Download order of operations - Belle Vernon Area School District

1-6 Order of Operations
Objective
Use the order of operations to simplify
expressions.
Holt Algebra 1
1-6 Order of Operations
Vocabulary
order of operations
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.
Order of Operations
First:
Perform operations inside grouping
symbols.
Second:
Evaluate powers.
Third:
Perform multiplication and division
from left to right.
Fourth:
Perform addition and subtraction from
left to right.
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.
Holt Algebra 1
Please
Excuse
Parentheses
Exponents
My
Dear
Aunt
Sally
Multiply
Divide
Add
Subtract
1-6 Order of Operations
Example 1: Translating from Algebra to Words
Simplify each expression.
A. 15 – 2 · 3 + 1
15 – 2 · 3 + 1
15 – 6 + 1
10
B. 12 – 32 + 10 ÷ 2
12 – 32 + 10 ÷ 2
12 – 9 + 10 ÷ 2
12 – 9 + 5
8
Holt Algebra 1
There are no grouping symbols.
Multiply.
Subtract and add from left to right.
There are no grouping symbols.
Evaluate powers. The
exponent applies only to the 3.
Divide.
Subtract and add from left to
right.
1-6 Order of Operations
Check It Out! Example 1a
Simplify the expression.
1
8 ÷2
Holt Algebra 1
·3
1-6 Order of Operations
Check It Out! Example 1b
Simplify the expression.
5.4 – 32 + 6.2
Holt Algebra 1
1-6 Order of Operations
Check It Out! Example 1c
Simplify the expression.
–20 ÷ [–2(4 + 1)]
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
10 – x · 6
First substitute 3 for x.
10 – 3 · 6
Multiply.
Subtract.
10 – 18
–8
Holt Algebra 1
1-6 Order of Operations
Example 2B: Evaluating Algebraic Expressions
Evaluate the expression for the given value of x.
42(x + 3) for x = –2
42(x + 3)
42(–2 + 3)
42(1)
Perform the operation
inside the parentheses.
16(1)
Evaluate powers.
16
Holt Algebra 1
First substitute –2 for x.
Multiply.
1-6 Order of Operations
Check It Out! Example 2a
Evaluate the expression for the given value of x.
14 + x2 ÷ 4 for x = 2
Holt Algebra 1
1-6 Order of Operations
Check It Out! Example 2b
Evaluate the expression for the given value of x.
(x · 22) ÷ (2 + 6) for x = 6
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
Example 3A: Simplifying Expressions with Other
Grouping Symbols
Simplify.
2(–4) + 22
42 – 9
2(–4) + 22
42 – 9
–8 + 22
42 – 9
–8 + 22
16 – 9
14
7
2
Holt Algebra 1
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.
1-6 Order of Operations
Example 3B: Simplifying Expressions with Other
Grouping Symbols
Simplify.
3|42 + 8 ÷ 2|
3|42 + 8 ÷ 2|
The absolute-value symbols act as
grouping symbols.
3|16 + 8 ÷ 2|
Evaluate the power.
Divide within the absolute-value
symbols.
3|16 + 4|
3|20|
Add within the absolute-symbols.
3 · 20
Write the absolute value of 20.
60
Holt Algebra 1
Multiply.
1-6 Order of Operations
Check It Out! Example 3a
Simplify.
5 + 2(–8)
(–2)3 – 3
Holt Algebra 1
1-6 Order of Operations
Check It Out! Example 3b
Simplify.
|4 – 7|2 ÷ –3
Holt Algebra 1
1-6 Order of Operations
Check It Out! Example 3c
Simplify.
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
sum
product
quotient
Holt Algebra 1
subtract
add
multiply
divide
1-6 Order of Operations
Example 4: Translating from Words to Math
Translate each word phrase into a numerical
or algebraic expression.
A. the sum of the quotient of 12 and –3 and
the square root of 25
Show the quotient being added to
B. the difference of y and the product of 4
and
Use parentheses so that the
product is evaluated first.
Holt Algebra 1
.
1-6 Order of Operations
Check It Out! Example 4
Translate the word phrase into a numerical
or algebraic expression: the product of 6.2
and the sum of 9.4 and 8.
Holt Algebra 1
1-6 Order of Operations
Example 5: Retail Application
A shop offers gift-wrapping services at three
price levels. The amount of money collected
for wrapping gifts on a given day can be
found by using the expression 2B + 4S + 7D.
On Friday the shop wrapped 10 Basic
packages B, 6 Super packages S, and 5
Deluxe packages D. Use the expression to
find the amount of money collected for gift
wrapping on Friday.
Holt Algebra 1
1-6 Order of Operations
Example 5 Continued
2B + 4S + 7D
2(10) + 4(6) + 7(5)
20 + 24 + 35
44 + 35
79
First substitute the
value for each variable.
Multiply.
Add from left to right.
Add.
The shop collected $79 for gift wrapping on Friday.
Holt Algebra 1
1-6 Order of Operations
Check It Out! Example 5
Another formula for a player's total number of bases
is Hits + D + 2T + 3H. Use this expression to find
Hank Aaron's total bases for 1959, when he had 223
hits, 46 doubles, 7 triples, and 39 home runs.
Holt Algebra 1
1-6 Order of Operations
Lesson Quiz
Simply each expression.
1. 2[5 ÷ (–6 – 4)]
3. 5  8 – 4 + 16 ÷ 22
2.
52 – (5 + 4)
|4 – 8|
Translate each word phrase into a numerical
or algebraic expression.
4. 3 three times the sum of –5 and n
5. the quotient of the difference of 34 and
9 and the square root of 25
6. the volume of a storage box can be found
using the expression l · w(w + 2). Find the
volume of the box if l = 3 feet and w = 2 feet.
Holt Algebra 1