gat rules flashcards

pemdas

parantheses / exponents / multiply and divide ( left to right ) / add and subtract ( left to right )

divisibility rules > x2

the last digit will be an even number ( 0, 2, 4, 6, 8,)

divisibility rules > x3

the sum of all digits is divisible by 3 / ex. 405 = 4+0+5=9

divisibility rules > x4

the last two digits are divisible by 4 (anything divisible by 4 is also divisible by 2, but not vise versa)

divisibility rules > x5

the last digit will be 0 or 5

divisibility rules > x6

apply both divisibility rules x2 and x3

divisibility rules > x7

1. double the last digit

2. subtract it from the remaining number

3. the result must be divisible by 7

divisibility rules > x8 /// CASE 1

if the hundreds digits is even, the last two digits must be divisible by 8

624 > 24 > divisible

divisibility rules > x8 CASE 2

if the hundreds digits is even is odd, the last two digits +4 must be divisible by 9

352 > 52+4 =56 > divisible by 8

divisibility rules > x9

the sum of the digits must be divisible by 9

divisibility rules > x10

last digit will be 0

divisibility rules > x11 /// METHOD 1

add the alternation sum of the digits

91802 > 9-1+8-0+8-2 =22 divisible by 11

divisibility rules > x11 /// METHOD 2

add the digits in blocks of two from right to left

1375 > 75+13=88 divisible by 11

divisibility rules > x12

apply both divisibility rules x3 and x4

divisibility rules > x15

apply both divisibility rules x3 and x5

prime number

a whole number greater than 1 whose only factors are 1 and itself

composite numbers

numbers with multiple factors

prime numbers between 1 and 10

2 / 3 / 5 / 7

prime numbers between 11 and 20

11 / 13 / 17 / 19

prime numbers between 21 and 30

23 / 29

prime numbers between 31 and 40

31 / 37

prime numbers between 41 and 50

41 / 43 / 47

prime numbers between 51 and 70

53 / 59 / 61 / 67

prime numbers between 71 and 90

71 / 73 / 79 / 83 / 89 / 97

factoring difference of squares

a² - b² = (a+b)(a-b)

factoring perfect square

(a+-b)² = a² +- 2ab + b²

+- = plus or minus depending on question

unit conversions - meter

1 kilometer - 1000 meter

1 meter - 100 centimeter

1 centimeter - 10 milimeter

unit conversions - gram

1 kilogram - 1000 gram

1 gram =1,000 milligrams

unit conversion - liters

1 liter - 1000 mililiter

gcf

greatest common factor is the biggest number that divides two or more numbers without a remainder

lcm

least common multiple is the smallest number that is a multiple of two or more numbers

how to find gcf or lcm

1. Prime factorization of both numbers.

2. GCF: Identify common prime factors with the lowest powers and multiply them.

3. LCM: Identify all prime factors with the highest powers and multiply them.

gcf and lcm special case

if one number is a multiple of the other then the least number is the gcf and the greatest number is the lcm

improper fraction

has a numerator that is greater than the denominator

mixed number

has a whole number part and a fraction part

how to convert mixed number to improper fraction

1. multiply the whole number by the denominator

2. add that number to the numerator

3. the sum becomes the new numerator

4. the denominator remains the same

convert improper fraction to mixed number

divide the numerator by the denominator

the quotient becomes the whole number

the remainder becomes the new numerator

the denominator remains the same