BIDMAS – a way of remembering the order of operations to complete a calculation
Note: BIDMAS is an acronym that stands for Brackets, Indices, Division, Multiplication, Addition, and Subtraction.
To remember the meaning of BIDMAS, use the following mnemonic:
I bid on the massive (BIDMAS) calculator in order to complete a calculation.
BIDMAS is the memory aid used to work out which order mathematical calculations should be completed in:
The above is the order you complete any calculation.
| Brackets | - | ( ) |
| Indices | - | To the power e.g. |
| `3^3=3times3times3` or `sqrt9=9^(1/2)=3` | ||
| Division | - | Divide |
| Multiplication | - | Multiply |
| Addition | - | Add |
| Subtraction | - | Take away |
For example, in the expression 3 + 4 X 2, you must do the multiplication first (getting 8) and then add 3 to get 11, rather than adding 3 + 4 first and then multiplying by 2, which would incorrectly give 14.
Other examples include:
Example 1
`30-:-5+4times-2+14`
| Stage 1 | - | Division | `30-:-5` | `=` | `-6` | Therefore | `-6+4times-2+14` |
| Stage 2 | - | Multiplication | `4times-2` | `=` | `-8` | Therefore | `-6-8+14` |
| Stage 3 | - | Addition | `-8+14` | `=` | `6` | Therefore | `-6+6` |
| Final stage | - | Subtraction | `-6+6` | `=` | `0` |
Example 2
`(4times5)^2+2times2^2`
| Stage 1 | - | Brackets | `4times5` | `=` | `20` | Therefore | `20^2+2times2^2` |
| Stage 2 | - | Indices | `20^2=400` | and | `2^2=4` | Therefore | `400+2times4` |
| Stage 3 | - | Multiplication | `2times4` | `=` | `8` | Therefore | `400+8` |
| Final stage | - | Addition | `400+8` | `=` | `408` |
Example 3
What is `x`?
`4times4+4times4+4-4times4=x`
| Stage 1 | - | Multiplication | `4times4=16` | and | `-4times4=-16` | Therefore | `16+16+4-16` |
| Stage 2 | - | Addition | `16+16+4` | `=` | `36` | Therefore | `36-16` |
| Final stage | - | Subtraction | `36-16` | `=` | `20` | Therefore | `x=20` |
Example 4
`6-:2(1+2)`
| Stage 1 | - | Brackets | `1+2` | `=` | `3` | Therefore | `6-:2times3` |
| Stage 2 | - | Division | `6-:2` | `=` | `3` | Therefore | `3times3` |
| Final stage | - | Multiplication | `3times3` | `=` | `9` |
Some countries use different acronyms for the same concept, such as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) or BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction), but they all refer to the same fundamental principle of operation order.
