I am tutoring someone in pre algebra and she was having trouble reducing equations so I wrote a little basic English language algorithm for doing it:
1- Do everything in the innermost parentheses, if any.
2- Do all exponents and square roots, working from left to right.
3- Do all multiplications and divisions, working from left to right.
4- Do all additions and subtractions, working from left to right.
If there were no parenthesis, you are done. If there were one or more parenthesis, make another line in your solution without the parenthesis you just solved, and everything else in the equation the same.
If there are more parentheses, go to step one.
If there are no more parentheses, go to step two, and you should have your answer!
Is this correct?
/yah I understand the that due to the commutative property “working from left to right” is optional, but it keeps it organized!
Well, even so, there’s no need to include a rule which she will later discover to be incorrect. If there are no compound exponents, then you don’t even need to mention the order of associativity for exponentiation.
Still, you might as well get it right when you first learn it, rather than finding out later that there were “errors” in what you were told.
When I was in grade school, before we discussed the number line and negative numbers, the teacher thought it would be simpler to tell the class, “You can’t subtract a larger number from a smaller number.” When she wanted to get into negative numbers, she was met with a wall of protests: “But you said we can’t subtract a larger number from a smaller number!”
Just sayin’. It might be simpler to go right-to-left out of the gate.
Well, he did say “due to the commutative property”; I assume he knows that addition and multiplication are commutative whereas subtraction and division are not.
You have the basic idea right, but I can offer a few nitpicks:
I was confused as to how the instructions at the end related to the rest of it. At first I assumed this
was something you were doing after steps 1 through 4, which made no sense to me.
If there’s an expression (more complicated than a single number) under a radical sign, you have to evaluate that expression before taking the square root. I don’t know whether your tutee is seeing things like sqrt(16+9) yet (with the “16+9” all under the square root sign), but if so, the radical sign acts as a grouping symbol, in the sense that you have to do the 16+9 before taking the square root.
And a pet peeve: you’re using the word equation when you actually mean expression. Don’t call it an “equation” unless it has a left side and a right side separated by an = sign. Failure to make this distinction can lead to confusion over what the equals sign actually means, as noted here.
Actually, it’s the associative property, not the commutative property, that’s relevant here.
If it’s all addition, or all multiplication, it doesn’t matter whether you go from left to right or not, because addition and multiplication are associative. So (13)6 is equal to 1(36); and (7+3)+2 = 7+(3+2). Subtraction and division are not associative: (7-3)-2 does not equal 7-(3-2).
If the tutee has learned about operations with negative numbers, she can be taught to think of subtraction as addition of negatives, and then the order wouldn’t matter: 7 - 3 - 2 is the numbers 7, -3, and -2 added in any order.