Deck 1: An Introduction to Algebra

Question 1

Use the formula to complete the table. $d = 300 + L$ Lunch time (minutes)L School day (minutes)d 30 40 45

A)Lunch time School day (minutes)L (minutes)d 30 330 40 340 45 345
B)Lunch time School day (minutes)L (minutes)d 30 250 40 355 45 240
C)Lunch time School day (minutes)L (minutes)d 30 275 40 335 45 340
D)Lunch time School day (minutes)L (minutes)d 30 265 40 255 45 350
E)Lunch time School day (minutes)L (minutes)d 30 340 40 350 45 355

Answer 1

Lunch time School day (minutes)L (minutes)d 30 330 40 340 45 345

Question 2

Find the prime factorization of the number. 968

A) $2 ^ { 2 } \cdot 3 ^ { 3 }$
B) $4 ^ { 2 } \cdot 3 ^ { 2 }$
C) $2 ^ { 3 } \cdot 5$
D) $2 ^ { 3 } \cdot 9$
E) $2 ^ { 3 } \cdot 11 ^ { 2 }$

Answer 2

$2 ^ { 3 } \cdot 11 ^ { 2 }$

Question 3

What variable does the equation contain? 7 $-$ 1 = 12 $-$ y

A)v
B)a
C)y
D)7
E)12

Answer 3

y

Question 4

Classify the item as either an algebraic expression or an equation . 18 x

Question 5

Simplify the fraction to lowest terms. $\frac { 4 } { 7 }$

A) $0.4$
B) $\frac { 2 } { 7 }$
C) $\frac { 2 } { 4 }$
D) $\frac { 7 } { 4 }$
E)Does not simplify further.

Question 6

Find the quotient. $\frac { 1 } { 4 } \div \frac { 11 } { 7 }$

A) $\frac { 1 } { 6 }$
B) $\frac { 7 } { 44 }$
C) $\frac { 10 } { 49 }$
D) $\frac { 11 } { 46 }$
E) $\frac { 4 } { 15 }$

Question 7

Use the formula to complete the table. $w = \frac { s } { 10 }$ Inches of snow s Inches of water w 20 30 70

A)Inches Inches of snow s of water w 20 4 30 12 70 10
B)Inches Inches of snow s of water w 20 2 30 3 70 7
C)Inches Inches of snow s of water w 20 11 30 12 70 4
D)Inches Inches of snow s of water w 20 11 30 4 70 12
E)Inches Inches of snow s of water w 20 7 30 3 70 2

Question 8

Simplify the fraction to lowest terms. $\frac { 48 } { 60 }$

A) $\frac { 4 } { 6 }$
B) $\frac { 12 } { 15 }$
C) $\frac { 4 } { 5 }$
D) $\frac { 16 } { 20 }$
E)Does not simplify further.

Question 9

Simplify the fraction to lowest terms. $\frac { 76 } { 19 }$

A) $\frac { 1 } { 19 }$
B) $19$
C) $\frac { 1 } { 4 }$
D) $4$
E) $\frac { 19 } { 76 }$

Question 10

Find the prime factorization of the number. 140

A) $2 \cdot 2 \cdot 5 \cdot 7$
B) $4.5.7$
C) $2 \cdot 5\cdot7$
D) $2 \cdot 5 \cdot 7 \cdot 7$
E) $2 \cdot 2 \cdot 5$

Question 11

Graph the integers between 2 and 6 on the number line.

Question 12

Find the quotient. $\left( - \frac { 3 } { 11 } \right) \div \left( - \frac { 19 } { 44 } \right)$

A) $\frac { 12 } { 209 }$
B) $- \frac { 12 } { 19 }$
C) $\frac { 12 } { 19 }$
D) $- \frac { 4 } { 19 }$
E) $\frac { 4 } { 19 }$

Question 13

Perform the operation. $\frac { 11 } { 3 } \left( - \frac { 9 } { 11 } \right)$

A) $11$
B) $- 3$
C) $- 11$
D) $3$
E)none of these

Question 14

The line graph shows the number of cars parked in a parking structure from 6 P.M. to 12 midnight on a Saturday. How many cars were in the parking structure at 10 P.M.? __________ cars

Question 15

Translate the verbal model into an equation. The cost of dining out equals the cost of the meal plus $5 for parking.

