils should be able to use mixed operation equations to represent the relationships:

5 × 6 = 3 × 6 + 2 × 6  3 × 6 = 5 × 6 – 2 × 6    2 × 6 = 5 × 6 – 3 × 6

Again, pupils should understand that multiplication takes precedence: the multiplications are calculated first, and then the products are added or subtracted.  Pupils can use language patterns to support their reasoning.

Language focus “5 is equal to 3 plus 2, so 5 times 6 is equal to 3 times 6 plus 2 times 6.”