Understanding and Using Number Operations and Their Relationships
Number operations are the basic calculations used in mathematics: addition, subtraction, multiplication, and division. These operations are connected through inverse relationships and are organised using the hierarchy of operations, which tells us the correct order to perform calculations.
Inverse operations are pairs of operations that undo each other.
- Addition and subtraction are inverses
- Multiplication and division are inverses
For example:
$$
7 + 5 = 12
$$
can be undone by:
$$
12 - 5 = 7
$$
Similarly:
$$
4 \times 6 = 24
$$
can be undone by:
$$
24 \div 6 = 4
$$
Inverse operations are especially useful for checking answers and for solving equations.
The hierarchy of operations (sometimes called BIDMAS or BODMAS) tells us the order in which calculations must be carried out to get the correct result.
The correct order is:
- Brackets
- Indices (powers)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
For example:
$$
3 + 4 \times 5 = 23
$$
because multiplication is done before addition.
However:
$$
(3 + 4) \times 5 = 35
$$
because the brackets change the order of calculation.
Division and multiplication have equal priority, as do addition and subtraction. This means calculations are carried out from left to right.
$$
20 \div 4 \times 5 = 25
$$
Always follow the hierarchy carefully. Ignoring the correct order can completely change the result, even when all the numbers and operations are the same.