A)c = m + 5
B)c = 5 m
C)c = m
D)c + m = 5
E)c = 5

Question 16

Express the statement using one of the words sum , difference , product , or quotient . 3 x = 10

A)The difference of 3 and x is 10.
B)The quotient of 3 and x is 10.
C)The product of 3 and x is 10.
D)The difference of 10 and x is 3.
E)The sum of 3 and x is 10.

Question 17

Graph the whole numbers less than 7 on a number line.

Question 18

Find the prime factorization of the number. 288

A) $4 ^ { 4 } \cdot 3 ^ { 2 }$
B) $5 ^ { 2 } \cdot 2 ^ { 7 } \cdot 3 ^ { 2 }$
C) $2 ^ { 5 } \cdot 3 ^ { 2 }$
D) $2 ^ { 2 } \cdot 3 ^ { 5 }$
E) $2 ^ { 5 } \cdot 3 ^ { 3 }$

Question 19

Translate "the sum of a number and 4 is 13" into an equation.

A) $x - 4 = 13$
B) $x = 4 + 13$
C) $x + 4 = 13$
D) $x + 13 = 4$

Question 20

Translate the verbal model into an equation. The amount of sand that should be used is the product of 2 and the amount of cement used.

A)s = 2 * c
B)s = 2 + c
C)s = 2 $-$ c
D)s = c $-$ 2
E)s = 2

Question 21

On a number line, what number is 10 units to the right of -2?

A)-11
B)-8
C)-12
D)9
E)8

Question 22

The set of __________ numbers is {0, 1, 2, 3, ...}.

A)irrational
B)integer
C)whole
D)natural
E)negative

Question 23

Multiply and reduce your answer to lowest terms. $- \frac { 38 } { 3 } \cdot \frac { 9 } { 19 } \cdot \frac { 1 } { 18 }$

A) $- \frac { 1 } { 3 }$
B) $\frac { 1 } { 3 }$
C)-1
D)1
E) $- \frac { 3 } { 19 }$

Question 24

What two numbers on a number line are a distance of 8 away from -1?

A)-8 , 8
B)8 , -10
C)6 , -8
D)7 , -9
E)-7 , 9

Question 25

Do the addition. Simplify the result when possible. $\frac { 1 } { 5 } + \frac { 1 } { 10 }$

A) $\frac { 3 } { 2 }$
B) $\frac { 2 } { 10 }$
C) $\frac { 3 } { 10 }$
D) $\frac { 3 } { 5 }$
E) $\frac { - 5 } { 10 }$

Question 26

Multiply and reduce your answer to lowest terms. $\left( - \frac { 19 } { 15 } \right) \cdot \left( - \frac { 3 } { 76 } \right)$

A) $- 20$
B) $- \frac { 1 } { 20 }$
C) $- \frac { 1 } { 57 }$
D) $\frac { 1 } { 20 }$
E) $20$

Question 27

Multiply and reduce your answer to lowest terms. $\frac { 5 } { 7 } \cdot \frac { 1 } { 6 }$

A) $\frac { 1 } { 5 }$
B) $5$
C) $42$
D) $\frac { 1 } { 42 }$
E) $\frac { 5 } { 70 }$

Question 28

Subtract as indicated, and express your answer in lowest terms. $- \frac { 1 } { 13 } - \frac { 10 } { 39 }$

A) $- \frac { 1 } { 3 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 2 } { 3 }$
E) $- \frac { 2 } { 3 }$

Question 30

List the numbers in the set that are natural numbers. $$\left\{ - 3 , - 1 , - \frac { 1 } { 2 } , 0,1 , \frac { 4 } { 3 } , 2 , \sqrt { 7 } , 2.75,6,10 \right\}$$

A) $1,2,6,10$
B) $- 3 , - 1 , - \frac { 1 } { 2 } , 0,1 , \frac { 4 } { 3 } , 2,2.75,6,10$
C) $- 3 , - 1 , - \frac { 1 } { 2 } , 0,1,2,2.75,6,10$
D) $- 3 , - 1 , - \frac { 1 } { 2 } , 0,1 , \frac { 4 } { 3 } , 2 , \sqrt { 7 } , 2.75,6,10$
E) $- 3 , - 1,0,1,2,2.75,6,10$

Question 31

Write the equivalent of the fraction using a denominator of 33. $$\frac { 4 } { 11 }$$

A) $\frac { 33 } { 11 }$
B) $\frac { 1 } { 33 }$
C) $\frac { 33 } { 12 }$
D) $\frac { 12 } { 33 }$
E) $\frac { 4 } { 33 }$

Question 32

Complete the fact about fraction.

