Math
Sum of the angles in a triangle =
180 degrees
a number n less than 2
2 - n
least common multiple (LCM)
The smallest multiple (other than zero) that two or more numbers have in common. Ex: the LCM of 6 and 8 is 24, since 24 is the smallest number that is divisible by both 6 and 8.
place value
The value of a digit based on its position within a number
in a clothing store, the manager earns 1/4 more than her salesperson. What percentage of the manager's salary is the salesperson's salary?
Translate: m = s + 0.25s; m = 1.25s; s = m/1.25 = 1/1.25 x m = 0.8m = 80% The salesperson's salary is 80% of the manager's salary
product of x and y
X x Y
base-10 system
a place value system in which each digit (numeric symbols 0-9) in a number is worth ten times as much as the number to the right of it.
An _____ is a set of steps to follow when performing mathematical operations.
algorithm
regular polygons are polygons with sides that are ...
all the same length
Another way to represent multiplication is by using an ____ ____ (promotes the understanding of place value)
area model (AKA box method)
One way to visually represent a multiplication problem is with an ________
array
expanded form
breaking up a number by the value of each digit Ex: the expanded form of 321 is written as 300 + 20 + 1
fractions can be converted into decimals ....
by dividing the numerator by the denominator
When adding and subtracting fractions, each fraction must have a ______ ______
common denominator (the operation is performed in the numerator and the denominator remains the same)
Two angles that add up to 90 degrees are
complementary
In division, -The number that is being divided into groups is called the _____ -The number by which the number is divided is the _____ -The answer is called the _____
dividend divisor quotient
percentages can be converted to decimals by...
dividing by 100 or move the decimal 2 places to the left
inverse operations
each operation cancels out the other operation Ex: 2 + 3 = 5 is true and so is the inverse, 5 - 3 = 2
composite numbers can be broken down into prime numbers using ____ ____
factor trees
In multiplication, the two numbers multiplied together are called ____ The answer is called the ____
factors product
addition and subtraction are considered _______ ______ (so are multiplication and division)
inverse opporations
The opposite of a number
is the negative version of that number (or positive version if the number is negative) -remember that the distance between a number and 0 on the number line is the same as the distance between the opposite of that number and 0.
The absolute value of a number
is the positive value of a number or its opposite. Ex: |-3| = 3 and |3| = 3 (ALWAYS POSITIVE)
one-dimensional objects can be measured in only one dimension:
length
two dimensional objects can be measured in 2 dimensions:
length and width
three dimensional objects can be measured in three dimensions:
length, width, and height
slope formula
m=y2-y1/x2-x1
if b books cost d dollars each and each student must buy 2 books, how much will each student pay for his/her books?
make it into an easier problem. if 100 books cost $2,000, each student would have to pay 2,000/100 x 2 or $40. -this is the same as b/d x2 or 2d/b
decimals can be converted to percentages by...
multiplying the decimal by 100 or move the decimal 2 places to the right
a number n less 2
n - 2
a number n reduced by 2
n - 2
when converting a decimal to scientific notation, if the number between 1 and 10 is larger than the number you started with, the power of 10 will be ____. (Ex: 0.0012 = 1.2 x 10^?) if the number between 1 and 10 is smaller than the number you started with, then the power of 10 will be ____. (Ex: 8,500 = 8.5 x 10^?)
negative positive
Rational numbers
numbers that can be made by dividing two integers. -Must be expressed as a terminating or a repeating decimal such as 0.321 or 0.666666.... -Pi would NOT be a rational number because it goes on forever with no repeating pattern -integers are rational numbers because they can be written as a fraction with a denominator of 1.
When solving a multi-step equation, the__________ must be used to get the correct answer. Problem should be worked in the following order: -Parenthesis and brackets -Exponents and square roots -Multiplication and Division -Addition and Subtraction PEMDAS
order of operations
p percent
p/100 , or move decimal 2 places to the left
decimals can be converted into fractions by ...
placing the numbers to the right of the decimal over the appropriate base-10 power (tenths, hundredths, thousandths, etc.) and simplify
_____ are two-dimensional shapes, such as triangles or squares, that have 3 or more straight sides.
polygons
Multiplication and division positive x positive = ______: 5 x 3 = ___ negative x negative = ______: -6 x -5 = ___ negative x positive = ______: -5 x 4 = ____ 3 x -6 = ____
positive: 15 positive: 30 negative: -20 -18
Addition and subtraction positive + positive = ______: 4 + 5 = ____ negative + negative = ________: -4 + -5 = ____ -4 - 5 = ____ negative + positive = depends: subtract the absolute values of the two numbers (|larger| - |smaller|) and make the sign the same of the largest absolute value of the numbers -15 + 9 = ____
positive: 9 negative: -9 -6
a ______ is an equation stating that two ratios are equal
proportion
A _______ is the opposite of an exponent and is an expression that has a square root, cube root, or a higher root.
radical Ex: square root of 16 = 4, since 4^2 = 16
when adding or subtracting negative numbers, look at a number line. when adding two numbers, whether they are positive or negative, count to the _____; When subtracting, count to the ____. *Note that adding a negative value is the same thing as _______ ; subtracting a negative value is the same thing as ______.
