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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