Suppose I have an expression like this:
$$9\div 7 \times \ 8 - 4 \times 9 + 3 \times 2 \div 4$$
How do I evaluate this expression?
I'm trying to recover my math knowledge. I always check the PEMDAS acronym to see what I evaluate first. But in school I was taught that if two or more operations have equal precedence you solve it left to right.
That seems confusing to me. Can someone clarify what should be done in this case and why?
Multiplying and division are "stronger" than adding and subtracting,so you do them first.But when you have only multiplying and divison they are equal.If you keep the first number in place,you can change the order of the other operations,for example:
$1000 \times 6 \div 5 \times 7 \div 2$ is the same as $1000 \times 7 \div 2 \div 5 \times 6$ or $1000 \div 2 \times 6 \times 7 \div 5$.
Also adding and subtracting are equal.When evaluating you usually go from left to right,but first do the multiplying and division,then return back to the left side and start again, this time adding and subtracting.There are other operations that are even "stronger",but what comes in brackets must always be done first!
In your example you go like this:
$$9 \div 7 \times 8 - 4 \times 9 + 3 \times 2 \div 4=(9 \div 7 \times 8)-(4 \times 9) + (3 \times 2 \div 4)$$
There are many other rules and shortcuts that help us calculate faster,but you should first get used to the basics.