Order of OperationsDate: 01/25/98 at 04:26:11 From: ANDREW HATFIELD Subject: MATH Evaluate the expression: 2 3 30-5 +4 Date: 01/28/98 at 12:44:21 From: Doctor Joe Subject: Re: MATH Dear Andrew, First of all, let's realise that there are three major operations involved in this question: (1) subtraction (2) addition (3) multiplication. Though it does not appear in your question, there is another operation, called division. I assume that you know how to do each operation on its own; for example, you already know how to compute: (a) 23 + 34 = 57 (b) 40 - 11 = 29 (c) 23 x 4 = 92 You can see that there may be some trouble if the operations are written in a linear sequence; for example: 3 - 4 x 5 One does not know which operation to perform first. The solution to the problem is this: by convention, we compute the sequence using these rules: (1) Perform the operation first if the terms involved are bracketed. For instance: 2 - (3 + 5) We do the (3 + 5) bit first! So, the next step is: 2 - (3 + 5) = 2 - 8 Okay so far? (2) After evaluating bracketed terms, perform multiplication or division in that order. For example: 3 + 4 x 5 / 2 (where / means divided by) So, multiply 4 and 5 together first. That's 20. Then we divide it by 2 to get 10. Next, we add 3 to 20. We obtain 23 as the final answer. (3) Last of all perform addition or subtraction in that order; for example: 3 - 4 + 5 So we subtract 4 from 3, to obtain -1. Then we add -1 to 5 to obtain 4 as the final answer. Let's try practising these rules in the following problems: (1) 20 + 34 - 4 x 5 Answer: 20 + 34 - 4 x 5 = 20 + 34 - 20 = 54 - 20 = 34. (2) 30 - 5 + 4 x 2 Answer: 30 - 5 + 4 x 2 = 30 - 5 + 8 = 25 + 8 = 33. Finally, let's discuss some notation found in your question: 2 What does 5 (also written as 5^2, using my notation) mean? Well, it simply means 5 x 5, i.e. 5 multiplied by itself, and together you have a product of two 5's. In general, n^m means n x n x n x ... x n (altogether, m copies of n's). Here's another example: 4^6 = 4 x 4 x 4 x 4 x 4 x 4. There are 6 copies of 4. Let's do one more problem: Question: 2^4 - 5^2 + 100 Answer: 2^4 - 5^2 + 100 = 2 x 2 x 2 x 2 - 5 x 5 + 100 = 4 x 2 x 2 - 25 + 100 = 8 x 2 - 25 + 100 = 16 - 25 + 100 = -9 + 100 = 91 Working out your problem: 2 3 30-5 +4 = 30 - 5 x 5 + 4 x 4 x 4 You complete the rest of the problem. Feel free to write if you have further queries. -Doctor Joe, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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