Examples and Exercises

Answers

Example 2.8

(a) 4+3⋅7
Are there any parentheses? No.
Are there any exponents? No.
Is there any multiplication or division? Yes.
Multiply first. 4+3⋅7
Add. 4+21

25
(b)

(4+3)⋅7
Are there any parentheses? Yes.

(4+3)⋅7
Simplify inside the parentheses.  (7)7
Are there any exponents? No
Is there any multiplication or division? Yes.
Multiply 49


Example 2.9

(a) 18÷9⋅2
Are there any parentheses? No.
Are there any exponents? No.
Is there any multiplication or division? Yes.
Multiply and divide from left to right. Divide.  2 \cdot 2
Multiply. 4
(b)
 18⋅9÷2
Are there any parentheses? No.
Are there any exponents? No.
Is there any multiplication or division? Yes.
Multiply and divide from left to right.
Multiply. 162 ÷ 2
Divide. 81


Example 2.10

18÷6+4(5−2)

Parentheses? Yes, subtract first.

 18÷6+4(3)
Exponents? No.
Multiplication or division? Yes.
Divide first because we multiply and divide left to right.
 3+4(3)
Any other multiplication or division? Yes.
Multiply.
 3+12
Any other multiplication or division? No.
Any addition or subtraction? Yes.
 15


Example 2.11

5+2^3+3[6−3(4−2)]

Are there any parentheses (or other grouping symbol)? Yes.


Focus on the parentheses that are inside the brackets.
 5+2^3+3[6−3(4−2)]
Subtract.
 5+2^3+3[6−3(2)]
Continue inside the brackets and multiply.
 5+2^3+3[6−6]
Continue inside the brackets and subtract.
 5+2^3+3[0]
The expression inside the brackets requires no further simplification.
Are there any exponents? Yes.
Simplify exponents.
 5+2^3+3[0]
Is there any multiplication or division? Yes.
Multiply.
 5+8+3[0]
Is there any addition or subtraction? Yes.
Add.
 5+8+0
Add.
 13+0
13


Example 2.12

2^3+3^4÷3−5^2
If an expression has several exponents, they may be simplified in the same step.
Simplify exponents.
 2^3+3^4÷3−5^2
Divide.
 8+81÷3-25
Add.
 8+27-25
Subtract. 35-25
10


Try It 2.15
  1. 2
  2. 14


Try It 2.16
  1. 35
  2. 99


Try It 2.17

18


Try It 2.18

9


Try It 2.19

16


Try It 2.20

23


Try It 2.21

86


Try It 2.22

1


Try It 2.23

81


Try It 2.24

75
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