Lesson Order of Operations
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Algebra: Evaluation of expressions, parentheses
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<div> Without a standard set of rules to refer to, different students could get different answers for a problem like <p align="center"> <font color = "blue" size = "+3">5 + 3 * 2</font>. Should you <p align="center"> <font color = "red" size = "+1">Add first: 5 + 3 * 2 = 8 * 2 = 16</font> <p align="center"> OR <p align="center"> <font color = "green" size = "+2">Multiply first: 5 + 3 * 2 = 5 + 6 = 11</font> <p align="center"> ???</p></p> The order of operations answers this its a set of rules for what order to do things in, so that everyone will get the same answer (as long as they dont make mistakes!) Here it is </p> <center> <u>Order of operations</u> </p> <br/><br/> <table border="1" cellpadding="0" cellspacing="0" bgcolor = "#FFEBCD"> <tbody> <tr> <td valign="top" width="638"> <br/> <b><font size = "+1"> 1. Do the operations inside parentheses & exponentiations first. If there are more than one such operations, do the one on the left first and work to the right. <br/> <br/> 2. Do the multiplications and divisions. If there are more than one of these, do the one on the left first and work to the right. <br/> <br/> 3. Do the additions and subtractions. If there are more than one of these, do the one on the left first and work to the right. </font></b> <br/><br/> <u> </u> </td> </tr> </tbody> </table> </center> Since multiplication comes before addition, this means that 11 is the correct answer to the problem above. Here are two examples that show the order of operations in action! If you think you've got it, you can <a href = "http://www.mathick.com/mathick.php?topic=orderofoperations">try a practice problem here</a>. <div align="center"> <table width="671" border="1" cellpadding="0" cellspacing="5"> <tbody> <tr> <td width="105"> <center> Simplify:</center> </td> <td width="251"> <center> 12 + 6 ๗ 3 - 4 2</center> </td> <td width="32" bgcolor = "blue"> </td> <td width="258"> <center>(12 + 6) ๗ 3 - 4 2</center> </td> </tr> <tr> <td width="105"> <center>Operation with the highest precedence:</center> </td> <td width="251"> <center><b>Division</b></center> </td> <td width="32" bgcolor = "blue"> </td> <td width="258"> <center><b>Addition (since it's in Parentheses)</b></center> </td> </tr> <tr> <td width="105"> <center>Simplifies to:</center> </td> <td width="251"> <center>12 + 2 - 4 2</center> </td> <td width="32" bgcolor = "blue"> </td> <td width="258"> <center>18 ๗ 3 - 4 2</center> </td> </tr> <tr> <td width="105"> <center>Operation with the highest precedence:</center> </td> <td width="251"> <center><b>Multiplication</b></center> </td> <td width="32" bgcolor = "blue"> </td> <td width="258"> <center><b>Division</b></center> </td> </tr> <tr> <td width="105"> <center>Simplifies to:</center> </td> <td width="251"> <center>12 + 2 - 8</center> </td> <td width="32" bgcolor = "blue"> </td> <td width="258"> <center>6 - 4 2</center> </td> </tr> <tr> <td width="105"> <center>Operation with the highest precedence:</center> </td> <td width="251"> <center><b>Addition</b></center> </td> <td width="32" bgcolor = "blue"> </td> <td width="258"> <center><b>Multiplication</b></center> </td> </tr> <tr> <td width="105"> <center>Simplifies to:</center> </td> <td width="251"> <center>14 - 8</center> </td> <td width="32" bgcolor = "blue"> </td> <td width="258"> <center>6 - 8</center> </td> </tr> <tr> <td width="105"> <center>Operation with the highest precedence:</center> </td> <td width="251"> <center><b>Subtraction</b></center> </td> <td width="32" bgcolor = "blue"> </td> <td width="258"> <center><b>Subtraction</b></center> </td> </tr> <tr> <td width="105"> <center>Simplifies to:</center> </td> <td width="251"> <center>6</center> </td> <td width="32" bgcolor = "blue"> </td> <td width="258"> <center>-2</center> </td> </tr> </tbody> </table> </div> <center> <a href = "http://www.mathick.com/mathick.php?topic=orderofoperations">Try one out!</a> </center> </div>
