Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

Chapter 2

The Language of Algebra

Educators


Problem 1

Translate from algebraic notation to words.
$16-9$

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Problem 2

Translate from algebraic notation to words.
$25-7$

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Problem 3

Translate from algebraic notation to words.
5$\cdot 6$

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Problem 4

Translate from algebraic notation to words.
3$\cdot 9$

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Problem 5

Translate from algebraic notation to words.
$28 \div 4$

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Problem 6

Translate from algebraic notation to words.
$45 \div 5$

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Problem 7

Translate from algebraic notation to words.
$x+8$

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Problem 8

Translate from algebraic notation to words.
$x+11$

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Problem 9

Translate from algebraic notation to words.
$(2)(7)$

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Problem 10

Translate from algebraic notation to words.
$(4)(8)$

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Problem 11

Translate from algebraic notation to words.
$14<21$

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Problem 12

Translate from algebraic notation to words.
$17<35$

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Problem 13

Translate from algebraic notation to words.
$36 \geq 19$

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Problem 14

Translate from algebraic notation to words.
$42 \geq 27$

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Problem 15

Translate from algebraic notation to words.
$3 n=24$

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Problem 16

Translate from algebraic notation to words.
$6 n=36$

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Problem 17

Translate from algebraic notation to words.
$y-1>6$

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Problem 18

Translate from algebraic notation to words.
$y-4>8$

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Problem 19

Translate from algebraic notation to words.
$2 \leq 18 \div 6$

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Problem 20

Translate from algebraic notation to words.
$3 \leq 20 \div 4$

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Problem 21

Translate from algebraic notation to words.
$a \neq 7 \cdot 4$

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Problem 22

Translate from algebraic notation to words.
$a \neq 1 \cdot 12$

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Problem 23

Determine if each is an expression or an equation.
$9 \cdot 6=54$

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Problem 24

Determine if each is an expression or an equation.
$7 \cdot 9=63$

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Problem 25

Determine if each is an expression or an equation.
$5 \cdot 4+3$

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Problem 26

Determine if each is an expression or an equation.
$6 \cdot 3+5$

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Problem 27

Determine if each is an expression or an equation.
$x+7$

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Problem 28

Determine if each is an expression or an equation.
$x+9$

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Problem 29

Determine if each is an expression or an equation.
$y-5=25$

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Problem 30

Determine if each is an expression or an equation.
$y-8=32$

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Problem 31

Write in exponential form.
3$\cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3$

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Problem 32

Write in exponential form.
4$\cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4$

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Problem 33

Write in exponential form.
$x \cdot x \cdot x \cdot x \cdot x$

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Problem 34

Write in exponential form.
$y \cdot y \cdot y \cdot y \cdot y \cdot y$

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Problem 35

Write in expanded form.
$5^{3}$

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Problem 36

Write in expanded form.
$8^{3}$

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Problem 37

Write in expanded form.
$2^{8}$

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Problem 38

Write in expanded form.
$10^{5}$

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Problem 39

Simplify.
(a) $3+8 \cdot 5$
(b) $(3+8) \cdot 5$

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Problem 40

Simplify.
(a) $2+6 \cdot 3$
(b) $(2+6) \cdot 3$

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Problem 41

Simplify.
$2^{3}-12 \div(9-5)$

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Problem 42

Simplify.
$3^{2}-18 \div(11-5)$

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Problem 43

Simplify.
$3 \cdot 8+5 \cdot 2$

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Problem 44

Simplify.
$4 \cdot 7+3 \cdot 5$

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Problem 45

Simplify.
$2+8(6+1)$

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Problem 46

Simplify.
$4+6(3+6)$

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Problem 47

Simplify.
4$\cdot 12 / 8$

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Problem 48

Simplify.
2$\cdot 36 / 6$

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Problem 49

Simplify.
$6+10 / 2+2$

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Problem 50

Simplify.
$9+12 / 3+4$

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Problem 51

Simplify.
$(6+10) \div(2+2)$

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Problem 52

Simplify.
$(9+12) \div(3+4)$

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Problem 53

Simplify.
$20 \div 4+6 \cdot 5$

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Problem 54

Simplify.
$33 \div 3+8 \cdot 2$

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Problem 55

Simplify.
$20 \div(4+6) \cdot 5$

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Problem 56

Simplify.
$33 \div(3+8) \cdot 2$

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Problem 57

Simplify.
$4^{2}+5^{2}$

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Problem 58

Simplify.
$3^{2}+7^{2}$

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Problem 59

Simplify.
$(4+5)^{2}$

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Problem 60

Simplify.
$(3+7)^{2}$

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Problem 61

Simplify.
$3(1+9 \cdot 6)-4^{2}$

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Problem 62

Simplify.
$5(2+8 \cdot 4)-7^{2}$

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Problem 63

Simplify.
2$[1+3(10-2)]$

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Problem 64

Simplify.
5$[2+4(3-2)]$

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Problem 65

Basketball In the 2014 NBA playoffs, the San Antonio Spurs beat the Miami Heat. The table below shows the heights of the starters on each team. Use this table to fill in the appropriate symbol $(=,<,>)$
(a) Height of Tim Duncan ____ Height of Rashard Lewis
(b) Height of Boris Diaw ____ Heightof LeBron James
(c) Height of Kawhi Leonard ____ Height of Dwyane Wade
(d) Height of Danny Green ____ Height of Ray Allen

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Problem 66

Elevation In Colorado there are more than 50 mountains with an elevation of over 14,000 feet. The table shows the ten tallest. Use this table to fill in the appropriate inequality symbol.
(a)Elevation of La Plata Peak____Elevation of Mt. Antero
(b) Elevation of Blanca Peak____Elevation of Mt. Elbert
(c) Elevation of Gray’s Peak____Elevation of Mt. Lincoln
(d) Elevation of Mt. Massive____Elevation of Crestone Peak
(e) Elevation of Mt. Harvard____Elevation of Uncompahgre Peak

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Problem 67

Explain the difference between an expression and an equation.

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Problem 68

Why is it important to use the order of operations to simplify an expression?

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