Deck 1: Introduction to Real Numbers and Algebraic Expressions

Question 1

Find all the factors of the number

-30

A) $1,5,6,30$
B) $5,6,10,30$
C) $1,2,3,5,6,10,20,30$
D) $1,2,3,5,6,10,15,30$

Answer 1

$1,2,3,5,6,10,15,30$

Question 2

Find the prime factorization of the number.

-20

A) $2 \cdot 2 \cdot 5$
B) $4 \cdot 2$
C) $5 \cdot 5$
D) $4 \cdot 5$

Answer 2

$2 \cdot 2 \cdot 5$

Question 3

Find the prime factorization of the number.

-252

A) $2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 7$
B) $2 \cdot 2 \cdot 2 \cdot 2 \cdot 7$
C) $2 \cdot 2 \cdot 3 \cdot 3 \cdot 7$
D) $3 \cdot 3 \cdot 3 \cdot 3 \cdot 7$

Answer 3

$2 \cdot 2 \cdot 3 \cdot 3 \cdot 7$

Question 4

Find the prime factorization of the number.

-42

A) $2 \cdot 3 \cdot 3$
B) $2 \cdot 3 \cdot 7$
C) $2 \cdot 2 \cdot 7$
D) $7 \cdot 6$

Question 5

Find the prime factorization of the number.

-350

A) $2 \cdot 5 \cdot 7$
B) $2 \cdot 5 \cdot 5 \cdot 7$
C) $2 \cdot 2 \cdot 5 \cdot 5 \cdot 7$
D) $14 \cdot 5 \cdot 5$

Question 6

Find the prime factorization of the number.

-87

A) $3 \cdot 3 \cdot 29$
B) $3 \cdot 27$
C) $3 \cdot 29$
D) $3 \cdot 3$

Question 7

Find the prime factorization of the number.

-63

A) $21 \cdot 3$
B) $3 \cdot 7 \cdot 3$
C) $7 \cdot 7 \cdot 3$
D) $3 \cdot 3 \cdot 3$

Question 8

Find the LCM using prime factorization.

-60,90

A) 180
B) 30
C) 540
D) 360

Question 9

Find the LCM using prime factorization.

- $45,56,150$

A) 2520
B) 1050
C) 1260
D) 12,600

Question 10

Find the LCM using prime factorization.

- $48,162,3$

A) 648
B) 1296
C) 324
D) 432

Question 11

Find the LCM using prime factorization.

- $8,10,12,15$

A) 60
B) 120
C) 90
D) 108

Question 12

Solve the problem.

-At a national computer show, two software companies continuously run videos showing their products. Company A's video repeats every 33 minutes, while Company B's video repeats every 15 minutes. If both companies begin the videos at 1:00 P.M. when the show opens, how many minutes will elapse before they are in sync again?

A) 55 minutes
B) 110 minutes
C) 330 minutes
D) 165 minutes

Question 13

Solve the problem.

-Tom and Larry are food inspectors at a cookie making company. Tom tests every 16th batch of dough for fat percentage. Larry tests every 28th batch of dough for carbohydrate percentage. If they both start working at the same time, which batch will be the first that they both test?

A) 28
B) 56
C) 112
D) 224

Question 14

Solve the problem.

-Cory and Melissa are racing electronic cars around a circular track. They begin at the same time going in the same direction. Cory's car completes a revolution in 40 seconds, while Melissa's car completes a revolution in 35 seconds. How long will it take them before both cars reach the starting point again simultaneously?

A) 56 seconds
B) 280 seconds
C) 112 seconds
D) 560 seconds

Question 15

Solve the problem.

-Robert has built a mechanical model solar system with three balls representing planets at the ends of rods attached to the center representing the sun. The planets are aligned when he turns on the motor. The innermost planet makes a revolution in 12 seconds, the middle planet makes a revolution in 30 seconds, and the outermost planet makes a revolution in 42 seconds. After how many seconds will the planets be aligned again?

A) 210 seconds
B) 840 seconds
C) 630 seconds
D) 420 seconds

Question 16

Solve the problem.

-A cereal manufacturer uses three large overhead bins to hold the three ingredients in one of its cereal mixes. Bin A delivers a premeasured quantity of dried fruit every 21 minutes, bin B delivers raisins every 33 minutes, and bin $C$ delivers flakes every 6 minutes. If they start the morning shift at the same time, how long before they deliver their ingredients at the same time again?

