Explore the use of brackets and order of operations to write number sentences (ACMNA134)
Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)
The order of operations
The result of a list of calculations using some or all of the four arithmetic operations – addition, subtraction, multiplication and division – can vary depending on the order in which the calculations are performed.
For example, look at the following calculation.
4 + 4 × 4 – 4 ÷ 4 =
If we perform this calculation from left to right, we get an answer that is incorrect:
4 + 4 is 8, 8 × 4 = 32, 32 – 4 is 28, 28 ÷ 4 is 7
The correct method is to do the multiplication and division first, and then do the subtraction from left to right.
Care must be taken to avoid ambiguity. Brackets override all conventions and are always performed first, from the inside out. Sometimes we insert brackets to remove all doubt.
For example, 4 + (4 × 4) – (4 ÷ 4).
The following conventions are used when working with more than one of the operations in a calculation:
- Perform calculations inside brackets first.
- In the absence of brackets, carry out operations in the following order:
- multiplication and division from left to right
- addition and subtraction from left to right.