Number Types
Prime Factorization
Divisibility Rules
Mean, Median, Mode, Range
Geometry
Order of Operations
Mix
Mix #2
100
What is a mixed number?
A mixed number consists of a whole number and a proper fraction. It is written in the form of a whole number followed by a fraction (example: 2 ½, 3 4/7, …)
100
What is the prime factorization of 24?
24 = 2 x 2 x 2 x 3
100
The number 93754242 is
A . Divisible by 2 only
B. Divisible by 4 only
C. Divisible by both 2 and 4
D. Divisible by neither 2 nor 4
A. Divisible by 2 only
100
Find the median:
6, 17, 10, 5, 25, 14
12
100
Eva has a fish tank. It is 10 inches long, 6 inches wide, and 20 inches tall. How many cubic inches of water will she need to fill up the entire tank?
10 x 6 x 20 = 60 x 20 = 1200 in3
100
62 ÷ (32 − 29)2
4
100
Which fraction is equivalent to 50%?
A. 1/2
B. 3/4
C. 1/50
D. 10/50
A. 1/2
100
What is the LCM of 12 and 18?
36
200
What are composite numbers?
A number that is divisible by more than just one and itself.
200
What is the prime factorization of 99?
99 = 3 x 3 x 11
200
Which number is divisible by both 3 and 4?
A. 321
B. 3,212
C. 32,112
D. 99,992
C. 32,112
200
Find the mode:
9, 4, 3, 6, 2, 0
No mode
200
A Rubik’s cube has a side length of 5 cm. What is its volume?
5 x 5 x 5 = 125 cm3
200
[(21 − 17) × (14 − 9)]2
400
200
A small cube has side length 1 meter. A large cube has side length 3 meters. How many small cubes can fit inside the large cube?
The small cube has a volume of 13 = 1 meter3. The large cube has a volume of 33 = 27 meter3. Then 27 small cubes fit into the large cube
200
What is the value of x in the equation 3x – 8 = 16?
x = 8
300
What are consecutive numbers?
Consecutive numbers or integers are numbers that follow each other in order without gaps. (example: 5, 6, 7, 8)
300
What is the prime factorization of 64?
64= 2 x 2 x 2 x 2 x 2 x 2
300
Which number is divisible by 9?
A. 888
B. 777
C. 666
D. 555
C. 666
300
Find the range:
305, 148, 187, 165, 249, 107
198
300
Calculate the volume of the rectangular prism below.
12 x 4 x 3 = 12 x 12 = 144 cm3
300
112 − 3 × 8 − 52 − 19
53
300
Write an expression that represents “5 times x decreased by 10”
5x-10
300
What is the value of 4/5+3/4 as a mixed number?
1 11/20
400
What are integers?
Integers are numbers without decimals or fractions that are both positive and their opposites (negative). (example: …, -3, -2, -1, 0, 1, 2, 3, …)
400
What is the prime factorization of 72?
72 = 2 x 2 x 2 x 3 x 3
400
Is 90,008 divisible by 4?
Yes – the last three digits are 008, which is a multiple of 8
400
Find the mean:
1.5, 0, 2, 2.5, 2, 4
2
400
The rectangular prism below is made up of congruent small cubes. The volume of the entire rectangular prism below is 72 cubic units. What is the volume of each small cube?
Dimensions of large cube: 4 x 3 x 3 = 36 small cubes. 72 / 36 = 2 cubic units
400
112 − {3 × [8 − (52 − 19)]}
115
400
The first seven numbers in a pattern are:
2, 3, 5, 7, 11, 13, 17
What is the next number in the pattern?
A. 18
B. 19
C. 21
D. 23
The numbers are the prime numbers. The next prime number is 19
400
Which property is illustrated in the following: (2 + 3) + 8 = 2 + (3 + 8)
A. Commutative Property
B. Associative Property
C. Distributive Property
D. Identity Property
B. Associative Property
500
Which answer choice best describes the set?
{2, 3, 5, 7, 11, 13}
A. Consecutive even numbers
B. Consecutive composite numbers
C. Consecutive odd numbers
D. Consecutive prime numbers
D. Consecutive prime numbers
500
What is the prime factorization of 108?
108 = 2 x 2 x 3 x 3 x 3
500
The three-digit number 91x is divisible by 3, where x is the units digit of the number. What are all possible values that x could be?
The sum of the digits is 9 + 1 + x = 10 + x. This is a multiple of 3 if x = 2, 5, or 8. So x could be any of those three numbers.
