What is Math Fundamentals? Flashcards
Numbers and equations form the basis of all the math questions on the GRE. Simply put, the more comfortable you are working with numbers and equations, the easier the math portion of the exam will be. This chapter gives you a review of all the basic mathematical concepts including properties of numbers, factors and multiples, fractions and decimals, math vocabulary, and some basic rules of math.
0.01=
1/100
1%
0.1
1/10
10%
0.2
1.5
20%
0.25
1/4
25%
0.33
1/3
33 1/3%
0.4
2/5
40%
0.5
1/2
50%
0.6
3/5
60%
Digit
the numbers that make up other numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
Numbers
made up of their a digit or collection of digits
integers
numbers that have no fractional or decimal part
can be positive or negative
zero is an integer :)
positive or negative
negative are less than zero, positive are greater than zero
even or odd
even integers are divisible by 2. odd integers are not
only integers can be either even or odd– no fractions or decimals
zero
-even
-0 plus another number is equal to the other number
-0 multiplied by another number is 0
-you cannot divide by 0
-is a multiple of every number
consecutive integers
integers listed in order of value without any integers missing in between them
fractions and decimals cannot be consecutive
can always be written algebraically, with the smallest number in the set as ‘n’
absolute value
the distance of a number from zero
distance cannot be negative, so always a positive integer
rule of divisibility
2
an integer is divisible by 2 if its units digit is divisible by 2
rule of divisibility
3
an integer is divisible by three if the sum of its digits is divisible by 3
rule of divisibility
4
an integer is divisible by 4 if its last two digits form a number that is divisible by four
form–not sum
rule of divisibility
5
an integer is divisible by 5 if its units digit is either 0 or 5
rule of divisibility
6
an integer is divisible by 6 if it’s divisible by both 2 and 3
rule of divisibility
7
no special rule
rule of divisibility
8
an integer is divisble by 8 if its last three digits form a number that is divisible by 8
rule of divisibility
9
an integer is divisible by 9 if the sum of its digits is divisible by 9
remainder
the integer left over after division by one integer that is not divisible by another
factor
a number that divides evenly into a particular integer; factor pairs always begin with 1 and end with the integer itself
multiples
multiples of an integer are all the integers that are the product of that integer and another integer– zero is a multiple of every number
prime numbers
an integer that has only 2 factors– itself and 1
order of operations
PEMDAS
parentheses
exponents
multiplication
division
addition
subtraction
fractions
an expression of the number of parts out of a whole
fractions express a relationship between numbers, not actual amounts
numerator
numerator– how many ‘parts’
denominator
denominator–indicates how many parts equal a whole
adding and subtracting fractions
- find common denominator
- expand into equivalent fractions*
- add or subtract the numerators, which now have the same denominator
*multiply the numerator and denominator by x, where x is the number of
Bowtie Method
a technique to add and subtract fractions with different denominators:
1. multiply the denominators of each fraction (gives you a common denominator)
2. multiply each denominator by the numerator of the other fraction
3. add or subtract per the expression
first described p 296
multiplying fractions
- multiply the first numerator by the second numerator
- multiply the first denomiator by the second denominator
- reduce the expression
you can “reduce diagonally”– meaning you don’t have to be in the same f
dividing fractions
- multiply numerator and denominator by the reciprocal of the divisor
if a numerator or denominator is itself a fraction, rewrite horizontally
7/(1/4) = 7 ÷ 1/4– then you would multiply the reciprocal, so 7/1 x 4/1 = 28
comparing fractions
variant bowtie method:
1. multiply the denominators and numerators of two different fractions.
2. the fraction with the greater product in the numerator is the greater fraction
comparing more than two fractions
strategy:
1. use variant bowtie method to compare two fractions at a time
mixed number
a number that is represented as an integer and a fraction, like 2 2/5
mixed number –> fraction
- multiply the denominator of the fraction by the integer
- add the result to the numerator
- put the sum over the denominator
fraction –> decimal
to turn a fraction into its decimal equivalent, multply the numerator by the denominator
percentage
a particular kind of fraction that always has 100 as the denominator
decimals –> percentages
move the decimal point two places to the right
0.8 = 80%
translation:
percent
/100
translation:
is
=
translation:
of, times, product
x
translation:
what (or any unknown value)
any variable (x, k, b)
defintion:
percentage increase/decrease
the percentage by which something has increased or decreased
formula
percent change=
difference/original x 100
given two numbers, usually:
difference– the result when the lesser number is subtracted from the greater number
original– whichever number you started with
laws
associative laws
when you are adding or multiplying a group of numbers, you can regroup the numbers in any way you’d like
(a+b) + (c+d) = a + (b+c+d)
distributive law
multiplying a number by a group of numbers added together is the same as doing each multiplication seperately
a(b-c)=ab - ac
terminating decimals
a decimal that ends (i.e., one that is not repeating)
1/4 is a terminating decimal, but 1/3 is a repeating decimal.
comparing decimals
example:
0.00099
0.00100
-
099
100
-
strategy:
1. line up the numbers by their decimal points
2. fill in the missing zeroes
3. compare
