Set Theory
Number Theory 1
Number Theory 2
Base -10 and Base-5
Fractions
Decimals
Ratios & Proportions
100
How would you define:
a) natural numbers
b) whole numbers
c) integers
d) rational numbers
e) irrational numbers
a) the counting numbers {1, 2, 3, ...}
b) the natural numbers and zero
c) the set containing zero and all the natural numbers and their opposites
d) the set of all numbers p/q where p and q are integers
e) the complement of rational numbers
100
List all the factors and then the first 5 multiples of:
a) 12
b) 28
c) 17
a) factors: 1, 2, 3, 4, 6, 12
multiples: 12, 24, 36, 48, 60
b) factors: 1, 2, 4, 7, 14, 28
multiples: 28, 56, 84, 112, 140
c) factors: 1, 17
multiples: 17, 34, 51, 68, 85
100
Match each property:
a) commutative 1) (2+5)+7=2+(5+7)
b) associative 2) 7(a - 4)=(7 x a) - (7 x 4)
c) multiplicative identity 3) 81 x 1 = 81
d) distributive 4) 19 + 12 = 12 + 19
a, 4
b, 1
c, 3
d, 2
100
Identify the following place values in the base-10 number system using words and numbers:
___ ___ ___ . ___ ___ ___
hundreds, tens, ones . tenths, hundredths, thousandths
100, 10, 1, 1/10, 1/100, 1/1000
10^2, 10^1, 10^0, 10^-1, 10^-2, 10^-3
100
Rewrite each fraction in simplest terms:
a)
84/144
b)
208/272
c)
- 930/1290
a) 7/12
b) 13/17
c) 31/43
100
Find each of the following:
a)
253.29times1000
b)
253.29div10^3
c)
34.764div10,000
d)
34.764times10^2
a) 253,290
b) 0.25329
c) 0.0034764
d) 3,476.4
100
There are 5 bananas, 9 strawberries, and 6 lemons in the produce bag. What is the ratio of:
a) bananas to strawberries
b) bananas to fruit
c) yellow fruit to non-yellow fruit
a)
5:9 or 5/9
b)
5:20 or 5/20=1/4
c)
11:9 or 11/9
200
Universal - {red, orange, yellow, green, blue, purple}
P - {red, yellow, blue}
S - {orange, green, purple}
True/False:
a) Yellow
in P
b)
S sub P
c)
A nn B = O/
d)
S uu P = U
a) True
b) False
c) True
d) True
200
Classify each number as prime or composite:
2, 5, 10, 31, 51, 75
Primes: 2, 5, 31
Composites: 10, 51, 75
200
Round each number to the indicated place:
a) 347, nearest hundred
b) 347, nearest ten
c) 0.347, nearest hundredth
d) 0.347, nearest tenth
a) 300
b) 350
c) 0.35
d) 0.3
200
Identify the following place values in the base-5 number system using words and numbers:
___ ___ ___ . ___ ___ ___
twenty-fives, fives, ones, fifths, twenty fifths, one hundred twenty fifths
25, 5, 1, 1/5, 1/25, 1/125
5^2, 5^1, 5^0, 5^-1, 5^-2, 5^-3
200
Convert the mixed number to an improper fraction and the improper fraction to a mixed number:
a)
2 8/15
b)
325/40
a) 38/15
b) 8 1/8
200
Write in expanded notation:
a) 24.357
b) 0.24357
a) 2times10+4times1+3times1/10+5times1/100+7times1/1000
b) 2*1/10+4*1/100+3*1/1000+5*1/10000+7*1/100000
200
Solve each proportion:
a) 5/70=12/x
b) 329/x=23/16
a) x=128
b) x=228.87
300
Let
U={1, 2, 3, ..., 20}
List the members of each set:
a)
{x in U|6<x<=13}
b)
{x in U| x=n^2, n in N}
a) {7, 8, 9, 10, 11, 12, 13}
b) {1, 4, 9, 16}
300
Find the prime factorization of:
a) 7,938
b) 24,750
a) 7938=2times3^4times7^2
b)
24750=2times5^3times9times11
300
Find the sum or difference by hand:
a) 59 + 37
b) 59 - 37
c) -59 + 37
d) -59 - (-37)
a) 96
b) 22
c) -22
d) -22
300
Convert the following base-10 number to base-5:
48
4810=1435
300
Put the following fractions in increasing order:
3/8, 15/20, 10/16, 7/10
3/8<10/16<7/10<15/20
300
Write each decimal as a fraction and a percent:
a) 0.19
b) 0.812
c) 4.56
a) 0.19=19/100=19%
b) 0.812=812/1000=203/250=81.2%
c) 4.56=4 56/100=4 14/25=456%
300
Rice costs $2.39 for 10 oz. How much should it cost for 32 oz of rice?
32 oz would cost $7.65
400
Let
U={a, b, c, d, e, f, g, h}
A={a, b, c, d, e}
B={b, d, f, h}
Draw a Venn Diagram that represents these sets.
400
Use Divisibility Tests to determine if 2,783,428 is divisible by:
a) 3
b) 4
c) 5
a) Since
2+7+8+3+4+2+8=34
34 is not divisible by 3, so 2,783,428 is not divisible by 3.
b) The last two digits, 28, are divisible by 4, so 2,783,428 is also divisible by 4.
c) The last digit is not a 5 or 0, so 2,783,428 is not divisible by 5.
400
Find the product/quotient (with remainder) by hand:
a)
175times13
b)
175div13
c)
-8 times-5
d)
54div-9
a) 2275
b) 13 remainder 6
c) 40
d) -6
400
Convert the following base-5 number to base-10:
4235
4235=11310
400
Find the sum/difference:
a)
9/4+ - 7/8
b)
2 1/3 - 5 3/4
a) 11/8 = 1 3/8
b) -41/12 = -3 5/12
400
Write each fraction as a decimal and a percent:
a)
2/5
b)
420/80
c)
3/7
a) 2/5=0.4=40%
b) 420/80=5.25=525%
c) 3/7=0.bar(428571)=42.86%
400
Solve each percentage problem:
a) What is 11.5% of 63?
b) What percent of 82 is 63?
c) 36 is 120% of what number?
a) 7.245
b) 76.83%
c) 30
500
Let
U={a, b, c, d, e, f, g, h}
A={a, b, c, d, e}
B={b, d, f, h}
Find:
a)
A nn B
b)
A uu B
c)
barA
d)
n(barA)
a) {b, d}
b) {a, b, c, d, e, f, h}
c) {f, g, h}
d) 3
500
Find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of 425 and 9025.
GCF = 25
LCM = 153,425
500
Use the rectangular array model to show:
a)
4times7=28
b)
28div4=7
500
Find the sum of the two base-5 numbers below (keep your answer in base-5):
423_5+14_5
423_5+14_5=442_5
500
Find the product/quotient:
a)
14/15 times 60/7
b)
4 1/2 div 3/4
a) 8
b) 6
500
Find the answer to each by hand:
a) 3.78 + 2.4
b) 3.78 - 2.4
c) 3.78 x 2.4
d) 3.78 div 2.4
a) 6.18
b) 1.38
c) 9.072
d) 1.575
500
A spring jacket is on sale for 40% off. If the sale price is $58.99, what was the original price?
$147.48