Page 348 - Basic College Mathematics with Early Integers

S E C T I O N 4.5 I FRACTIONS, DECIMALS, AND ORDER OF OPERATIONS 325

Example 9 Insert 6, 7, or = to form a true statement. PRACTICE 9
Insert 6, 7, or = to form a
0.7 7 true statement.
9 1 b. 0.4 4
a. 0.54
7 2 9
Solution: We write as a decimal and then compare.
9 5
c. 0.72
0.77 Á= 0.7 Original numbers 0.7 7 7
9
97.00
Decimals 0.7 0.7
- 63
70 Compare 0.7 = 0.7
- 63
7
7 Thus, 0.7 =
9
Work Practice 9

Example 10 Write the numbers in order from smallest to largest. PRACTICE 10
Write the numbers in order
9 4 from smallest to largest.
, , 0.456
20 9 1 3
a. , 0.302,
Solution: 3 8
1 2
b. 1.26, 1 , 1
9 4 4 5
Original numbers 0.456
20 9
5
c. 0.4, 0.41,
Decimals 0.450 0.444 Á 0.456
7
Compare in order 2nd 1st 3rd
Written in order, we have
1st 2nd 3rd
T T T
4 9
, , 0.456
9 20
Work Practice 10

Objective Simplifying Expressions with Decimals
and Fractions

In the remaining examples, we will review the order of operations by simplifying
expressions that contain decimals and fractions.

Order of Operations
1. Perform all operations within parentheses ( ), brackets [ ], or other grouping
symbols such as fraction bars or square roots.
2. Evaluate any expressions with exponents.
3. Multiply or divide in order from left to right. Answers
4. Add or subtract in order from left to right. 9. a. 6 b. = c. 6
1 3 1 2
10. a. 0.302, , b. 1 , 1.26, 1
3 8 4 5
5
c. 0.4, 0.41,
7