FTCE General Knowledge Math - Numeration and Operations

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numeration and operations section

operations

addend+addend=sum
sum-addend=difference
factorXfactor=product
dividend ÷ divisor = quotient

division

dividend
---------- = quotient
divisor

divide by zero

any number ÷ 0 = can't do it
0 ÷ any number = 0
0 cannot be a divisor

prime number

whole number greater than 1 that is divisible only by itself and 1

composite

whole number greater than 1 that are not prime

prime factors

use factor tree - e.g. 36 = 2∗2∗3∗3

GCF greatest common factor

the greatest number that will divide evenly into the two numbers list factors of each then chose the highest one

LCM least common multiple

the least product that is a multiple of each of the counting numbers....factor each a build a product consisting of each factor the most number of times it appears as a factor in any one of the counting numbers in the set. e.g...24=2∗2∗2∗3 36=2∗2∗3∗3 so LCM (24,36) = 2∗2∗2∗3∗3 =72

1 is neither prime or composite

...

rational numbers

whole numbers, integers, positive and negative fractions, decimals, and percents

whole numbers

counting numbers and 0

integers

numbers that are either negative or positive and 0....o is not positive or negative

rational numbers

all numbers that can be written as positive or negative fractions ...rational numbers can be expressed as fractions, decimals, or percents

fractions

denominator is on bottom, numerator is on top

percents

to make an equivalent decimal number slide decimal two places to the left and drop the percent sign e.g....75% = .75

100%=1.00=1

...

75%=.75=3/4

...

50%=.50=.5=1/2

...

25%=.25=1/4

...

90%=.90=.9=9/10

...

80%=.80=.8=4/5

...

70%=.70=.7=7/10

...

60%=.60=.6=3/5

...

40%=.40=.4=2/5

...

30%=.30=.3=3/10

...

20%=.20=.2=1/5

...

10%=.10=.1=1/10

...

87 1/2% = .875=7/8

...

62 1/2 %=.625=5/8

...

37 12%=.375=3/8

...

12 1/2% = .125=1/8

...

66 2/3%=.66 2/3 =2/3

...

33 1/3% = .33 1/3 = 1/3

...

5%=.05=1/20

...

4%=.04=1/25

...

1%=.01=1/100

...

irrational square roots

irrational square roots do not have a number that they are evenly multiplied by...if given an irrational square root to estimate find the 2 numbers it falls between e.g. square root of 41 is between 6 and 7

rational square roots

nonnegative number that multiplies by itself to get the number e.g...square root of 1=1, square root of 25 is 5

1/0 a real number

NO...0 cannot be a divisor

exponential notation

eg...3⁴ = 3∗3∗3∗3=81

neagtive exponents eg. 2⁻³=½₃ = 1/8=.125

any number with 0 as an exponent is 1 e.g...3⁰=1

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