Arithmetic

Question 1

Integers

Answer 1

Positive and negative numbers, including 0

Question 2

Positive and Negative integers

Answer 2

Positive Integers are greater than 0
Negative Integers are smaller than 0
0 is neither positive or negative

Question 3

Multiplication of Integers (positive and negative)

Answer 3

The product of two positive integers is as positive integer
The product of two negative integers is a positive integer
The product of a positive and negative integer is a negative integer

Question 4

Factors (or Divisors)

Answer 4

Integers which are multiplied with other integers are factors of the resulting integer.

Question 5

Multiples and Divisible

Answer 5

An integer is the multiple of all of its factors and divisible by all of its divisors

Each nonzero integer has infinite multiples

Question 6

Least common multiple

Answer 6

The LCM of two nonzero integers c and d is the least positive integer which is a multiple of both c and d

Question 7

The greatest common divisor or greatest common factor

Answer 7

The GCD(F) of two integers c and d is the greatest positive integer which is a divisor of both c and d

Question 8

Quotient and remainder

Answer 8

When integer c is divided by positive integer d the greatest multiple of d that is less than c can be multiplied by q.
q is the quotient and c - qd is the remainder (always > 0 and < d)

When dividing an integer c by an integer d which is a divisor of c then the result is always a divisor of c.

If d is not a divisor then the result can be viewed as a fraction or decimal or a quotient with a remainder.

Question 9

Even and Odd integers

Answer 9

If an integer is divisible by 2 then it is an even integer, otherwise it is an odd integer

Even integers contain 0

Question 10

Even and odd integers facts

Answer 10

E + E  = E
O + O = E
E + O = O
E * E = E
O * O = O
E * O = E

Question 11

Prime Number

Answer 11

Integer grater than 1 which has only two possible divisors, 1 and itself

Question 12

Prime divisors

Answer 12

Every integer grate than 1 is either a prime number or van be uniquely expressed as a product of factors or prime divisors

Question 13

Prime factorization

Answer 13

Expression of an integer in the form of products of prime divisors

Question 14

Composite Number

Answer 14

Integer grater than 1 which is not a prime number

Question 15

Fractions

Answer 15

number in the form c/d where c and d are integers and d is different from 0

c is the numerator and d is the denominator

Question 16

Rational numbers

Answer 16

Numbers in the form of c/d

Every integer n is a rational number n is equal to n/1

Question 17

Equivalent fractions

Answer 17

if a fraction c/d is multiplied at the nominator and denominator by an integer n the resulting fraction is equivalent

-c/d and c/-d and -(c/d) are all equivalent

If a numerator and denominator have common factor they can be factored to reduce the fraction to an equivalent fraction

Question 18

Adding and subtracting fractions

Answer 18

If the denom is equal then just add the numerator

If the denoms are different then find a common denom (a multiple of both denoms) and then convert both fractions to equivalent fractions with the same denom, then add the numerators and keep the common denom

Question 19

Multiplying and Dividing fractions

Answer 19

Multiplications of fractions is done by multiplying num with num and denom with denom

Division of fractions is done by finding reciprocal of second fraction and then multiplying the first with the reciprocal od the second

Question 20

Mixed numbers

Answer 20

An expression which consists of an integer part and a fraction part n * (c/d) where the fraction part has a value between 0 and 1

Question 21

Converting mixed number to fraction

Answer 21

Convert integer part to a equivalent fraction with same denominator of the fraction and then add it to the fraction part

Question 22

Fractional expressions

Answer 22

numbers in the form of c/d where either c or d is not an integer and d is different from 0

Question 23

Exponents

Answer 23

Used to denote the repeated multiplication of a number by itself

n^e where n is the base and e is the exponent

For all nonzero numbers n^0 = 1
0^0 is undefined

n^(-e) = 1/(n^e)

n*n^(-1) = 1

Question 24

Squaring

Answer 24

A expression with an exponent of value 2

Question 25

Negative and positive numbers raised to an exponent

Answer 25

A negative number raised to an even power is always positive

A negative number raised to a odd exponent is always negative

Question 26

Square root

Answer 26

The square root of a number n is a number r such that r^2 = n

All positive numbers have two square roots, one positive and one negative

The square root of 0 is 0

Square roots of negative numbers are not defined in the real number system

Question 27

4 rules for square roots operations

Answer 27

(√a)^2 = a

√(a^2) = a

√a√b = √(ab)

√a/√b = √(a/b)

Question 28

Odd and even order roots

Answer 28

Odd order roots there is exactly one root for every number n even when n is negative

Even order roots there are exactly two roots for every positive number n and no roots for any negative number n

Question 29

Decimals

Answer 29

A decimal is number which has nonzero values after the decimal point (or that has nonzero values of 10^-x)

A decimal can terminate or repeat without end.

Every fraction with integers in the num and denom is equivalent to a decimal which either terminates or repeats

Every rational number can be expressed as a terminating or repeating decimal and every decimal as a rational numbers

Question 30

Irrational numbers

Answer 30

A decimal which does not terminate or repeat as √2

Question 31

Real numbers

Answer 31

Set that consists of both rational and irrational numbers (it includes all integers, fractions and decimals)

The real numbers can be represented on a line where each point corresponds to a real number (continuous)

Question 32

Absolute value

Answer 32

the distance between a number x and 0

written as |x|

|-x| = x and |x| = x

The absolute value of any nonzero number is positive

Question 33

12 real numbers properties

Answer 33

r+s = s+r and rs = sr

(r+s)+t = r+(s+t) and (rs)t = r(st)

r(s+t) = rs + rt

r + 0 = r and r0 = 0 and r1 = r

if rs = 0 then either r = 0 or s = 0 or both

Division by 0 is undefined

If r and s are positive then r + s and rs is positve

If r and s are negative then r + s is negative and rs is positive

If r is positive and s is negative then rs is negative

|r + s| ≤ |r| + |s| triangle inequality

|r|*|s| = |rs|

if r > 1 then r^2 > r if 0 < s < 1 then s^2 < s

Question 34

Ratio

Answer 34

Proportion between two quantities which expresses their relative sizes

The first quantity is the num and the second is the denom

apples to oranges is expressed as apples/oranges or apples:oranges

Ratios can be reduced to equivalent ratios

Question 35

Proportion

Answer 35

An equation which relates two ratios which can be solved by cross multiplication

Question 36

Percent

Answer 36

means per hundred or hundreths

Ratios which are used to represent parts of a whole considered to have 100 parts

Question 37

Percents to decimals and fractions

Answer 37

1% is equal to 1/100 or 0.01

Question 38

Converting part and whole to percent

Answer 38

Divide part by whole and then multiply by 100

Question 39

Find part that is a certain percent of a whole

Answer 39

Multiply the whole by the decimal equivalent of the percent

Set up a proportion to find a part

Question 40

Given the percent and the part calculate whole

Answer 40

Use decimal equivalent of percent
- whole = part/percent
Use proportions
- whole = (part * 100)/perc

Question 41

Percent grater than 100%

Answer 41

If the numerator of a percent is greater than the denominator then the percent is greater than 100

Question 42

Percent change

Answer 42

Amount of change between two values in percent of the initial value

Question 43

Percent increase

Answer 43

(new - previous)/previous

Question 44

percent decrease

Answer 44

(previous - new)/previous