A) 462 minutes
B) 231 minutes
C) 924 minutes
D) 154 minutes

Question 17

Write an equivalent expression using the indicated name for 1.

- $\frac{2}{6}$ (Use $\frac{5}{5}$ for 1 .)

A) $\frac{6}{10}$
B) $\frac{60}{20}$
C) $\frac{10}{30}$
D) $\frac{12}{10}$

Question 18

Write an equivalent expression using the indicated name for 1.

- $\frac{14}{12}$ (Use $\frac{20}{20}$ for 1 .)

A) $\frac{280}{12}$
B) $\frac{140}{120}$
C) $\frac{14}{240}$
D) $\frac{280}{240}$

Question 19

Find an equivalent expression with the given denominator.

- $\frac{1}{12}$ (Denominator: 24)

A) $\frac{1}{24}$
B) $\frac{24}{288}$
C) $\frac{2}{24}$
D) $\frac{12}{24}$

Question 20

Find an equivalent expression with the given denominator.

- $\frac{14}{2}$ (Denominator: 5)

A) $\frac{56}{8}$
B) $\frac{28}{4}$
C) $\frac{35}{5}$
D) $\frac{14}{4}$

Question 21

Simplify.

- $\frac{3}{15}$

A) 7
B) $\frac{1}{4}$
C) 5
D) $\frac{1}{5}$

Question 22

Simplify.

- $\frac{56}{84}$

A) $\frac{56}{84}$
B) $\frac{2}{3}$
C) $\frac{83}{55}$
D) $\frac{3}{2}$

Question 23

Simplify.

- $\frac{38}{80}$

A) $\frac{40}{19}$
B) $\frac{79}{37}$
C) $\frac{13}{27}$
D) $\frac{19}{40}$

Question 24

Simplify.

- $\frac{178}{218}$

A) $\frac{89}{109}$
B) $\frac{109}{89}$
C) $\frac{179}{219}$
D) $\frac{217}{177}$

Question 25

Simplify.

- $\frac{76}{840}$

A) $\frac{839}{75}$
B) $\frac{77}{841}$
C) $\frac{19}{210}$
D) $\frac{210}{19}$

Question 26

Simplify.

- $\frac{140}{280}$

A) 2
B) $\frac{1}{2}$
C) $\frac{141}{281}$
D) $\frac{279}{139}$

Question 27

Simplify.

- $\frac{560}{35}$

A) 40
B) 16
C) 14
D) 8

Question 28

Simplify.

- $\frac{11 \cdot x}{66 \cdot x}$

A) $\frac{x}{6}$
B) $\frac{1}{6}$
C) 6
D) $6 \mathrm{x}$

Question 29

Simplify.

- $\frac{8 \cdot x}{10 \cdot x}$

A) $\frac{4}{5}$
B) $\frac{5}{4}$
C) $\frac{4 x}{5}$
D) $\frac{5 x}{4}$

Question 30

Perform the indicated operation and, if possible, simplify.

- $\frac{3}{6}+\frac{2}{6}$

A) 1
B) $\frac{1}{6}$
C) $\frac{5}{12}$
D) $\frac{5}{6}$

Question 31

Perform the indicated operation and, if possible, simplify.

- $\frac{3}{14}+\frac{3}{14}$

A) $\frac{3}{14}$
B) 0
C) $\frac{9}{14}$
D) $\frac{3}{7}$

Question 32

Perform the indicated operation and, if possible, simplify.

- $\frac{7}{10}+\frac{5}{7}$

A) $\frac{99}{17}$
B) $\frac{99}{70}$
C) $\frac{12}{17}$
D) $\frac{6}{35}$

Question 33

Perform the indicated operation and, if possible, simplify.

- $\frac{11}{12}+\frac{2}{9}$

A) $\frac{41}{36}$
B) $\frac{41}{7}$
C) $\frac{13}{108}$
D) $\frac{13}{21}$

Question 34

Perform the indicated operation and, if possible, simplify.

- $\frac{4}{12}+\frac{10}{18}$

A) $\frac{7}{108}$
B) $\frac{7}{15}$
C) $\frac{8}{9}$
D) $\frac{32}{5}$

Question 35

Perform the indicated operation and, if possible, simplify.

