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2.1 Use the Language of Algebra

Variables and comparison symbols, telling an expression from an equation, exponent notation, and the order of operations for grouped expressions.

Prealgebra 2e, 2.1 Use the Language of Algebra

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65 exercises

2.1 Exercise 1

Before you get started, take this readiness quiz.

Add:43+69.\text{Add}: 43 + 69 .
If you missed this problem, review the reference.

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2.1 Exercise 2

Multiply:(896)201.\text{Multiply}: \left(896\right) 201 .
If you missed this problem, review the reference.

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2.1 Exercise 3

Divide:7,263÷9.\text{Divide}: 7,263 \div 9 .
If you missed this problem, review the reference.

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2.1 Exercise 4

Translate from algebra to words:

  1. ⓐ 12+1412 + 14
  2. ⓑ (30)(5)\left(30\right) \left(5\right)
  3. ⓒ 64÷864 \div 8
  4. ⓓ x−yx - y

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2.1 Exercise 5

Translate from algebra to words.

  1. ⓐ 18+1118 + 11
  2. ⓑ (27)(9)\left(27\right) \left(9\right)
  3. ⓒ 84÷784 \div 7
  4. ⓓ p−qp - q

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2.1 Exercise 6

Translate from algebra to words.

  1. ⓐ 47−1947 - 19
  2. ⓑ 72÷972 \div 9
  3. ⓒ m+nm + n
  4. ⓓ (13)(7)\left(13\right) \left(7\right)

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2.1 Exercise 7

Translate from algebra to words:

  1. ⓐ 20≤3520 \leq 35
  2. ⓑ 11≠15−311 \neq 15 - 3
  3. ⓒ 9>10÷29 > 10 \div 2
  4. ⓓ x+2<10x + 2 < 10

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2.1 Exercise 8

Translate from algebra to words.

  1. ⓐ 14≤2714 \leq 27
  2. ⓑ 19−2≠819 - 2 \neq 8
  3. ⓒ 12>4÷212 > 4 \div 2
  4. ⓓ x−7<1x - 7 < 1

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2.1 Exercise 9

Translate from algebra to words.

  1. ⓐ 19≥1519 \geq 15
  2. ⓑ 7=12−57 = 12 - 5
  3. ⓒ 15÷3<815 \div 3 < 8
  4. ⓓ y-3>6y - 3 > 6

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2.1 Exercise 11

Use the figure to fill in the appropriate symbol,=,<,or>.\text{symbol} , = , < , \text{or} > .

  1. ⓐ MPG of Prius_____MPG of Versa
  2. ⓑ MPG of Mini Cooper_____ MPG of Corolla

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2.1 Exercise 12

Use the figure to fill in the appropriate symbol,=,<,or>.\text{symbol} , = , < , \text{or} > .

  1. ⓐ MPG of Fit_____ MPG of Prius
  2. ⓑ MPG of Corolla _____ MPG of Fit

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2.1 Exercise 13

Determine if each is an expression or an equation:

  1. ⓐ 16−6=1016 - 6 = 10
  2. ⓑ 4·2+14 \cdot 2 + 1
  3. ⓒ x÷25x \div 25
  4. ⓓ y+8=40y + 8 = 40

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2.1 Exercise 14

Determine if each is an expression or an equation:

  1. ⓐ 23+6=2923 + 6 = 29
  2. ⓑ 7·3−77 \cdot 3 - 7

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2.1 Exercise 15

Determine if each is an expression or an equation:

  1. y÷14y \div 14
  2. x−6=21x - 6 = 21

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2.1 Exercise 16

Write each expression in exponential form:

  1. ⓐ 16·16·16·16·16·16·1616 \cdot 16 \cdot 16 \cdot 16 \cdot 16 \cdot 16 \cdot 16
  2. ⓑ 9·9·9·9·99 \cdot 9 \cdot 9 \cdot 9 \cdot 9
  3. ⓒ x·x·x·xx \cdot x \cdot x \cdot x
  4. ⓓ a·a·a·a·a·a·a·aa \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a

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2.1 Exercise 17

Write each expression in exponential form:

41·41·41·41·4141 \cdot 41 \cdot 41 \cdot 41 \cdot 41

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2.1 Exercise 18

Write each expression in exponential form:

7·7·7·7·7·7·7·7·77 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7

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2.1 Exercise 19

Write each exponential expression in expanded form:

  1. ⓐ 868^{6}
  2. ⓑ x5x^{5}

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2.1 Exercise 20

Write each exponential expression in expanded form:

  1. ⓐ 484^{8}
  2. ⓑ a7a^{7}

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2.1 Exercise 21

Write each exponential expression in expanded form:

  1. ⓐ 88\left( 8\right)^{8}
  2. ⓑ b6b^{6}

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2.1 Exercise 22

Simplify: 34.3^{4} .

