Chapter 2 Flashcards
equation
a mathematical sentence that shows that two expressions are equivalent
solution of an equation
a value of values that make the equation or inequality true
Additional Property of Equality
For real numbers a, be, and c, if a = b, then a+c=b+c
Subtraction Property of Equality
If a, b, and c are real numbers and a=b, then a-c=b-c
Opposites
The opposite of a number a, denoted -a, is the number that is the same distance from zero as a, on the opposite side of the number line. The sum of opposites is 0.
Additive Inverses
The opposite of a number. Two numbers are additive inverses if their sum is zero.
Identity element
An equation that is true for all values of the variables.
Multiplication Property of Equality
If a, b, and c are real numbers and a=b, then ac=bc.
Division Property of Equality
For real numbers a, b, and c, where c does not =0, if a =b, then a/c=b/c
Distributive Property
For all real numbers a, b, and c, a(b+c) = ab+ac, and: (b+c)a=ba+ca.
Least common denominator
The least common multiple of two or more given denominators
Greatest common factor
The product of the greatest integer and the greatest power of each variable that divides evenly into each term of the expression.
identity
An equation that is true for all values of the variables.
contradiction
An equation that has not solutions.
ratio
A comparison of two numbers by division
rate
A ratio that compares two quantities measured in different units.
scale
The ratio of any length in a drawing to the corresponding actual length.
unit rate
A rate in which the second quantity in the comparison is one unit.
conversion factor
The ratio of two equal quantities, each measured in different units.
proportion
An equation that states that two ratios are equal
cross product
In the statement a/b=c/d, the product of the means bc and the product of the extremes ad are called the cross products
means
The sum of all the values in a data set divided by the number of data values. Also call the average.
extremes
In the proportion a/b=c/d a and d are the extremes. If the proportion is written as a:b = c:d, the extremes are in the first and last positions.
scale drawings
A drawing that uses a scale to represent an object as smaller or larger than the original object.
scale model
A three-dimensional model that uses a scale to represent an object as smaller or larger than the actual object.
similar
Two figures that have the same shape, but not necessarily the same size.
corresponding sides
Sides in the same relative position in two different polygons that have the same number of sides.
corresponding angles
Angles in the same relative position in two different polygons that have the same number of angles.
indirect measurement
A method of measuring an object by using formulas, similar figures, and/or proportions.
scale factor
In a dilation, the ratio of a linear measurement of the image to the corresponding measurement of the preimage.
percent
A ratio that compares a number to 100
is
equal
of
multiply
part
divide
commission
Money paid to a person or company for making a sale; usually a percent of the sale amount
interest
The amount of money charged for borrowing money or the amount of money earned when saving or investing money
sales tax
A percent of the cost of an item that is charged by governments to raise money
principal
An amount of money borrowed or invested
tip
An amount of money added to a bill for service; usually a percent of the bill.
whole
The set of natural numbers and zero
percent change
An increase or decrease given as a percent of the original amount. Percent increase describes an amount that has grown. Percent decrease describes an amount that has been reduced.
percent increase
An increase given as a percent of the original amount
percent decrease
A decrease given as a percent of the original amount
discount
An amount by which an original price is reduced
markup
The amount by which a wholesale cost is increased