500
Find the median:
38, 23,
48, 22,
36, 37,
23, 37
36.5
500
Find the area of the shape below:
12 x 4 = 48 cm2
500
42 + 32 − {25 − [2 × (11 + 9 − 13)]}
14
500
A data set has values 1, 5, 9, 10, and 1,000. Which of the following values is the largest?
A. Mode
B. Mean
C. Range
D. Median
C. Range
500
What is 2/5 of 45?
18
600
TRUE OR FALSE:
The quotient of a dividend and a divisor is always an integer if both the dividend and divisor are whole numbers.
FALSE
600
What is the prime factorization of 76?
76 = 2 x 2 x 19
600
Is the number 33333333333333333333353 divisible by 3
No. All of the numbers are 3, but then you are adding a 5, so the sum will not be a multiple of 3, so the number will not be divisible by 3.
600
Find the mean:
75, 74,
54, 30,
35, 47,
14
47
600
Maria’s garden is 4 ft by 5 ft. She wants to make her garden larger, so she triples the length and width. How many times larger will the area of her new garden be?
Original area: 20 ft2
New length and width: 12 ft by 15 ft
New area: 180
20 = 9 times larger
600
102 × 9 − (43 − 4 × 10)
876
600
The formula F = 9/5C + 32 can be used to convert between Fahrenheit and Celsius. If it is 20 degrees Celsius outside, what is the temperature, in Fahrenheit?
68
600
Which is the smallest fraction?
A. 3/5
B. 4/7
C. 9/14
D. 6/11
D. 6/11
700
TRUE OR FALSE:
Every integer is a rational number, but not every rational number is an integer.
True
700
What is the prime factorization of 980?
980= 2 x 2 x 5 x 7 x7
700
The four-digit number 592x is divisible by 9, where x is the units digit of the number. What is the one possible value that x could be?
The sum of the digits is 5 + 9 + 2 + x = 16 + x. This is a multiple of 9 if x = 2
700
Find the mean:
87, 70,
27, 17,
45, 43,
65, 12,
48
46
700
Tom has a photograph that is 12 inches long and 10 inches wide. Unfortunately, it is too large to fit in the frame he bought, so he prints out a smaller version that has half the length and the width. How many times smaller is the area of the new photograph?
Original area: 120 in2
New length: 6 in
New width: 5 in
New area: 30 in2
120 30 = 4 times smaller (it is ¼ of the area of the original)
700
12 × (3 + 11 + 6) ÷ 23
30
700
Several test scores are 84, 82, 90, and x. If the average of the test scores is 85, what is the value of x?
If the average is 85, then the four scores must add to 4(85) = 340
Then 84 + 82 + 90 + x = 340 256 + x = 340 x = 340 – 256 = 84
700
12 students have a dog and 5 have a cat. However, there are only 15 students in the class, and 2 students do not have a pet. How many have both a dog and a cat? Use a Venn diagram to support your answer.
4
800
What is an irrational number? Define and give an example.
Irrational numbers are numbers that cannot be expressed as a fraction of two integers, and their decimal expansions neither terminate nor repeat. Pi is an irrational number!!!!
800
What is the prime factorization of 143000?
143000 = 2⋅2⋅2⋅5⋅5⋅5⋅11⋅13
800
How many prime numbers between 0 and 10, inclusive, is the number 714 divisible by?
- 714 is divisible by 2, since it ends in an even digit.
- 714 is divisible by 3, since the sum of its digits is 12, which is a multiple of 3.
- 714 is not divisible by 5, since it does not in 5 or 0.
- 714 is divisible by 7, since 700 is divisible by 7 and 14 is divisible by 7.
- Then 714 is divisible by three prime numbers between 0 and 10.
800
Find the mean:
61, 63,
34, 12,
25, 87,
47, 61,
61, 89
54
800
What is the area of the shaded trapezoid as shown below if the base of each triangle measures 3 ft?
area of triangle = 3*10 / 2 = 15
area of rectangle =
12 * 10 = 120
area of trapezoid = 120 – 15 * 2 = 90 ft2
800
42 + 22 × [40 ÷ (31 − 29)2]
56
800
What is the sum of all whole numbers from 1 to 50?
0 + 1 + 2 + 3 + … + 48 + 49 + 50 = (1 + 50) + (2 + 49) + … , which is 25 pairs of numbers that sum to 51. Then 25(51) = 1,275
800
If 3.2 cm on a map represent 5 miles, how many miles does 9.6 cm represent?
15 miles