This document provides instruction on ratios, proportions, and how to solve proportions algebraically and through equivalent ratios. It defines ratios as a comparison of two quantities using division and proportions as equations stating that two ratios are equivalent. Examples are provided for setting up and solving proportions to find unknown values. Applications discussed include finding ratios in a volleyball team's match statistics and solving word problems involving printers, skiers, and snowboarders using proportions. Students are assigned even problems from page 165 to practice these concepts.

1. Write Ratios & Proportions
Section 3.5
P. 162-167

2. • We will review the concept of a ratio and a
proportion.
• We will solve proportions algebraically.
• We will relate proportions to real-world
situations.

3. • What is a ratio?
A ratio uses division to compare two
quantities.
• How can ratios be written?
a to b a:b a
b
All the above are read “ a to b.”
Ratios should be written in simplest
form.

4. • A volleyball team plays 14 home matches
and 10 away matches.
• Find the ratio of home matches to away
matches.
• Find the ratio of home matches to all
matches.
• Find the ratio of away to home matches.
• Write your answer in simplest form.

5. • What is a proportion?
• A proportion is an equation that states that two
ratios are equivalent.
a c
, where b, d 0
b d

6. • Many times one of the values of a
proportion is unknown. You can solve a
proportion using the same methods you
used to solve equations.
• Some proportions can also be solved by
the concept of equivalent ratios.

7. Setting up a proportion
• 3 is to 8 as x is to 32
solve for “x”
• y is to 10 as 7 is to 2
solve for “y”

8. w 4
35 7

9. 36 x
72 10
Hint: may need to simplify ratio first.

10. r 9
0.5 2.5

11. • A printer can print 12 color pages in 3
minutes. How many color pages can the
printer print in 9 minutes?
• Write a proportion and solve.

12. • One day, the ratio of skiers to
snowboarders on the mountain at a ski
resort was 13:10. The resort sold a total
of 253 lift tickets during the day.
• Find the ratio of snowboarders to all the
skiers and snowboarders.
• Use the ratio to find the number of lift
tickets sold to snowboarders during the
day.

13. • Assignment: P. 165
(#2-30 evens only)
Copy the problems