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"Reconsidering Your Answers to WARM UP Questions" | ||

Qu.1 in the WARM UPS tests order of operation. It was: Simplify: 3 + 4 x 5. There are two operations - addition and multiplication. Even though addition "comes first" when reading from left to right, multiplication has higher priority. The multiplication must be completed first, then the 3 is added to the result. The expression is equal to 23. This is the result in question 3 because one must "Multiply 4 and 5 and add 3 to the result." This is not the result in question 2 because one must "Add 3 and 4 then multiplying the result by 5." The result is 35. |

"Try A Question or Some Questions, or Take A Break, or Continue" |
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"Please, My Dear Aunt Sally" OR | ||

"But I Want It to Do Addition First" | ||

To answer question 4 "Write an expression which indicates that 4 and 8 are added and the result is multiplied by 2" you need to use parentheses or other marks of inclusion to indicate that addition is to be completed before the multiplication. An answer is (4 + 8) x 2. Other answers exist. - THE ORDER OF OPERATIONS (Topmost First)
- Parentheses or other Marks of Inclusion (Innermost First)
- Multiplication or Division (Leftmost First)
- Addition or Subtraction (Leftmost First)
Restated that's: Parentheses first, then Multiply or Divide then Add or Subtract: Please, My Dear Aunt Sally. Question 5 "Write an expression which indicates that 4 is multiplied by 2 then 8 is added to the result" does not require inclusion marks since multiplication has priority over addition. An answer is 4 x 2 + 8. Other answers exist. |

The Inclusion Bar | ||

The bar is an important mark of inclusion. It is used in 3 places: An example of the last use is shown and simplified below. |

"Stop. Take Notes. Take A Break. | |

Do Research on the Calculator. Then, | |

Answer Questions or Go Straight to the Quiz" |

© 2005, Agnes Azzolino www.mathnstuff.com/math/spoken/here/2class/80/c80b.htm |