1. Unit 1: Proportional Reasoning
Lesson 1: Vocabulary

2. Cornell Notes Header Topic: Ratios and Rates (Unit 1)
E. Q.: What kinds of questions can be answered using proportional reasoning?
Name: _____________________________
Date: _____________________________
Class: _____________________________
Chp. 4 Lesson 1 – Vocabulary

3. Ratio Vocabulary
ratio – A comparison between two quantities using division. Ex. a/b , 5/4
Can the second number in a ratio be zero?
No - Why?
equivalent ratios: Ratios that name the same comparison.
Ex. 1/2, 2/4, 3/6

4. Rate Vocabulary
rate - A ratio that compares two quantities that have different units of measure.
Ex. miles/gallons quantity/money meters/min
unit rate - A rate in which the second quantity (term) in the comparison is 1.
Ex. $4.20/pound, 25 miles per gallon
equivalent rate: Rates that name the same comparison.
Ex. 4apples/2dollars, 8apples/4dollars, 16apples/8dollars

5. Vocabulary Rational Number:
Any number that can be made by dividing one integer by another. The word comes from "ratio". Examples: 1/2 is a rational number (1 divided by 2, or the ratio of 1 to 2) 0.75 is a rational number (3/4) 1 is a rational number (1/1) 2 is a rational number (2/1) 2.12 is a rational number (212/100) -6.6 is a rational number (-66/10) But Pi is not a rational number, it is an "Irrational Number".

6. Vocabulary Proportion: Irrational Number:
A real number that cannot be written as a simple fraction - the decimal goes on forever without repeating.
Proportion:
Proportion says that two ratios (or fractions) are equal.

7. Vocabulary Similar: more ...
In Geometry, two shapes are Similar if the only difference is size (and possibly the need to turn or flip one around). These two shapes are Similar (one is smaller and flipped over, but otherwise the same)

8. Vocabulary
Indirect measurement: a technique that uses proportions to find a measurement when direct measurement is not possible.
Examples of Indirect Measurement
The length of a boat in a picture is given as 4 inches. The scale of the picture is given to be 1 inch : 13 feet. By setting up a proportion, the length n of the actual boat can be found.
Solving the proportion, we get n = 52 feet. 

9. Constant of Proportionality: Scale Factor:
Vocabulary
Constant of Proportionality:
If a quantity x is proportional (directly) to another quantity y, then x is written as x = ky, where k is called the Constant of Proportionality.
Scale Factor:
The ratio of any two corresponding lengths in two similar geometric figures is called its Scale Factor.
The ratio of the length of a scale drawing, or scale model, to the corresponding length of the actual object is called as Scale Factor

10. Scale Drawing
A drawing that shows a real object with accurate sizes except they have all been reduced or enlarged by a certain amount (called the scale). The scale is shown as the length in the drawing, then a colon (":"), then the matching length on the real thing.  Example: this drawing has a scale of "1:10", so anything drawn with the size of "1" would have a size of "10" in the real world, so a measurement of 150mm on the drawing would be 1500mm on the real horse.
Also Scale Model

11. Vocabulary Corresponding sides:
If the relative position of two sides is the same in two figures, then they are called Corresponding Sides.
Corresponding sides are proportional in similar figures.
Example of Corresponding Sides
In the figure, triangles ABC and XYZ are similar. The relative position of AB and XY is same, so they are corresponding sides Similarly, BC and YZ, are corresponding sides
also AC and XZ, are corresponding sides.