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0011 0010 1010 1101 0001 0100 1011 1 TEKS 6.2E 2 4 Lesson 6 (2nd 6 Weeks) 0011 0010 1010 1101 0001 0100 1011 • The order in which operations are computed in an expression. 1 2 4 0011 0010 1010 1101 0001 0100 1011 • Follow this order of operations: STEP 1: Simplify any operations in parentheses and brackets. If there is more than one operation within a set of parentheses, follow the order of operations in steps 2, and 3. 1 2 4 • STEP 2: Calculate all multiplication and division from left to right. 0011 0010 1010 1101 0001 0100 1011 • STEP 3: Calculate all addition and subtraction from left to right. 1 2 4 • A phrase that is helpful in 0011 0010 1010 1101 0001 0100 1011 remembering the order of operations is: “Please Excuse My Dear Aunt Sally” 1 2 4 Please (Parentheses, first) Excuse (Exponents-we don’t do) 0011 0010 1010 1101 0001 0100 1011 My Dear (Multiply and Divide from Left to Right) 1 2 4 Aunt Sally (Add and Subtract from Left to Right) 0011 0010 1010 1101 0001 0100 1011 • Remember: Multiplication is not always done before division. Work left to right. Whichever one comes first, is done first. Same for addition and subtraction. 1 2 4 0011 0010 1010 1101 0001 0100 1011 Performing operations left to right only 21 6 3 5 21 6 3 5 27 3 5 27 3 5 9 5 45 The rules for order of operations exist so that everyone can perform the same consistent operations and achieve the same results. Method 2 is the correct method. Performing operations using order of operations 21 6 3 5 21 6 3 5 21 2 5 21 2 5 21 10 31 1 2 Can you imagine what it would be like if calculations were performed differently by various financial institutions or what if doctors prescribed different doses of medicine using the same formulas and achieving different results? 4 Simplify the Expression 12÷3+4·6-2·3 0011 0010 1010 1101 0001 0100 1011 • 1. There are no parentheses • 2. Multiply and divide from left to right. 12÷3+4·6-2·3 4 + 24 - 6 1 2 4 0011 0010 1010 1101 0001 0100 1011 3. Add and subtract from left to right. 4+24-6 28-6 22 4. The expression simplifies to 22. 1 2 4 0011 0010 1010 1101 0001 0100 1011 1. (8+3)-5 11-5 6 A good rule of thumb is to underline the part of the expression that you are doing first. 1 2 4 2. 24 - (19 - 19) 24 – 0 24 0011 0010 1010 1101 0001 0100 1011 1 2 4 3. 5 x 8 - 3 x 4 40 -12 28 0011 0010 1010 1101 0001 0100 1011 1 2 4 4. 3+5·4 3 + 20 23 0011 0010 1010 1101 0001 0100 1011 1 2 4 0011 0010 1010 1101 0001 0100 1011 5. (24 - 10) - 3 · 3 14 – 3 · 3 14- 9 5 1 2 4 6. 4(22-18÷3) · 5 4(22- 6 )· 5 4·16 · 5 64·5 320 0011 0010 1010 1101 0001 0100 1011 1 2 4 7. 3(18 - 12) - (5 - 3) 3 x 6- 2 0011 0010 1010 1101 0001 0100 1011 18- 2 16 1 2 4 If a = 5 and b = 4, solve 5a – 3b 5 x 5a – 3 x 4b 25 - 12 13 0011 0010 1010 1101 0001 0100 1011 1 2 4 A family of five is going to the zoo. Adult tickets are $7 each and children’s tickets are $5 each. 0011 0010 1010 1101 0001 0100 1011 1 2 4 Write an equation to find c, the total cost of going to the zoo if you buy two adult and three children’s tickets. 0011 0010 1010 1101 0001 0100 1011 1 2 4 0011 0010 1010 1101 0001 0100 1011 Solve the equation you wrote. 1 2 4 (2 x 7) + (3 x 5) = c 0011 0010 1010 1101 0001 0100 1011 (2 x 7) + (3 x 5) = c 14 +15 = c $ 29 = c 1 2 4