They are all basically the same thing. Brackets (aka parenthesis) are done first - that’s basically the entire point of brackets. Then you do all the multiplication stuff, which includes division (which is just multiplication in reverse), fractions (which are another way of writing division) and exponentials (which are a shorthand for multiplication of a number by itself). Then you do all the addition/subtraction stuff. Within those three groups it doesn’t really matter which ones you do first.
It helps to think of it in terms of something concrete - biscuits are good. Multiplication type maths is dealing with packets, addition is like individual biscuits. So if you have 3 packets containing 12 tim tams, plus 5 tim tams, to work out how many you need to work out how many in packets first, then add the individual biscuits - so 3 x 12 + 5, equals 36+5. When you look at it that way it becomes fairly clear that adding your pack of 12 to 5 individual biscuits and then mulitplying that by the 3 packs just doesn’t make sense.
Within those three groups it doesn’t really matter which ones you do first
It absolutely does matter. You must do exponents after brackets and before multiplication and division, for the precise reason you said that exponents are shorthand for multiplication. In other words, there’s 4 groups, not three.
But if you use biscuits once you get to the last bit and do the subtraction it all becomes worthwhile. If I have three packets of 12 tim tams and eat four tim tams what do I have? I have four tim tams in my tummy. Best maths ever.
See, I learned Bomdas first, then was informed it was wrong and to use PEMDAS. I have no idea which one is the correct one anymore.
They are all basically the same thing. Brackets (aka parenthesis) are done first - that’s basically the entire point of brackets. Then you do all the multiplication stuff, which includes division (which is just multiplication in reverse), fractions (which are another way of writing division) and exponentials (which are a shorthand for multiplication of a number by itself). Then you do all the addition/subtraction stuff. Within those three groups it doesn’t really matter which ones you do first.
It helps to think of it in terms of something concrete - biscuits are good. Multiplication type maths is dealing with packets, addition is like individual biscuits. So if you have 3 packets containing 12 tim tams, plus 5 tim tams, to work out how many you need to work out how many in packets first, then add the individual biscuits - so 3 x 12 + 5, equals 36+5. When you look at it that way it becomes fairly clear that adding your pack of 12 to 5 individual biscuits and then mulitplying that by the 3 packs just doesn’t make sense.
It absolutely does matter. You must do exponents after brackets and before multiplication and division, for the precise reason you said that exponents are shorthand for multiplication. In other words, there’s 4 groups, not three.
And this is why I use a calculator
But if you use biscuits once you get to the last bit and do the subtraction it all becomes worthwhile. If I have three packets of 12 tim tams and eat four tim tams what do I have? I have four tim tams in my tummy. Best maths ever.
Just make sure you don’t use an e-calculator, nor a Texas Instruments calculator.
They’re all correct, since the mnemonics are just ways to remember the actual rules