1. Make-Up Tests?
K. Academy Topics
Warm-Up: (0 Questions)
Ratios/Rates/Unit Rates
Measurement Ratios
Class Work

2. 1. Ratio Word Problems
2. Rate Problems .5
3. Rates & Proportional Relationships
Topics are due by December 20 for online and Alt.Khan.
**Waaaaay too many people have a grade
of zero for their homework grade
(Khan), which is 20% of your overall
grade.

3. A
fraction is a 'part over the whole' comparison of
one number. Remember the root comes from the
Latin "to break up". We are taking one number and
breaking it up.
A ratio is the comparison of two different
numbers. Therefore, we must solve ratio problems
differently.

4. Class Notes Section of Notebook. please

5. A Ratio is a comparison of two numbers by division. Ratios can
be expressed by: 4:3, or 4 to 3, or 4/3.
A Proportion is an equation that two ratios are equal. To
determine if ratios are equal, cross-multiply and check for
equality. 2/5 and 6/15 are proportional ratios.
A Rate is the comparison (ratio) of two different units of
measure. Ex: miles per hour, gallons an hour, dollars a pound
We have used the Percent Proportion to solve percent
problems, but there are other problems which do not involve
percents.

6. Example 1: Ben runs 4 miles in 45 minutes. If he only has 30
minutes, how far can he run?
Set up a proportion and solve: 4 (miles) = x (miles)
45 (min.) 30 (min.)
Example 2: Jill can jump rope 420 times in 2.5 minutes. At this
rate, how many can she do in 30 minutes?
Set up a proportion and solve: 402(jumps) = x (jumps)
2.5 (min.)
30 (min.)

7. Proportions and Similar Figures.
You can use proportions to find dimensions of
objects that are difficult to measure directly…
In the Figure below,
ABC ~ (is similar)
C
E
18 cm
21 cm
A
15 cm
B
Set up the proportion:
15 = 21
10
x
x
D
10 cm
DFE. Find DE.
F

8. Example 1: Writing Ratios in Simplest Form
Write the ratio 15 bikes to 9 skateboards in simplest
form.
bikes
= 15
skateboards
9
15 ÷ 3
= 5
=
9÷3
3
Write the ratio
as a fraction.
Simplify.
The ratio of bikes to skateboards is 5 , 5:3, or 5 to 3.
3

9. Example 1: Using Ratios
The ratio of the number of bones in a human’s ears to the
number of bones in the skull is 3:11. There are 22 bones in
the skull. How many bones are in the ears?
Write a ratio comparing bones in
ears to bones in skull.
Write a proportion. Let x be the
number of bones in ears.
Since x is divided by 22, multiply
both sides of the equation by
22.
There are 6 bones in the ears.

10. The ratio of games lost to games won for a baseball team
is 2:3. The team has won 18 games. How many games did
the team lose?
Write a ratio comparing games lost to games won.
Write a proportion. Let x be the number of games lost.
Since x is divided by 18, multiply
both sides of the equation by 18.
The team lost 12 games.

11. The ratio of games lost to games won for a baseball team
is 2:3. The team has played 45 games. How many games
did the team lose?
Write a ratio comparing games lost to total games
Write a proportion. Let x be the number of games lost.

13. Rate: 90 miles
3 hours
Read as “90 miles
per 3 hours.”