PREALGEBRA REVIEW DEFINITIONS
Factor - One of two or more quantities that divides a given quantity without a
remainder. For example, 2 and 3 are factors of 6; a and b are factors of ab.
Factor X Factor = Product
Product - The number or quantity obtained by multiplying two or more numbers
together.
Factor X Factor = Product
Dividend - A quantity to be divided.
Divisor - The quantity by which another quantity, the dividend, is to be divided.
Quotient - The number obtained by dividing one quantity by another. In 45 ÷ 3 =
15, 15 is the quotient.
Dividend/ Divisor = Quotient
or Dividend ÷Divisor = Quotient
quotient
divisor dividend
Remainder - The number left over when one integer is divided by another: The
remainder plus the product of the quotient times the divisor equals the dividend.
If there is a remainder, then
Dividend = Quotient X Divisor + Remainder
Least Common Multiple (LCD) - The smallest quantity that is divisible by two or
more given quantities without a remainder: 12 is the least common multiple of 2, 3,
4, and 6. Also called lowest common multiple.
Greatest Common Factor (GCF) - The largest number that divides evenly into
each of a given set of numbers. The greatest common divisor is useful for reducing
a fraction into lowest terms. Consider for instance
PREALGEBRA REVIEW DEFINITIONS
where we cancelled 14, the greatest common factor of 42 and 56.
Prime number is a whole number that has exactly two factors: itself and 1.
Composite number is a whole number that has more than two factors.
The prime factorization of a whole number is the number written as the
productof its prime factors.
EXAMPLE 2
Write the prime factorization of 72.
Solution
We start building a factor tree for 72 by dividing 72 by the smallest prime, 2.
Because 72 is 2 · 36, we write both 2 and 36 underneath the 72. Then we circle the
2 because it is prime.
Next we divide 36 by 2, writing both 2 and 18, and circling 2 because it is prime.
Below the 18, we write 2 and 9, again circling the 2. Because 9 is not divisible by
2, we divide it by the next smallest prime, 3. We continue this process until all the
factors in the bottom row are prime.
The prime factorization of 72 is the product of the circled factors.
72 = 2 × 2 × 2 × 3 × 3
We can also write this prime factorization as
.
Absolute Value - The numerical value of a real number without regard to its sign.
For example, the absolute value of −4 (written |-4|) is 4.
PREALGEBRA REVIEW DEFINITIONS
Mixed Number - A number, such as 71/4, consisting of an integer and a fraction or
decimal.
Improper Fraction - A fraction in which the numerator is larger than or equal to
the denominator. Converting from mixed number to improper fraction:
71/4 = (7x4 + 1)/4 = 29/4
Mixed numbers must be converted to improper fractions or decimals before
doing ANY MULTIPLICATION OR DIVISION OPERATIONS on them.
Exponent - A number or symbol, as 3 in (x + y)3, placed to the right of and above
another number, symbol, or expression, denoting the power to which that number,
symbol, or expression is to be raised. Also called power.
Properties of Exponents
If m and n are integers and x ≠ 0 , then
If m and n are integers, then
m n
m+ n
x x =x
If m and n are integers, then
(x ) = x
m n
m⋅n
If x is a real number and x ≠ 0 , then
x0 = 1
If m, n, and p are integers, then
n
n n
, and
( xy ) = x y
( x m y n ) p = x m⋅ p y n⋅ p
xm
m− n
x
=
xn
If n is a positive integer (-n is negative) ,
and x ≠ 0 , then
x −n =
1
xn
1
= xn
−n
x
and
If n is an integer and b ≠ 0 , then
n
an
⎛ a⎞
=
⎜ ⎟
⎝ b⎠
bn
If n is a positive integer (-n is negative) ,
and b ≠ 0 , then
⎛ a⎞
⎜ ⎟
⎝ b⎠
−n
⎛ b⎞
=⎜ ⎟
⎝ a⎠
Perimeter – distance around the edges of an object
Area – amount of surface covered by an object.
n
PREALGEBRA REVIEW DEFINITIONS
FINANCE FORMULAS:
(1) SIMPLE INTEREST FORMULA
I = Prt A = P + Prt or A = P(1+rt) (A=Future Value, P,r,t same as above)
From the formula A= P + Prt, you should also be able to solve for P, r, or t if given
the other values.
I=Interest,
P=Principal or original amount,
r = rate
t = time in years
(2) COMPOUND INTEREST FORMULA
FUTURE VALUE
A = P(1 + r/n )nt
A = Future Value, or Total amount after n periods.
P = Principal, or original amount.
r = annual interest rate
n = number of compounding periods per year.
t = time in years.
i = interest per compounding period
GEOMETRY
x- intercept - point where graph crosses x-axis. y = 0 at this point.
y-intercept – point where graph crosses y-axis. x = 0 at this point.
slope = rise/run of a line. If linear equation is in the form y = mx + b, m is the
slope.
straight angle = 180 degrees. Adjacent angles the form a straight angle add up to
180 degrees.
right angle = 90 degrees. Adjacent angles the form a right angle add up to 90
degrees.
acute angle = less than 90 degrees
obtuse angle = greater than 90 degees.
Angles of a triangle add up to 180 degrees.
Vertical angles (opposite angles formed from intersecting lines) are congruent
(the same).