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