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**Related topic**

find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations (AC9M5A02)

- using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that \(3\times5=15\) and \(30\div2=15\) then \(3\times5=30\div2\) therefore the solution to \(3\times5=30\div\square\) is \(2\)
- using relational thinking, an understanding of equivalence and number properties to determine and reason about numerical equations; for example, explaining whether an equation involving equivalent multiplication number sentences is true, such as \(15 ÷ 3 = 30 ÷ 6\)
- using materials, diagrams and arrays to demonstrate that multiplication is associative and commutative but division is not; for example, using arrays to demonstrate that \(2 \times 3 = 3 \times 2\) but \(6 ÷ 3\) does not equal \(3 ÷ 6\); demonstrating that \(2 \times 2 \times 3 = 12\) and \(2 \times3 \times2 = 12\) and \(3 \times 2 \times 2 = 12\); understanding that \(8 ÷ 2 ÷ 2 = (8 ÷ 2) ÷ 2 = 2\) but \(8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8\)
- using materials, diagrams or arrays to recognise and explain the distributive property; for example, where \(4 \times 13 = 4 \times 10 + 4 \times 3\)
- constructing equivalent number sentences involving multiplication to form a numerical equation, and applying knowledge of factors, multiples and the associative property to find unknown values in numerical equations; for example, considering \(3 \times 4 = 12\) and knowing \(2 \times 2 = 4\) then \(3 \times 4\) can be written as \(3\times\) (\(2 \times 2\)) and using the associative property (\(3 \times 2) \times 2\) so \(3 \times 4 = 6 \times 2\) and so \(6\) is the solution to \(3 \times 4 = \square\times 2\)

Mathematical expressions, Factors