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# 1-4 Order of Operations Learn to use the order of operations.

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1-4 Order of Operations Learn to use the order of operations.

1-4 Order of Operations Vocabulary numerical expressions simplify order of operations

1-4 Order of Operations A numerical expression is a mathematical phrase that includes only numbers and operation symbols. Numerical Expressions 4 + 8 ÷ 2  6 371 – 203 + 2 5,006  19 When you simplify a numerical expression, you find its value.

1-4 Order of Operations When an expression has more than one operation, you must know which operation to do first. To make sure that everyone gets the same answer, we use the order of operations. ORDER OF OPERATIONS 1. Perform operations in parentheses. 2. Find the values of numbers with exponents. 3. Multiply or divide from left to right as ordered in the problem. 4. Add or subtract from left to right as ordered in the problem.

1-4 Order of Operations The first letters of these words can help you remember the order of operations. PleaseParentheses ExcuseExponents MyMultiply/ Dear Divide AuntAdd/ Sally Subtract Helpful Hint

1-4 Order of Operations Additional Example 1A: Using the Order of Operations Simplify the expression. There are no parentheses or exponents. 15 – 5 Divide. 10 Subtract. 15 – 10 ÷ 2

1-4 Order of Operations Additional Example 1B: Using the Order of Operations Simplify the expression. 9 + (21 ÷ 7)  5 Perform operations within parentheses. Multiply. 9 + 3  5 9 + 15 Add. 24

1-4 Order of Operations Check It Out: Example 1A Simplify the expression. There are no parentheses or exponents. 12 – 3 Divide. 9 Subtract. 12 – 6 ÷ 2

1-4 Order of Operations Check It Out: Example 1B Simplify the expression. 7 + (24 ÷ 6)  3 Perform operations within parentheses. Multiply. 7 + 4  3 7 + 12 Add. 19

1-4 Order of Operations Additional Example 2A: Using the Order of Operations with Exponents Simplify the expression. 2 4 + 6  4 There are no parentheses.Multiply. 16 + 6  4 16 + 24 Add. 40 2 + 6  4 4 Find the value of numbers with exponents.

1-4 Order of Operations Additional Example 2B: Using the Order of Operations with Exponents Simplify the expression. 24 ÷ (9 – 6)  3 2 – 10 Perform operations within parentheses. Multiply. 8  9 – 10 72 – 10 Divide. 62 Find the value of numbers with exponents. 24 ÷ (9 – 6)  3 2 – 1024 ÷ 3  3 2 – 10 24 ÷ 3  9 – 10 Subtract.

1-4 Order of Operations Check It Out: Example 2A Simplify the expression. 4 2 + 3  7 There are no parentheses.Multiply. 16 + 3  7 16 + 21 Add. 37 4 2 + 3  7 Find the value of the number with the exponent.

1-4 Order of Operations Check It Out: Example 2B Simplify the expression. 32 ÷ (8 – 4)  2 2 – 12 Perform operations within parentheses. Multiply. 8  4 – 12 32 – 12 Divide. 20 Find the values of numbers with exponents. 32 ÷ (8 – 4)  2 2 – 12 32 ÷ 4  2 2 – 12 32 ÷ 4  4 – 12 Subtract.

1-4 Order of Operations Additional Example 3: Consumer Application 24 + 15 39 Mr. Kellett spent \$39 on CDs. Mr. Kellett bought 6 used CDs for \$4 each and 5 used CDs for \$3 each. Simplify the following expression to find the amount Mr. Kellett spent on CDs. 6  4 + 5  3

1-4 Order of Operations Check It Out: Example 3 Ms. Nivia bought 4 new CDs for \$8 each and 6 used CDs for \$4 each. Simplify the following expression to find the amount Ms. Nivia spent on CDs. 4  8 + 6  4 32 + 24 56 Ms. Nivia spent \$56 on CDs.

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