Inverse operations

Recognising the inverse relationships between the operations equips students with greater flexibility in working with numbers than if the facts are learned in isolation.

Students should recognise that for a fact such as 3 + 4 = 7 there are three other facts:

• 4 + 3 = 7
• 7 − 3 = 4 
• 7 − 4 = 3.

Knowing this relationship can assist students to think 'addition' when presented with a situation such as 15 – 6 = ? which can be thought of as ? + 6 = 15. Knowing such relationships can also assist with addition and subtraction of multi-digit numbers.

Tens frames, bead strings and number lines are useful tools to assist students to see these relationships.

The same thinking applies to multiplication and division.

For example, the numbers 4, 5 and 20 have four related facts: 4 \(\times\) 5 = 20, 5 \(\times\) 4 = 20, 20 ÷ 5 = 4 and 20 ÷ 4 = 5.

Knowing inverse relationships can assist students: 48 ÷ 6 = ? can be thought of as 6 × ? = 48 or ? × 6 = 48.

Rectangular arrays are a useful tool to assist students to see these relationships.