Arithemetic Flashcards
Common fraction - decimal conversions
1/3
0.333
Greatest common divisor Using Euclid’s algorithm
A much more efficient method is the Euclidean algorithm, which uses a division algorithm such as long division in combination with the observation that the gcd of two numbers also divides their difference. Ignore the quotient in each step except to notice when the remainder reaches 0, signalling that we have arrived at the answer.
gfc(a,b)
a -> remainder1 -> remainder2
__ __________ ___________
b a remainder1
GFC=quotient when remainder =0
To compute gcd(48,18), divide 48 by 18 to get a quotient of 2 and a remainder of 12. Then divide 18 by 12 to get a quotient of 1 and a remainder of 6. Then divide 12 by 6 to get a remainder of 0, which means that 6 is the gcd.
Common fraction - decimal conversions
1/5 =
0.2
Common fraction - decimal conversions
1/6 =
1/2 *1/3 = 0.333/2 = 0.167
Common fraction - decimal conversions
1/8 =
1/2 * 1/4 = 0.25/2 = 0.125
Common fraction - decimal conversions
1/9 =
1/3 * 1/3 = 0.333/3 = 0.111
Common fraction - decimal conversions
1/7 =
0.143
Manipulating fractions
4/9 =
4 * 1/9 = 4 * 0.111 = 0.444
Manipulating fractions
7/8 =
1 - 1/8 = 1 - 0.125 = 0.875
Multiplying large numbers - trick
Using answers
Check answers where units digit agrees
If there is more than 1, use approximation
Multiplication Table
6 x 12
72
Multiplication Table
6 x 13
78
Multiplication Table
6 x 14
84
Multiplication Table
6 x 15
90
Multiplication Table
7 x12
84
Multiplication Table
7 x13
91
Multiplication Table
7 x 14
98
Multiplication Table
7 x 15
105
Multiplication Table
8 x 12
96
Multiplication Table
8 x 13
104
Multiplication Table
8 x 14
112
Multiplication Table
8 x 15
120
Multiplication Table
9 x 12
108
Multiplication Table
9 x 13
117
Multiplication Table
9 x 14
126
Multiplication Table
9 x 15
135
Multiplication Table
11 x 11
121
Multiplication Table
11 x 12
132
Multiplication Table
11 x 13
143
Multiplication Table
11 x 14
154
Multiplication Table
11 x 15
165
Multiplication Table
12 x 12
144
Multiplication Table
12 x 13
156
Multiplication Table
12 x14
168
Multiplication Table
12 x 15
180
Multiplication Table
13 x 13
169
Multiplication Table
13 x 14
182
Multiplication Table
13 x 15
195
Multiplication Table
14 x 14
196
Multiplication Table
14 x 15
210
Multiplication Table
15 x 15
225
Prime Numbers
Between 0 and 10
2
3
5
7
Prime Numbers
Between 10 and 20
11
13
17
19
Prime Numbers
Between 20 and 30
23
29
Prime Numbers
Between 30 and 40
31
37
Prime Numbers
Between 40 and 50
41
43
47
How to check for prime
Check for divisibility big primes:
2 & 5 3 7 11 13
Remember that you can stop when you have checked the primes up to the sqroot of the number
Check for how many primes exist between two numbers
1) write down all odd #’s (eliminates all multiples of 2)
2) eliminate all multiples of 3 & 5
3) eliminate all multiples of 7 & 11 & 13
Finding how many unique primes for a number
Do prime factorization of the number and count the unique
Ex.
20 = 2^2 x 5
So it has 2 unique primes
Finding the number of unique factors for a number
1) Do prime factorization of the number
2) Add 1 to the exponent of each prime
3) Multiply the result
Ex
20 = 2^2 x 5
Number of unique factors = (2+1)(1+1) = 6
How to check if an integer is divisible by a #
Prime factorization of the number
See if the factors can be combined to equal the #
Divisibility Rules
When is a number divisible by 4
If last 2 digits are divisible by 4
Divisibility Rules
When is a number divisible by 6
If it is even and divisible by 3
Divisibility Rules
When is a number divisible by 9
If the sum of the digits is a multiple of 9
Lowest Common Multiplier
How to find LCM of two numbers
1) Perform prime factorization on each number
2) Take each prime at its highest power and multiply
What is the terminology for the terms in division?
Numerator –> Dividend
_____________ = Quotient
Denominator –> Divisor
What is a composite?
A Non-prime number
What are the properties of 0?
It is an even number
It is neither + nor -
It is a multiple of all numbers
It is never a factor of any number
What are the common factors shared by x and (x+1)?
None, except 1
What is the LCM of x and (x+1)?
(X)(x+1)
Properties of even/odd numbers
Addition/Subtraction
odd +/- odd = even
even +/- even = even
odd +/- even = odd
Properties of even/odd numbers
Multiplication/Division
odd x odd = odd
even x even = even
odd x even = even
Inclusive Sets
Find the multiples of x in set a..b
b - a
____ + 1
x
If set is not inclusive move range inward to next numbers that are multiples if x