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2.1 Exercise 23

Simplify:

  1. ⓐ 535^{3}
  2. ⓑ 171^{7}

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2.1 Exercise 24

Simplify:

  1. ⓐ 727^{2}
  2. ⓑ 050^{5}

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2.1 Exercise 26

Simplify the expressions:

  1. ⓐ 12−5·212 - 5 \cdot 2
  2. ⓑ (12−5)·2\left(12 - 5\right) \cdot 2

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2.1 Exercise 27

Simplify the expressions:

  1. ⓐ 8+3·98 + 3 \cdot 9
  2. ⓑ (8+3)·9\left(8 + 3\right) \cdot 9

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2.1 Exercise 29

Simplify:

42÷7·342 \div 7 \cdot 3

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2.1 Exercise 30

Simplify:

12·3÷412 \cdot 3 \div 4

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2.1 Exercise 32

Simplify:

30÷5+10(3−2)30 \div 5 + 10 \left(3 - 2\right)

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2.1 Exercise 33

Simplify:

70÷10+4(6−2)70 \div 10 + 4 \left(6 - 2\right)

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2.1 Exercise 35

Simplify:

9+53−[ 4(9+3) ]9 + 5^{3} - \left[4 \left(9 + 3\right)\right]

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2.1 Exercise 36

Simplify:

72−2[4(5+1) ]7^{2} - 2 \left[4 \left(5 + 1\right)\right]

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2.1 Exercise 38

Simplify:

32+24÷2+433^{2} + 2^{4} \div 2 + 4^{3}

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2.1 Exercise 39

Simplify:

62−53÷5+826^{2} - 5^{3} \div 5 + 8^{2}

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2.1 Exercise 40

Translate from algebraic notation to words.

16−916 - 9

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2.1 Exercise 42

Translate from algebraic notation to words.

5·65 \cdot 6

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2.1 Exercise 44

Translate from algebraic notation to words.

28÷428 \div 4

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2.1 Exercise 46

Translate from algebraic notation to words.

x+8x + 8

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2.1 Exercise 48

Translate from algebraic notation to words.

(2)(7)\left(2\right) \left(7\right)

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2.1 Exercise 50

Translate from algebraic notation to words.

14<2114 < 21

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2.1 Exercise 52

Translate from algebraic notation to words.

36≥1936 \geq 19

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2.1 Exercise 54

Translate from algebraic notation to words.

3n=243 n = 24

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2.1 Exercise 56

Translate from algebraic notation to words.

y−1>6y - 1 > 6

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2.1 Exercise 58

Translate from algebraic notation to words.

2≤18÷62 \leq 18 \div 6

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2.1 Exercise 60

Translate from algebraic notation to words.

a≠7·4a \neq 7 \cdot 4

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2.1 Exercise 62

Determine if each is an expression or an equation.

9·6=549 \cdot 6 = 54

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2.1 Exercise 64

Determine if each is an expression or an equation.

5·4+35 \cdot 4 + 3

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2.1 Exercise 66

Determine if each is an expression or an equation.

x+7x + 7

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2.1 Exercise 68

Determine if each is an expression or an equation.

y−5=25y - 5 = 25

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2.1 Exercise 70

Write in exponential form.

3·3·3·3·3·3·33 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3

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2.1 Exercise 72

Write in exponential form.

x·x·x·x·xx \cdot x \cdot x \cdot x \cdot x

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2.1 Exercise 74

Write in expanded form.

535^{3}

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2.1 Exercise 76

Write in expanded form.

282^{8}

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2.1 Exercise 78

Simplify.

  1. ⓐ 3+8·53 + 8 \cdot 5
  2. ⓑ (3+8)·5(\text{3}+\text{8}) \cdot 5
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2.1 Exercise 80

Simplify.

23−12÷(9−5)2^{3} - 12 \div \left(9 - 5\right)

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2.1 Exercise 82

Simplify.

3·8+5·23 \cdot 8 + 5 \cdot 2

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2.1 Exercise 84

Simplify.

2+8(6+1)2 + 8 \left(6 + 1\right)

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2.1 Exercise 86

Simplify.

4·12/84 \cdot 12 / 8

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2.1 Exercise 88

Simplify.

6+10/2+26 + 10 / 2 + 2

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2.1 Exercise 90

Simplify.

(6+10)÷(2+2)\left(6 + 10\right) \div \left(2 + 2\right)

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2.1 Exercise 92

Simplify.

20÷4+6·520 \div 4 + 6 \cdot 5

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2.1 Exercise 94

Simplify.

20÷(4+6)·520 \div \left(4 + 6\right) \cdot 5

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2.1 Exercise 96

Simplify.

42+524^{2} + 5^{2}

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2.1 Exercise 98

Simplify.

(4+5)2\left(4 + 5\right)^{2}

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2.1 Exercise 100

Simplify.

3(1+9·6)−423 \left(1 + 9 \cdot 6\right) - 4^{2}

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2.1 Exercise 102

Simplify.

2[1+3(10−2)]2 \left[1 + 3 \left(10 - 2\right)\right]

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Adapted from Prealgebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Prealgebra 2e. Imported at revision 77a933c.