1-3 Order of Operations

Warm UpPerform the operations in order from left to right.

1. 8 + 4 – 22. 9 3 + 13. 7 – 3 + 54. 20 ÷ 4 + 6

10

289

11

1-3 Order of Operations

Problem of the Day

0 1 2 3 4 5 6 7 8 9 = 1Put the appropriate plus or minus signs between the numbers so that the total equals 1.

0 + 1 – 23 + 45 + 67 – 89 = 1

1-3 Order of Operations

Vocabulary

numerical expressionssimplifyorder of operations

Learn to use the order of operations.

1-3 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.

1-3 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 OPERATIONS1. 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.

1-3 Order of Operations

The first letters of these words can help you remember the order of operations.Please ParenthesesExcuse ExponentsMy Multiply/Dear DivideAunt Add/Sally Subtract

Helpful Hint

1-3 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

15 – 10 ÷ 2

1-3 Order of Operations

Additional Example 1B: Using the Order of Operations

Simplify the expression.

9 + (21 ÷ 7) 5

9 + (21 ÷ 7) 5

Perform operations within parentheses.

Multiply.

9 + 3 5

9 + 15

Add. 24

1-3 Order of Operations

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1-3 Order of Operations

Additional Example 2A: Using the Order of Operations with Exponents

Simplify the expression.

24 + 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.

1-3 Order of Operations

Additional Example 2B: Using the Order of Operations with Exponents

Simplify the expression.

24 ÷ (9 – 6) 32 – 10

Perform operations within parentheses.

Multiply.

8 9 – 10

72 – 10

Divide.

62

Find the value of numbers with exponents.

24 ÷ (9 – 6) 32 – 10

24 ÷ 3 32 – 10

24 ÷ 3 9 – 10

Subtract.

1-3 Order of Operations

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1-3 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

1-3 Order of Operations

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1-3 Order of Operations

1. Simplify the expression.

17 + 6 3

A. 26

B. 35

C. 42

D. 69

Lesson Quiz for Student Response Systems

1-3 Order of Operations

2. Simplify the expression.

(14 – 6)2 – 12

A. 52

B. 58

C. 62

D. 64

Lesson Quiz for Student Response Systems

1-3 Order of Operations

3. Simplify the expression.

4 + 8 3 – 7

A. 11

B. 19

C. 21

D. 29

Lesson Quiz for Student Response Systems

1-3 Order of Operations

4. Simplify the expression.

53 – 93 3

A. 94

B. 84

C. 74

D. 64

Lesson Quiz for Student Response Systems

1-3 Order of Operations

5. Philip bought 5 papayas for $2 each and 7 pineapples for $3 each. Simplify the expression to find the amount Philip spent on fruits: 5 2 + 7 3.

A. $12

B. $15

C. $31

D. $35

Lesson Quiz for Student Response Systems