Is the 2 Related to the Numbers in Parentheses?Date: 10/05/2001 at 11:13:49 From: Tressie Grant Subject: Order of operations I'm having difficulty understanding the correct procedure for an order of operations 6th grade math problem. My math-oriented family disagrees with the teacher. Which is the correct way to solve this problem: 36/2(8-5) = ? A) The 2 is related to the numbers in the parentheses. Using the distributive property to show this, the equation would then be 36 / (2x8 -2x5) = 36 / (16-10) = 36 / 6 = 6 or B) 36/2(8-5) = also written 36/2x(8-5) = parenthesis first and then they disappear 36/2x3 = order of operations says divide and multiply in order so 36/2 = 18 then multiply 18x3 = 54 The answer changes due to the division taking precedence when following the right-to-left order for division and multiplication. Date: 10/05/2001 at 12:14:29 From: Doctor Ian Subject: Re: Order of operations Hi Tressie, If the person who wrote the expression intended for the 2 to be related to the numbers in the parentheses, he should have written 36/(2(8-5)) As it is, the standard order of operations specifies that parentheses are to be resolved before anything else; and once parentheses have been resolved, multiplications and divisions should be resolved next, working from left to right; so 36/2(8-5) = 36 / 2 * (8 - 5) = 36 / 2 * 3 = 18 * 3 = 54 The original expression, without the extra parentheses, is a little like this sentence: "Bob and Alice were drunk, so we took their keys and drove them home." Most people would 'know' that the speaker drove Alice and Bob home; but the rules of English say that the speaker drove the keys home, leaving us in the dark about what happened to Alice and Bob. This kind of ambiguity is largely ignored in everyday language, where semantic information is sufficient for disambiguation. However, in math, numbers (like '2') have no semantic information associated with them, so it becomes essential to know what the rules are, and to follow them. Does this help? Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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