Is it possible to solve an equation with different operations in it correctly without using orders of operation? I was having a discussion with my friend who believes you can solve an equation from left to right no matter what the operations are. I told my friend that the answer you get would not be correct, but they still insist they are right. Who is right and why?
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You mean something like $1+23 \ne (1+2)3$? – Andre Apr 20 '15 at 23:13
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You're not really talking about solving equations here. You are talking about evaluating an expression. In such cases there are conventions that we use (the orders of operations) so that two people evaluating the same expression get the same value. It is possible to have a convention that works from left to right and is consistent with itself. It just isn't very "natural" to do so, but if your friend is working within such a convention then they will get their answers "right". – tomi Apr 21 '15 at 00:14
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1I mean for example: 7+7÷7+7×7-7=?.... my friend insists you solve from left to right which gives you an answer of 56....and I insist you solve using Order of Opperations and getting 50 as an answer! I know I'm right however I can't seem to convince her why I'm right and why her method doesn't work because it's not all addition or all multiplication in which it can be flipped around and still get the correct answer – Amanda Apr 21 '15 at 00:21
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You want to evaluate an expression.
You have to specify the order of evaluating if you concatenate several multiary operations (e.g. a o b o c). "Multiplication and division before addition and subtraction" is the law for the basic arithmetic operations.
The value of your expression is 50 therefore.
Other orders of operations can be specified in the expression by brackets.
If you don't want to use brackets, you can apply Reverse Polish notation or Polish notation.
IV_
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