right/ left subtracting / adding
_______ _______: A method of writing numbers using powers of ten.
scientific notation
Exponents
show how many times a number (the base) should be multiplied by itself. Ex: 2 x 2 x 2 = 8
Negative numbers with larger opposites are actually ...
smaller than negative numbers with smaller opposites. Ex: -40 < -2.4 < 0 < .1 < 20
three-dimensional objects are also called ____, and the shape of a flattened solid is called a ____
solid, net
two angles that add up to 180 degrees are
supplementary
Negative Exponent Rule
take the reciprocal of the base, and then make the exponent positive. Ex: 3^-2 = (1/3)^2 = 1/9
remainder
the amount left over when a number cannot be divided evenly
Greatest Common Factor (GCF) (AKA greatest common divisor)
the greatest number (other than 1) that each number in the set is divisible by without any remainders. Ex: for the numbers 4 and 8, the GCF is 4, since 4 goes into both 4 and 8.
Commutative Property
the order of the operation does not matter Applies to: addition a + b = b + a & multiplication ab =ba
real numbers
the set of all rational and irrational numbers -can be represented on a number line
A shopper buys 6 apples for $4.80. what is the unit rate of a pound of apples?
to get the unit rate, find the amount for one pound of apples; this is when x apples = 1. -set up a ratio: 4.8/6 = x/1; x = $0.80
sum of x and y
x + y
average of x, y, and z (and so on)
x + y + z +..... / how many #s on top
difference of x and y
x - y
quotient of x and y
x divided by y
ratio of x to y
x over y
half, twice
x/2 , 2x
y increased by x%
y + (y x X/100)
y decreased by x%
y - (y x X/100)
y is at most (or no more than) x
y < or equal to x
Linear equations follow a specific pattern that results in a straight line when graphed. the most common way to write a linear equation is slope- intercept form: ________
y = mx + b
y is at least (or no less than) x
y > or equal to x
Natural Numbers
The set of numbers 1, 2, 3, 4, ... Also called counting numbers.
Integers
The set of whole numbers and their opposites. (-3,-2,-1,0,1,2,3,.....) -NOT fractions or decimals
"what number" , "how much" means
"n" or any variable
the sum of all the interior angle measurements in a polygon with n sides is __________, and the sum of all the exterior angles is ____ degrees for any polygon
(n - 2) x 180 degrees 360
"in addition to", "increased by", "added to"
+
4 + -5 =
-1
-1 + -4 =
-5
opposite of x
-x
Every whole number, except ___, is either a prime or composite number
1
twice a man's age is no more than 5 years less than his father's age. if m represents the man's age, and f his father's age, what is the inequality that would represent this situation?
2m < or equal to f - 5
-2 + 5 =
3
"is", "will be", "yields" means
=
composite number
A natural number, greater than 1, than can be evenly divided by at least one other number besides 1 and itself. Ex: 6 is composite bc it can be divided by 1, 2, 3, and 6.
prime number
A natural number, greater than 1, that can be divided evenly only by 1 and itself. Ex: 7 is a prime number bc it can only be divided by 1 and 7.
Assosiative Property
Grouping of numbers does not matter Applies to: addition (a + b) + c = a + (b + c) & multiplication (a x b) x c = a x (b x c)
To which of the following number sets does 3 NOT belong? A. irrational B. rational C. whole D. integer
A: irrational the number 3 is not irrational bc it can be written as the fraction 3/1
Identity Property
Adding zero or multiplying by 1 will not change the original value. Applies to: addition a + 0 = a & multiplication a x 1 = a
irrational numbers
Any real number which cant be expressed as a fraction of two integers
What is the remainder when 397 is divided by 4? A. 0 B. 1 C. 2 D. 4
B: 1 Find the highest possible multiple of 4 that is less than or equal to 397, then subtract to find the remainder 99 x 4 = 396 397 - 396 = 1
What is the square root of 169? A. 9 B. 13 C. 16 D. 19
B: 13 (you have to find a number that can be multiplied by itself in order to get the number 169 as the product. 13 * 13 or 13^2 will give you 169)
What is the LCM of the numbers 10 and 12? A. 2 B. 24 C. 60 D. 120
C: 60 (write out the multiples of each number until reaching a number in both lists) 10: 10, 20, 30, 40, 50, 60 12: 12, 24, 36, 48, 60
Which of the following has the greatest value? A. -4(3)(-2) B. -16 - 17 + 31 C. 18 - 15 + 27 D. -20 +10 +10
C: = 30
Classify the number 13/14 A. irrational B. imaginary C. rational D. integer
C: rational 13/14 is a rational number bc it can be written as a fraction but not as a whole number (without the fraction). it is not imaginary bc it does not have an i component.
Distributive Property
Multiply the value by all the values inside brackets, then add. Applies to: multiplication a(b + c) = ab + ac
Zero Property
Multiplying any value by 0 equals 0 Applies to multiplication: a x 0 = 0
whole numbers
Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
Percent increase formula
New amount - Original amount ---------------------------------- x 100 Original amount
Percent decrease formula
Original amount - New amount ---------------------------------- x 100 Original amount