By Justin GoreschakHonors Geometry – Mod 9

RatioDEFINITION: The ratio is the quotient of two

numbers.

A Ratio can be written 3 other ways:Nota Bene: When creating a ratio, all numbers must be in the same unit of measure. For example both numbers need to be in centimeters rather than one in meters and the other in inches.

Nota Bene: When creating a ratio, all numbers must be in the same unit of measure. For example both numbers need to be in centimeters rather than one in meters and the other in inches.

If there are 12 girls and 6 boys in this class,

The fraction 12/6 simplifies to 2/1, and as a ratio,

it can be written 2:1, 2 to 1, or 2/1.Whichever way you write it, it means that there are 2 girls for

every boy.

Hello, Kitty.

ProportionDEFINITION: A proportion is an equation

stating that two or more ratios are equal, like so:

45:1515:5 3

2

15

10

6

4

y

x

Most proportions will only contain 2 ratios, such as . d

c

b

a

For example:For example:If a graph has two lines drawn upon it, and they eachhave the slopes and we can say they are parallel sincethe two slopes are ratios which can be reduced to the same .

10

5

4

2

2

1

In the equation , a is the first term, b is the second term, c is the third term and d is the fourth term.

THEOREM: In a proportion, the product of the means is equal to the product of the extremes. (Means-Extremes Product Theorem)

This allows cross multiplying of the proportions to develop a standard equation. The extremes, a and d, are multiplied by the means, b and c. → ad=cb

d

c

b

a

d

c

b

a

Geometric Means

The geometric mean is the value of the two mean values in a proportion. This is found by taking the square root of the product of the

extremes.

The geometric mean between 2 and 8 would be 41682

The arithmetic mean of two numbers is the average. To find an arithmetic mean, as you probably have learned prior to this lesson, the sum of numbers is

divided by the quantity of numbers.

For example: Joe got the following grades on his last few tests and wants to know his current average.

100, 95, 95, 102, 88

480881029595100

Average

965/480

Practice

#2

If Pip has 7 apples and Mrs. Joe has 3, what is

the geometric mean between 5 and 20?

#1

If a model airplane has a wing span of 11cm, and the ratio of the model to real life craft is 1:100,

what is the wing span of the real life craft?

ANSWERS!!!

#1

Cross-multiply to find the value of x. The actual wing span is 1100cm or 11m.

#2

Multiply the extremes and take the product’s square root to find the geometric mean to be

10.

x

x

1100

11

100

1

10100

100205

Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. New ed. Boston: McDougal Littell, 1997. 325-331.

"Ratios and Proportions." Math.Com. 2005. 27 May 2008 <http://www.math.com/>.