- $\frac{7}{9}-\frac{1}{9}$

A) $\frac{1}{3}$
B) $\frac{2}{3}$
C) $\frac{7}{9}$
D) $\frac{8}{9}$

Question 36

Perform the indicated operation and, if possible, simplify.

- $\frac{6}{19}-\frac{5}{19}$

A) $\frac{11}{19}$
B) $\frac{30}{19}$
C) $\frac{1}{38}$
D) $\frac{1}{19}$

Question 37

Perform the indicated operation and, if possible, simplify.

- $\frac{8}{9}-\frac{5}{8}$

A) $\frac{1}{24}$
B) $\frac{19}{9}$
C) $\frac{72}{19}$
D) $\frac{19}{72}$

Question 38

Perform the indicated operation and, if possible, simplify.

- $\frac{5}{7}-\frac{1}{5}$

A) $\frac{36}{7}$
B) $\frac{18}{35}$
C) $\frac{35}{18}$
D) $\frac{3}{70}$

Question 39

Perform the indicated operation and, if possible, simplify.

- $\frac{17}{23}-\frac{2}{5}$

A) $\frac{7}{575}$
B) $\frac{115}{39}$
C) $\frac{195}{23}$
D) $\frac{39}{115}$

Question 40

Perform the indicated operation and, if possible, simplify.

- $\frac{4}{9} \cdot \frac{1}{3}$

A) $\frac{3}{4}$
B) $\frac{5}{27}$
C) $\frac{4}{27}$
D) $\frac{5}{12}$

Question 41

Perform the indicated operation and, if possible, simplify.

- $\frac{2}{9} \cdot \frac{3}{8}$

A) $\frac{1}{36}$
B) $\frac{5}{17}$
C) $\frac{27}{16}$
D) $\frac{1}{12}$

Question 42

Perform the indicated operation and, if possible, simplify.

- $\frac{1}{2} \cdot \frac{11}{14}$

A) $\frac{1}{56}$
B) $\frac{11}{7}$
C) $\frac{11}{28}$
D) $\frac{25}{34}$

Question 43

Perform the indicated operation and, if possible, simplify.

- $\frac{14}{23} \cdot \frac{4}{7}$

A) $\frac{2}{69}$
B) $\frac{46}{49}$
C) $\frac{13}{22}$
D) $\frac{8}{23}$

Question 44

Perform the indicated operation and, if possible, simplify.

- $\frac{7}{9} \cdot \frac{7}{9}$

A) $\frac{7}{9}$
B) $\frac{49}{81}$
C) 1
D) $\frac{7}{243}$

Question 45

Perform the indicated operation and, if possible, simplify.

- $\frac{7}{2} \cdot \frac{5}{4}$

A) 2
B) $\frac{35}{8}$
C) $\frac{7}{8}$
D) $\frac{5}{14}$

Question 46

Perform the indicated operation and, if possible, simplify.

- $\frac{13}{15} \cdot \frac{15}{13}$

A) $\frac{15}{13}$
B) $\frac{13}{15}$
C) 1
D) 0

Question 47

Perform the indicated operation and, if possible, simplify.

- $\frac{3}{7} \div \frac{1}{3}$

A) $\frac{9}{7}$
B) $\frac{2}{5}$
C) $\frac{3}{7}$
D) $\frac{1}{7}$

Question 48

Perform the indicated operation and, if possible, simplify.

- $\frac{15}{19} \div \frac{11}{18}$

A) $\frac{270}{209}$
B) $\frac{26}{37}$
C) $\frac{15}{209}$
D) $\frac{55}{114}$

Question 49

Perform the indicated operation and, if possible, simplify.

- $\frac{48}{7} \div 6$

A) $\frac{8}{7}$
B) $\frac{288}{7}$
C) $\frac{48}{56}$
D) $\frac{7}{8}$

Question 50

Perform the indicated operation and, if possible, simplify.

- $2 \div \frac{8}{3}$

A) $\frac{16}{3}$
B) $\frac{3}{4}$
C) $\frac{4}{3}$
D) $\frac{8}{6}$

Question 51

Perform the indicated operation and, if possible, simplify.

- $\frac{\frac{2}{19}}{\frac{9}{13}}$

A) $\frac{26}{169}$
B) $\frac{24}{171}$
C) $\frac{26}{171}$
D) $\frac{25}{171}$

Question 52

Perform the indicated operation and, if possible, simplify.