Question 34

Find the sum. $$7 \frac { 3 } { 5 } + 8 \frac { 2 } { 11 }$$

A) $1 \frac { 2 } { 11 }$
B) $56 \frac { 23 } { 55 }$
C) $15 \frac { 2 } { 11 }$
D) $1 \frac { 43 } { 55 }$
E) $15 \frac { 43 } { 55 }$

Question 35

Build 5 to an equivalent fraction having the denominator 3.

A) $\frac { 5 } { 3 }$
B) $\frac { 12 } { 5 }$
C) $\frac { 12 } { 3 }$
D) $\frac { 15 } { 5 }$
E) $\frac { 15 } { 3 }$

Question 36

The number below the bar in a fraction is called the _____.

A)numerator
B)reciprocal
C)dividend
D)base
E)denominator

Question 37

Complete the fact about fraction.

Question 38

Which of the following numbers is farther from 2 on the number line?

A)3
B)-9
C)-18
D)12
E)22

Question 39

Write the number as a fraction. $- 23$

A) $\frac { 23 } { 1 }$
B) $- \frac { 1 } { 23 }$
C) $\frac { 1 } { 23 }$
D) $- \frac { 23 } { 23 }$
E) $- \frac { 23 } { 1 }$

Question 41

Graph the set on a number line. $$\left\{ - \frac { 5 } { 2 } , - 0.5,2.142765 \ldots , \frac { \pi } { 4 } , - \sqrt { 11 } , 2 \sqrt { 3 } \right\}$$

A)
B)
C)
D)
E)

Question 42

Write the expression in simpler form. $-$ | $-$ 8 |

A) $-$ 7
B) 8
C) 10
D) $-$ 8
E) 7

Question 43

Find the sum. 3.738 + ( 8.711)

Question 44

Subtract: $$- \frac { 2 } { 7 } - \frac { 5 } { 7 }$$

A) $- \frac { 1 } { 7 }$
B)1
C)- 1
D) $\frac { 7 } { 14 }$

Question 45

The identity element for addition is the number __________.

Question 46

Find the difference. $- \frac { 9 } { 8 } - \frac { 11 } { 8 }$

A) $- \frac { 5 } { 2 }$
B) $\frac { 5 } { 4 }$
C) $- \frac { 5 } { 4 }$
D) $\frac { 4 } { 5 }$
E) $\frac { 5 } { 2 }$

Question 47

Name the rational numbers in this set:

Question 48

Apply the associative property of addition to find the sum. $$( - 116 + 58 ) + ( - 58 )$$

A)58
B)116
C)232
D) $-$ 58
E) $-$ 116

Question 49

The set of rational numbers together with the set of irrational numbers form the set of __________ numbers.

A)real
B)negative
C)integer
D)prime
E)composite

Question 50

6 + 7 = 7 + 6 is an example of the __________ property of addition.

Question 51

A(n)__________ number is any number that can be expressed as a fraction with an integer numerator and a nonzero integer denominator.

A)whole
B)rational
C)positive
D)negative
E)real

Question 52

A(n)__________ number is a nonterminating, nonrepeating decimal.

A)irrational
B)odd
C)opposite
D)integer
E)even

Question 53

Find the sum. 15.5 + ( 6.1)

Question 54

Which numbers in the following set are irrational numbers? $$\left\{ \frac { 1 } { 9 } , 7 , \sqrt { 7 } , \pi , - 0.4 \right\}$$

A) $\sqrt { 7 } , \pi$
B) $\sqrt { 7 } , \pi , - 0.4$
C) $\frac { 1 } { 9 } , 7 , \sqrt { 7 } , \pi , - 0.4$
D) $\frac { 1 } { 9 } , 7 , - 0.4$

Question 55

Find the difference. $$\frac { 3 } { 16 } + \left( - \frac { 9 } { 2 } \right)$$

A)0
B) $\frac { 69 } { 16 }$
C) $- \frac { 75 } { 16 }$
D) $\frac { 75 } { 16 }$
E) $- \frac { 69 } { 16 }$

Question 56

Find the sum. $-$ 1 + ( $-$ 8)+ ( $-$ 18)+ 9

A)-34
B)36
C)-18
D)18
E)-16

Question 57

List the elements of $\left\{ - 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 5 } , 4 , \pi , 4.45,9,17 . \overline { 6 } \right\}$ that belong to the set of irrational numbers.

