Factors, Multiples, Divisibility and Remainders Flashcards
What is q and r (quotient and remainder) of an integer divided by a larger integer?
q = 0, r = integer. Example, 3/11 = 11(0) + 3 (11 is x, 0 is q or n)
What is a factor or divisor?
Factor or divisor is a number that is part of another number. y = factor*n (where n is the quotient)
E.g., 28 = 8n (8 is a factor of 28).
For a factor / divisor, there is no remainder in a division, so r = 0: 28 = 8q + 0
How are factors / divisors and quotients and remainders connected?
A factor is the number an integer is divided by if the division has no remainder. Otherwise, the number the integer is divided by is just x. Result (quotient) is q or n. n if the number is a factor of integer, q otherwise.
Quotient of an integer divided by factor and divided by non factor.
Divided by factor: q = n and r = 0 (e.g., 33/11, q=3, r=0)
Divided by non-factor: q = n but r ≠ 0 (e.g. 33/7, q= 4, r=5)
What is a quotient?
A non-negative integer. If quotient of a division between integer and non-factor, quotient is the rounded down non-negative integer
Remainder:
- Property (range)
- How do you find the remainder of 55/6?
- 0 ≤ r < x (=number you divide integer by = factor)
- 55 = 6n + r
55 = 69 + 1
Consecutive even integers
Consecutive odd integers
= -2, 0, 2, 4, 6, 8, 10, ….
= -3, -1, 1, 3, 5, ….
Properties of odd and even numbers
- Every number that has 2 as a factor (= multiplied by any even number) or product btw any even number and other number is EVEN
Otherwise product is ODD
= EVENanything = EVEN
ODDODD = ODD
- Sum / subtraction of odd/odd and even/even numbers is EVEN
Otherwise, sum / subtractions are ODD
EVEN+EVEN / EVEN-EVEN= EVEN
ODD+ODD / ODD-ODD = EVEN
EVEN+ODD / EVEN-ODD = ODD
What is a prime number
Number that has as only factors (=divisors) 1 and itself!
- Is 1 a prime number?
2. Why?
1.
No
2.
Because only divisible by itself
Opposite of prime number
Composite number
Exponent number component names
Base and exponent
Definition of a squared number
Exponent is number of times base is multiplied by itself
Square base > 1
Square 0 < base < 1
base > 1 -> square > base (3^2 = 9, 9 > 3)
0 < base < 1 -> square < base (0.2^2 = 0.04, 0.04 < 0.2)
Square root and cube root definition
number which squared (/cubed) equals number in square(/cube) root
x such that x^2 (x^3) = n
Real roots v root from squared / cubed root
Positive has 2 real square roots: positive and negative x
Positive number has 1 real cubed root: positive x
When you denote √ x^2, result is only positive x (so, √ x^2 = |x|, otherwise x could be either positive or negative!)
real square / cubed root of a negative number
No real root. Squared / cubed root is IMAGINARY number
meaning of “third power of 5”
5 to power of 3
meaning of “third power of 5”
5 to power of 3
Other name for decimal point
Period (=point)
one position from point
two positions from point
three positions from point
Ones/units - tenths
Tens - hundredths
Hundreds - thousandths
Thousands -
- how to convert number in scientific notation to decimal point?
- trick for moving x digits to the left when x is more than numbers before period
- move period x digits to right if positive exponent
move period x digits to left if negative exponent
2.
add zeros of -x-(numbers before period)
e.g., 2.3 * 10^-4 has 4-1 = 3 zeros
156.6 * 10^-4 has 4-3 = 1 zero
- name of terms in a multiplication
2. name of terms in division
- multiplicands, product
2.
dividend, divisor/factor, quotient (and remainder)
divide number by a decimal number, e.g. 689.12/14.4
move decimals and proceed with normal division (47,856)
