Chapter 3 Flashcards
Step 2
Simplify both sides of the equation
3.1
Solving literal equations
Step 1
Clear equations by multiplying both sides by the LCD using distributive property
Step 3
Collect all terms with the variables on 1 side of the equation
Step 4
Use the distributive property
Step 5
Divide both sides by the coefficient of the variable
3.2
Ratio
A comparison of two numbers by division and is often expressed as a fraction
Rate
Ratio comparing numbers with different numbers
Unit rate
Rate in which the denominator is one
Dimensional analysis (unit analysis)
A rate can be converted to an equivalent rate with different units
Unit multipliers
Rates with different expressions representing the same quality in the numerator and denominator, so their value is one
Proportion
A statement of equality between 2 ratios
Property of proportions
In a proportion, the product of the extremes equals the product of the means
Extremes
First and the last number
3.3
Similar figures
They have the same shape, but not the same size
Similar polygons
Polygons in which the corresponding angles are congruent and the sides are are proportional
Scale
The ratio of the dimensions of the drawing or model to the corresponding dimensions of the actual object
Scale drawing or model
Dimensions are the same scale or ratio to the actual dimensions of the object
Fibonacci and Golden Ratio Sequences
How can a Fibonacci sequence be defined recursively?
As An=An-1+An-2 , where A1 and A2 are any two integers
Standard Fibonacci sequence
Must have A1=1 and A2=1
Golden Ratio Sequence
Defined recursively as Bn=An+1
——-
An
Golden Ratio
Approximately 1.618
3.4
Percents
A ratio of one to one hundred. The symbol is %
The percent equation formula
Percent times whole= part
3.5
Percent change
amount of change
———————– X 100
Original amount
Experimental error
The difference between the experimental and known values
Percent error
|experimental value- known value|
—————————————–X 100%
Known value
Percent Difference
Often used to indicate the precision of repeated measurements when the outcome is expected to be the same
Percent difference formula
first value - second value|
——————————- X 100%
Average of the values
Percent change
The ratio of the change in value to the original value
3.6
Cost
Amount a merchant pays for the merchandise he will sell
Markup
Amount the merchant adds to his cost to arrive at the retail price
Markup rate
The amount of markup on an item as a percent of its cost
Retail price
Merchants cost plus markup, regular amount that merchant asks customer to pay
Discount rate
The percent by which the retail price is reduced
Discount
Amount by which the retail price is reduced
Sale price
Customers cost after the retail price is reduced
Tip
Amount paid for a personal service
Commission
Dollar amount an employee receives as a result of the sales he makes
Rate
Percent used to determine a tip or commission based on the amount of the bill or an employees sales
Percent formula
Percent times Whole=part
Markup formula
Markup rate times cost=markup
Discount formula
Discount rate times retail price= discount
Tip formula
Tip rate times total bill=tip
Commission formula
Commission rate times sales=commission
Simple interest formula
Principal times rate times time= interest
3.7
Distance formula
d=rt
