35 terms

Arithmetic and Number Properties- GRE

Magoosh. Gre Math Formalas
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Integers:
Any counting number including negative numbers.
-Whole numbers
-Ex: -3, -1, 2, 7... but not 2.5)
Real Numbers:
Numbers that appear on the number line including pi, the square toot of 2, etc.
-One that is not imaginary
Order of Operations: PEMDAS
1. Parentheses
2. Exponents
3. Multiplication/Division
4. Addition/Subtraction
PEMDAS Example:
2 + 6/2 x (5-1)^2 = _______
= 2 + 6/2 x 16
To get the number 16...
(5-1)^2
= (4)^2
=(4)(4)
= 16

= 2 + 48 = 50
To get the number 48...
6/2 x 16 = 48
You can also remember PEMDAS as...
Please Excuse My Dear Aunt Sally
The Commutative Property:
a + b = b + a,
a x b = b x a
The Associative Property:
(a + b) + c = a + ( b + c),
(a x b) x c = a x (b x c)
The Distributive Property:
a x (b + c) = ab + ac,
a x (b - c) = ab - ac
The Commutative and Associate Properties DO NOT WORK WITH...
Subtraction or division
Prime Number:
Is one that is divisible only by itself and 1.
-In other words, a positive integer with exactly positive divisors.
-This includes 2, 3, 5, 7, and 11
-NOT 9 because 3 x 3 = 9
What number is not a Prime Number?
1
What is the smallest Prime Number and the only even Prime Number?
2
Memorize all Primes below 60...
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59
Factorization:
If X can be multiplied by Y to get Z, assuming all of these are positive integers, then X and Y are considered factors of Z
Prime Factorization of a number is...
Dividing it into its constituent primes...
-For 20... this is 3 x 7;
-For 60... 2 x 2 x 3 x 5.
-For 7644...
2 x 2 x 3 x 7 x 7 x 13
To find the Prime Factorization of 60...
You can use...
60 = 30 x 2 = 15 x 2 x 2 = 5 x 3 x 2 x 2
16 has Five Positive Divisors:
1, 2, 4, 8, 16
40 has Eight Positive Divisors:
1, 2, 4, 5, 8, 10, 20, 40
Divisibility 3:
Sum of digits divisible by 3
Divisibility 4:
The last two digits of number are divisible by 4
Divisibility 5:
The last digit is either a 5 or a 0
Divisibility 6:
Even number and sum of digits is divisible by 3
Divisibility 8:
If the last three digits are divisible by 8
Divisibility 9:
Sum of digits is divisible by 9
Absolute Values:
The absolute value of a number is its distance from the number line.
|x| = x
|-x| = x
"Percent" =
Per 100;
19% = 19/100
0.43% = 0.43/100
= 43/10000
To find what percent some part is of a whole, use...
part/whole = percent/100
Ex: If 120 people of 800 people in town smoke, then...
120/800 = percent/100
So...
120 divided by 800
= 0.15
= 15/100
= 15% of the townspeople smoke
Percent Change:
% change =
change/original value
Example:
If the price of something goes from $40 to $52, the percent change is...
(52-40)/40 =
12/40
= 3/10
= 30/10
= 30%
The price increased 30%
From the example... this can also be written as...
(change x 100)/ original value

(52-40) x 100
---------------
40

= 1200/40
= 30%
Ratios:
Ratios let us compare the proportions of two quantities
If there is a 2:5 ratio of boys to girls at a school, that means...
That for every 5 girls, there are 2 boys.
SO there could be 2 boys and 5 girls,
20 boys and 50 girls
200 boys and 500 girls, etc.
Ratios are given by...
x:y
x to y
or
x/y

(Ratios can also be x:y:z)
Ratios can be simplified like fractions...
3:6 is the same as 1:2
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