Download Ratio and Proportion

Bellwork:

Solve for x.
1.
3 7

x 14
2.
2 x

x 18
8.1 Ratio and Proportion
Students will be able to:
1. Recognize and work with ratios and
proportions.
2. Find a fourth proportional.
3. Be able to apply the means/extremes
product theorem.
4. Calculate the geometric mean.
Ratio (Defn)

A quotient of two numbers
Please note:

A ratio can be written in 3 different ways.

Ratios can (and should) be reduced.
Proportion (Defn)

An equation stating that two ratios are equal.

Means

Extremes
4 8

5 10
Means-Extremes Products Theorem
(Toolbox!)

The product of the means is equal to the
product of the extremes.
4 8

5 10
Example 1

Find the fourth proportional for each set of
three terms.
1.
2, 3, 8
2.
a, 3b, 6
Example 2

Find the ratio of x to y if
7
9

x  4 y 2x  y
Toolbox: A “mean” proportion (Defn) or
Geometric mean (x in this case).

A proportion in which the means are the
same.

Ex.
3 x

x 12
Example 3


Find the geometric and arithmetic means
between 3 and 27. Note which is greater.
What is an arithmetic mean?
Example 4

Find the mean proportional between 4 and
12.
Example 5

6 is the geometric mean between 12 and
what number.
Example 6

a c
ab cd
Show that b  d is equivalent to b  d .
Ticket to Leave

Find the geometric mean between 5 and 20.

9 is the geometric mean between 27 and
what number?
Homework


Pg. 329 # 4 – 15, 17, 18, 24
Show work for credit!