6th Grade Math Textbook, Fundamentals

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1-10

Simplify: 12(2)^3 (10)

12(2)^3 (10) Simplify the exponent.

12[(2)(2)(2)] (10)

12(8)(10) Multiply.

 96 (10) Add.

 106

(^1) Simplify: [( 24 3)( 20 4)]  2
[( 24 3)( 20 4)]  2
[(8)(5)]  2 Multiply.
40  2 Divide.
20
Compute within
parentheses. Work
from left to right.
2
Grouping Symbols
parentheses ( )
brackets [ ]
Order of Operations
Objective To use the order of operations to simplify numerical expressions with grouping
symbols and exponents •To use a calculator to check solutions
When more than one operation is used in a mathematical expression,
you need to know which operation to perform first so there is only one
result. The is a set of rules that are used to simplify
mathematical expressions with more than one operation.
Todd and Ana both simplified this expression:
62 (8 2 • 2)  22
Todd’s answer was 4, and Ana’s answer was 33.
Which student was correct?

To simplify the expression, use the order of operations.

62 (8 2 • 2)  22

62 (8 2 • 2) 22

62  12  22 Simplify the exponents.

36  12  4 Divide.

36  3 Subtract.

33

Ana’s answer was correct.

Sometimes an expression contains more than one set of

grouping symbols. When this happens, begin simplifying

with the innermost set.

Simplify: [(32 43) (15)] • 2^3

[(32 43)(15)] • 2^3 Simplify within parentheses.

[75(15)] • 2^3 Simplify within the brackets.

5 • 2^3 Simplify the exponent.

5 • 8 Multiply.

 40

order of operations

Simplify within parentheses.

First multiply 2 • 2, then add.

Key Concept

Order of Operations

• Following the order of operations,
  first simplify operations within
  grouping symbols.


• Simplify exponents.


• Multiply or divide from left to right.


• Add or subtract from left to right.

Think

23 2 • 2 • 2