Order of Operations Giant Elephants May Attack

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Presentation transcript:

Order of Operations Giant Elephants May Attack When a numerical or algebraic expression contains more than one operation symbol, the order of operations tells which operation to perform first. Order of Operations Perform operations inside grouping symbols. First: Giant Elephants May Attack Second: Evaluate powers. Third: Perform multiplication and division from left to right. Perform addition and subtraction from left to right. Fourth:

Giant Elephants May Attack Grouping symbols Exponents Multiply/ Divide Grouping symbols include parentheses ( ), brackets [ ], braces { }, fraction bar /, absolute value | |, and square root . If an expression contains more than one set of grouping symbols, evaluate the expression from the innermost set first. Grouping symbols Exponents Multiply/ Divide left to right Addition/subtraction Giant Elephants May Attack

Example 1: Translating from Algebra to Words Simplify each expression. There are no grouping symbols or exponents. A. 15 – 2 · 3 + 1 = 15 – 2 · 3 + 1 = 15 – 6 + 1 Multiply. = 9 + 1 = 10 Subtract and add from left to right. B. 12 – 32 + 10 ÷ 2 = 12 – 32 + 10 ÷ 2 There are no grouping symbols. = 12 – 9 + 10 ÷ 2 Evaluate powers. The exponent applies only to the 3. = 12 – 9 + 5 Divide. Subtract and add from left to right. = 3 + 5 = 8

Check It Out! Example 3 Simplify the expression. –20 ÷ [–2(4 + 1)] There are two sets of grouping symbols. = –20 ÷ [–2(4 + 1)] Perform the operations in the innermost set. = –20 ÷ [–2(5)] Perform the operation inside the brackets. = –20 ÷ –10 = 2 Divide.

Example 4: Simplifying Expressions with Other Grouping Symbols The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing. 𝟐 −𝟒 +𝟐𝟐 𝟒 𝟐 −𝟗 = (𝟐 −𝟒 +𝟐𝟐) ( 𝟒 𝟐 −𝟗) Multiply to simplify the numerator. = −𝟖+𝟐𝟐 𝟒 𝟐 −𝟗 Evaluate the power in the denominator. = −𝟖+𝟐𝟐 𝟏𝟔−𝟗 Add to simplify the numerator. Subtract to simplify the denominator. = 𝟏𝟒 𝟕 = 2 Divide.

Example 5: Simplifying Expressions with Other Grouping Symbols The absolute-value symbols act as grouping symbols. 3|42 + 8 ÷ 2| = 3|42 + 8 ÷ 2| Evaluate the power within the absolute-value symbols. = 3|16 + 8 ÷ 2| Divide within the absolute-value symbols. = 3|16 + 4| = 3|20| Add within the absolute-symbols. = 3 · 20 Write the absolute value of 20. = 60 Multiply.

Check It Out! Example 6 Simplify. |4 – 7|2 ÷ –3 The absolute-value symbols act as grouping symbols. = |4 – 7|2 ÷ –3 = |–3|2 ÷ –3 Subtract within the absolute-value symbols. = 32 ÷ –3 Write the absolute value of –3. = 9 ÷ –3 Square 3. = –3 Divide.

Check It Out! Example 7 Simplify. The radical symbol acts as a grouping symbol. Subtract inside the radical. = 3 · 7 Take the square root of 49. = 21 Multiply.