- $\frac{18}{25} \div 45$

A) $\frac{2}{5}$
B) $\frac{5}{2}$
C) $\frac{125}{2}$
D) $\frac{2}{125}$

Question 53

Convert to fractional notation. Do not simplify.

-0.95

A) $\frac{190}{1000}$
B) $\frac{95}{100}$
C) $\frac{190}{100}$
D) $\frac{1}{95}$

Question 54

Convert to fractional notation. Do not simplify.

-0.116

A) $\frac{116}{1000}$
B) $\frac{232}{1000}$
C) $\frac{1}{116}$
D) $\frac{58}{1000}$

Question 55

Convert to fractional notation. Do not simplify.

-4.9

A) $\frac{1}{49}$
B) $\frac{49}{10}$
C) $\frac{98}{100}$
D) $\frac{98}{10}$

Question 56

Convert to fractional notation. Do not simplify.

-9.52

A) $\frac{476}{100}$
B) $\frac{1}{952}$
C) $\frac{952}{100}$
D) $\frac{1904}{100}$

Question 57

Convert to fractional notation. Do not simplify.

-5.35

A) $\frac{1}{535}$
B) $\frac{535}{100}$
C) $\frac{267.5}{100}$
D) $\frac{1070}{100}$

Question 58

Convert to decimal notation.

- $\frac{1}{10,000}$

A) 0.0001
B) 0.001
C) 0.00000001
D) 0.01

Question 59

Convert to decimal notation.

- $\frac{6}{10,000}$

A) 0.06
B) 0.0006
C) 0.006
D) 0.00000006

Question 60

Convert to decimal notation.

- $\frac{4937}{1000}$

A) 493.7
B) 49.37
C) 4.937
D) 0.4937

Question 61

Convert to decimal notation.

- $\frac{9}{10}$

A) 0.9
B) 0.009
C) 0.00009
D) 0.09

Question 62

Convert to decimal notation.

- $\frac{16}{10}$

A) 0.016
B) 0.16
C) 1.6
D) 160

Question 63

Convert to decimal notation.

- $\frac{306}{1000}$

A) 3.06
B) 0.0306
C) 30.6
D) 0.306

Question 64

Convert to decimal notation.

- $\frac{57}{100,000}$

A) 0.0057
B) 0.057
C) 0.00057
D) 0.000057

Question 65

Add.

-187.22
$+10.96$
_________

A) 198.18
B) 198.07
C) 198.08
D) 198.17

Question 66

Add.

-458.005
$+17.323$
------------------

A) 475.327
B) 475.228
C) 475.328
D) 475.318

Question 67

Add.

-613.589
$+254.337$
---------------

A) 867.925
B) 867.826
C) 867.916
D) 867.926

Question 68

Add.

- $0.433+57$

A) 57.434
B) 57.543
C) 57.423
D) 57.433

Question 69

Add.

- $56.1+41.68+0.087$

A) 98.867
B) 98.667
C) 97.667
D) 97.867

Question 70

Add.

- $4.23+0.82+24.52$

A) 29.67
B) 29.57
C) 28.57
D) 28.67

Question 71

Subtract.

-

A) 5.8
B) 5.9
C) 4.8
D) 4.7

Question 72

Subtract.

-

A) 3.69
B) 3.59
C) 2.59
D) 3.11

Question 73

Subtract.

-

A) 3.09
B) 2.99
C) 3.99
D) 3.0

Question 74

Subtract.

-

A) 4.532
B) 3.532
C) 3.668
D) 5.000

Question 75

Subtract.

-

A) 32.927
B) 32.917
C) 32.923
D) 34.000

Question 76

Subtract.

- $6.430-4.778$

A) 1.752
B) 1.652
C) 11.208
D) 10.208

Question 77

Subtract.

- $19.77-10.52$

A) 31.29
B) 30.29
C) 9.35
D) 9.25

Question 78

Subtract.

- $17.100-10.460$

A) 6.740
B) 6.640
C) 27.560
D) 6.540

Question 79

Subtract.

-98 - 5.52

A) 92.58
B) 103.52
C) 92.48
D) 91.98

Question 80

Subtract.

- $11.368-8.834$

A) 20.202
B) 2.534
C) 2.734
D) 2.634