Holt Algebra 1

1-6 Order of Operations1-6 Order of Operations

Holt Algebra 1

Warm Up

Lesson Presentation

Lesson Quiz

Holt Algebra 1

1-6 Order of Operations

Find each square root.

1.

Write all classifications that apply to each real

number.

3. -55

Bell Quiz 1-6

5 pts

possible

3 pts

2 pts25

Holt Algebra 1

1-6 Order of Operations

Questions on 1-5

Holt Algebra 1

1-6 Order of Operations

Use the order of operations to simplify expressions.

Objective

Holt Algebra 1

1-6 Order of Operations

order of operations

Vocabulary

Holt Algebra 1

1-6 Order of Operations

When a numerical or algebraic expression contains

more than one operation symbol, the order of operations tells which operation to perform first.

First:

Second:

Third:

Fourth:

Perform operations inside grouping symbols.

Evaluate powers.

Perform multiplication and division from left to right.

Perform addition and subtraction from left to right.

Order of Operations

Holt Algebra 1

1-6 Order of Operations

Grouping symbols include parentheses ( ), brackets [ ], and braces { }. If an expression contains more than one set of grouping symbols, evaluate the expression from the innermost set first.

Holt Algebra 1

1-6 Order of Operations

Helpful Hint

The first letter of these words can help you remember the order of operations.

Please

Excuse

My

Dear

Aunt

Sally

Parentheses

Exponents

Multiply

Divide

Add

Subtract

Holt Algebra 1

1-6 Order of Operations

Simplify each expression.

A. 15 – 2 · 3 + 1

There are no grouping symbols.

Multiply.

Subtract and add from left to right.

B. 12 – 32 + 10 ÷ 2

There are no grouping symbols.

Evaluate powers. The exponent applies only to the 3.

Divide.Subtract and add from left to right.

Example 1: Translating from Algebra to Words

Holt Algebra 1

1-6 Order of Operations

1a: 8 ÷ · 3

There are no

grouping symbols.

Divide. Multiply.

Check It Out! Example 1

Simplify each expression.1 2

1b: 5.4 – 32 + 6.2 There are no

grouping symbols.

Subtract. Add.

1c: –20 ÷ [–2(4 + 1)]There are two sets of

grouping symbols.

Perform the operations

in the innermost set.Perform the operation

inside the brackets.Divide.

Holt Algebra 1

1-6 Order of Operations

Example 2A: Evaluating Algebraic Expressions

Evaluate the expression for the given value

of x.

10 – x · 6 for x = 3

First substitute 3 for x.

Multiply.

Subtract.

Holt Algebra 1

1-6 Order of Operations

Evaluate the expression for the given value of x.

42(x + 3) for x = –2

First substitute –2 for x.

Perform the operation inside the parentheses.

Evaluate powers.

Multiply.

Example 2B: Evaluating Algebraic Expressions

Holt Algebra 1

1-6 Order of Operations

Evaluate the expression for the given value of x.

2a: 14 + x2 ÷ 4 for x = 2

2b: (x · 22) ÷ (2 + 6) for x = 6

Check It Out! Example 2

Holt Algebra 1

1-6 Order of Operations

Fraction bars, radical symbols, and absolute-value symbols can also be used as grouping symbols. Remember that a fraction bar indicates division.

Holt Algebra 1

1-6 Order of Operations

Simplify.

2(–4) + 22

42 – 9

Example 3A: Simplifying Expressions with Other

Grouping Symbols

The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing.

Multiply to simplify the numerator.

Evaluate the power in the denominator.

Add to simplify the numerator. Subtract to simplify the denominator.

Divide.

Holt Algebra 1

1-6 Order of Operations

Example 3B: Simplifying Expressions with Other

Grouping Symbols

Simplify.

3|42 + 8 ÷ 2|

The absolute-value symbols act as grouping symbols.

Evaluate the power.

Divide within the absolute-value

symbols.

Add within the absolute-symbols.

Write the absolute value of 20.

Multiply.

Holt Algebra 1

1-6 Order of Operations

3a: 5 + 2(–8)

(–2) – 3

3b: |4 – 7|2 ÷ –3

Check It Out! Example 3a

Simplify.

3

Holt Algebra 1

1-6 Order of Operations

Check It Out! Example 3c

Simplify.

The radical symbol acts as a grouping symbol.

Subtract.

Take the square root of 49.

Multiply.

Holt Algebra 1

1-6 Order of Operations

You may need grouping symbols when translating from words to numerical expressions.

Remember!

Look for words that imply mathematical operations.

difference subtractsum addproduct multiply

quotient divide

Holt Algebra 1

1-6 Order of Operations

HOMEWORKSec 1-6 (Pg 43)1, 2, 5, 8, 11, 14, 17, 24-38, 42-46, 66, 81, 83, 85, 87, 88

Holt Algebra 1

1-6 Order of Operations

HOMEWORK

Holt Algebra 1

1-6 Order of Operations

HOMEWORK