A) $- 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1,4,4.45,9,17 . \overline { 6 }$
B) $\sqrt { 5 } , \pi$
C) $\sqrt { 5 }$
D) $- 3,0,1,4,9$
E) $- 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 5 } , 4 , \pi , 4.45,9,17 . \overline { 6 }$

Question 58

List the elements of $\left\{ - 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 3 } , 3 , \pi , 4.45,7,17 . \overline { 6 } \right\}$ that belong to the set of rational numbers.

A) $- 3,0,1,3,7$
B) $\sqrt { 3 } , \pi$
C) $- 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1,3,4.45,7,17 . \overline { 6 }$
D) $- 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 3 } , 3 , \pi , 4.45,7,17 . \overline { 6 }$
E) $0,1,3,7$

Question 59

List the elements of $\left\{ - 3 , - \frac { 8 } { 5 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 5 } , 3 , \pi , 4.65,7,16 . \overline { 6 } \right\}$ that belong to the set of real numbers.

A) $- 3 , - \frac { 8 } { 5 } , 0 , \frac { 2 } { 3 } , 1,3,4.65,7,16 . \overline { 6 }$
B) $0,1,3,7$
C) $- 3 , - \frac { 8 } { 5 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 5 } , 3 , \pi , 4.65,7,16 . \overline { 6 }$
D) $\sqrt { 5 } , \pi$
E) $- 3,0,1,3,7$

Question 60

Find the sum. 18 + ( $-$ 18)

A) $-$ 36
B) $-$ 18
C)0
D)36
E)18

Question 61

Find the product.

Question 62

If a represents a negative number and b represents a positive number, which of the following products results in a positive answer ?

A) $- ( - a ) ( - b )$
B) $( - a ) ( - b )$
C) $( - a ) ( a )$
D) $( - b ) ( b )$

Question 63

Perform the operation. $$\frac { - 1 } { 8 } \div \frac { 2 } { 5 }$$

A) $\frac { 16 } { 5 }$
B) $516$
C) $- \frac { 5 } { 16 }$
D) $- \frac { 16 } { 5 }$
E) $\frac { 5 } { 16 }$

Question 64

Write a multiplication statement that is equivalent to the division statement. $$20 \div 4 = 5$$

A) $5 + 4 = 20$
B) $5.20 = 4$
C) $20 \div 5 = 4$
D) $5 \div 4 = 20$
E) $5 \cdot 4 = 20$

Question 65

The _________ property of multiplication states that changing the order when multiplying does not affect the answer.

Question 66

Use the rules of division and the rule for order of operations to simplify the expression as much as possible. $$- 63 \div ( 70 \div 10 )$$

A)2
B)-9
C)3
D)-2

Question 67

Perform the indicated operations: $$- 6 - 9 - ( - 7 )$$

A)-8
B)-22
C)22
D)8

Question 68

Perform the operation. $$\frac { 0 } { - 2 }$$

A) $- 2$
B)undefined
C)2
D)0

Question 69

Perform the operation. $$\frac { - 40 } { 5 }$$

A)9
B) $-$ 2
C) $-$ 8
D)8
E) $-$ 6

Question 70

What number is the base in the expression ?

Question 71

How many fewer Dalmatians were registered in 2000 than in the year when they were at their height of popularity?

Question 72

For a 29-mile trip, John paid the taxi driver $12.00. If $2 was a tip, how much was the fare? $__________

Question 73

Perform the operation. $$\frac { - 4.8 } { 10 }$$

A) $-$ 3.35
B) $-$ 0.48
C)0.16
D)0.48
E) $-$ 2.41

Question 74

Use the associative property of multiplication to find the product.

Question 75

A savings account contained $465. After a deposit of $54 and a withdrawal of $167, how much is in the account? $__________

Question 76

Multiply. $- 6.9 \cdot 2.5$

A)172.5
B)17.25
C)-17.25
D)-18.25
E)-172.5

Question 77

Evaluate.

Question 78

Evaluate the expression. $$3 \cdot 10 ^ { 3 } + 3 \cdot 10 ^ { 2 } + 8 \cdot 10 ^ { 1 } + 3$$

A)3,483
B)3,383
C)3,388
D)3,372
E)3,381

Question 79

Subtract. $0 - 9$

A) $- 9$
B) $10$
C) $- 10$
D)0
E) $9$

Question 80

Use a calculator to evaluate the expression.