6th Grade Math Textbook, Fundamentals

 &KDSWHU

5-13

Order of Operations with

Rational Numbers

Objective To use the order of operations to simplify numerical expressions containing

rational numbers• To use a calculator to check solutions

The order of operations is used to simplify expressions
that contain any form of rational numbers.

Simplify: (0.4)^3 • ()

4

(0.4)(0.4)(0.4) • ()()()() Multiply like terms.

0.064 • Multiply.

 2 Simplify.

To simplify expressions that contain more than

one grouping symbol, begin computing with the

innermost set.

Simplify:  (^6) (  )[(2.4 • 5)(1)^9 ]
 (^6) (  )[(2.4 • 5)(1)^9 ] Compute within parentheses.
 (^6) ()[12(1)^9 ] Simplify the power.
 (^6) ()[12(1)] Multiply.
(12)
(12) Simplify.

• Divide, multiply by the reciprocal.


•  Simplify.

Some calculators have a fraction key, , and an exponent

key, , which you can use to check your solution to an

expression involving fractions and powers.

Check: (^6) (  )(2.4 • 5)(1)^9
Press 6 2 3 5 9 2.4 5 1 9
So  (^6) (  )(2.4 • 5)(1)^9 .
 6
9
 2
3
 1
Simplify each power before
multiplying the factors.
1/18
 1
(^126)
 6
9
2
3

1
18
5
9
2
3
5
9
2
3
 1
12
 2
3
0.064 • 625
16
625
16
 40
16
1
2
1
18
1
9
1
9
5
9
2
3
5
9
2
3
 5
2
 5
2
 5
2
 5
2
 5
2
To Key Fractions with
Press 2 3
758 Press 7 5 8
2
3
Remember:
Order of Operations

• First, compute operations
  within grouping symbols.


• Next, simplify exponents.


• Then multiply or divide
  from left to right.


• Last, add or subtract from
  left to right.