The order of operations is a set of rules for solving math problems with mixed operations. The acronym PEMDAS is used to remember the order: parentheses, exponents, multiplication, division, addition, and subtraction. The left-to-right rule is also important. The order of operations ensures standardized results and universal communication in mathematics.
The order of operations is a set of rules that must be kept in mind when doing math problems. These rules tell people when to do various things in a math problem with mixed operations, such as (7 + 2) x 4 – 3. There are a number of possible answers to this problem, depending on the order in which the multiplication , subtraction , and addition are performed, but only one correct answer, because the order of operations tells people how to solve the problem.
According to the order of operations, when faced with a math problem that has mixed operations, one should do everything in parentheses first, followed by exponents and roots, and then, working from left to right, multiplication and division. Finally, also working from left to right, addition and subtraction. Sometimes people use the acronym PEMDAS, for parentheses, exponents, multiplication, division, addition and subtraction, to remember the order of operations. The “please excuse my dear Aunt Sally” mnemonic to help people learn this acronym is used in a number of beginner math lessons.
Taking the above example problem, the first thing we would do would be to add inside the bracket, 7+2, which equals 9. Then, we would have to do the multiplication, to reach 36. Finally, the 3 must be subtracted, for a total of 33. The order of operations applies to any math problem, from simple to complex. If no particular order were established, people could get equally correct results. For example, someone might read through the previous problem and find an answer of 9, adding 7+2 to get 9, subtracting 3 from 4 to get 1, and multiplying 9 by 1 to get 9.
The left-to-right rule for addition and subtraction and multiplication and division in the order of operations is also important. In a problem like 9 – 7 + (4 x 5) ÷ 10, for example, you would do the parenthesis first, ending up with 9 – 7 + 20 ÷ 10. Division comes later, so 20 ÷ 10 = 2. Addition It doesn’t take precedence over subtraction, so these are done left to right. The answer to the problem is therefore 4, because 9 – 7 = 2 and 2 + 2 = 4. Prioritizing addition over subtraction and not following the left-to-right rule would result in 9 – 9 = 0, a very different answer!
In a sense, the order of operations tells people how to read math problems, just like the rules of grammar tell people how to read written languages. The rules of grammar and mathematics are both designed to ensure that everyone can write and read universally, which ensures that people can communicate freely with people they may never interact with personally. The standardization created by the order of operations is especially important in mathematics because there are so many ways to work on complex problems without it, and this would result in a multitude of conflicting answers.
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