Use the Language of Algebra

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

2
14

Try It 2.16

35
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