Order of Operations & Inverse Operations 1 © 2013 Meredith S. Moody

Objective: You will be able to…  Use order of operations  Perform inverse operations 2 © 2013 Meredith S. Moody

Vocabulary  Order of operations: The standard order in which mathematical operations are performed Simplify inside parentheses or above/below the division bar Simplify exponents Multiply & divide (from left to right) Add & subtract (from left to right) 3 © 2013 Meredith S. Moody

Remembering the order  Please (parentheses)  Excuse (exponents)  My (multiplication)  Dear (division)  Aunt (addition)  Sally (subtraction) 4 © 2013 Meredith S. Moody

Example 1  Evaluate: 2(6+4) – 3 · 5 Simplify inside parentheses: 2(10) – 3 · 5 Multiply: 20 – 15 Subtract: 5 5 © 2013 Meredith S. Moody

Example 2  An auto mechanic ordered eight car spark plugs and four truck spark plugs. Car spark plugs cost $0.75 each and truck spark plugs cost $4.00 each. Find the total cost for these parts. 8 x x $18 6 © 2013 Meredith S. Moody

Vocabulary  Commutative property of addition: a + b = b + a  This means that when adding, the order of the numbers doesn’t matter is the same as They both = 7 7 © 2013 Meredith S. Moody

Vocabulary  Commutative property of multiplication: a x b = b x a  This means that the order of the numbers doesn’t matter 2 x 3 is the same as 3 x 2 They both = 6 8 © 2013 Meredith S. Moody

Vocabulary  Associative property of addition: a + (b + c) = (a + b) + c  This means that even if you group the numbers together differently, adding the same numbers in a different order will have the same answer 1 + (2 + 3)  = 6 (1 + 2) + 3  = 6 9 © 2013 Meredith S. Moody

Vocabulary  Associative property of multiplication: a x (b x c) = (a x b) x c  This means that even if you group the numbers together differently, multiplying the same numbers in a different order will have the same answer 2 x (3 x 4)  2 x 12 = 24 (2 x 3) x 4  6 x 4 = © 2013 Meredith S. Moody

Vocabulary  Distributive property: a(b + c) = a x b + a x c  This means that your answer will be the same whether you add what is in the parentheses and then multiply by your initial number OR multiply both values by your initial number and then add 2 x x 4  = 14 2(3 + 4)  2 x 7 = © 2013 Meredith S. Moody

Example  What property is being shown? 11 · (12 · 13) = (11 · 12) · 13  Associative property of multiplication =  Commutative property of addition 11 · ( ) = (11 · 12) + (11 · 13)  Distributive property 12 © 2013 Meredith S. Moody

Vocabulary  Inverse operations: Mathematical operations that reverse each other’s results addition and subtraction multiplication and division 13 © 2013 Meredith S. Moody

Example 1  Inverse operations reverse a result  Give Joe $10  take $10 away from Joe  Pass out a class set of novels  collect the novels from the students  I have 2  I multiply by 3  I have 6  I divide by 3  I have 2  You have 4  you subtract 1  you have 3  you add 1  you have 4 14 © 2013 Meredith S. Moody

Example 2  Start with the number 12  Add 3  Multiply by 7  Divide by 7  Subtract 3. What is your final number? © 2013 Meredith S. Moody

You try!  Choose a number  Add a value to your number  Multiply the new number by 2  Perform the inverse operations that would get you to your original number 16 © 2013 Meredith S. Moody