2. Warm-Up Questions
1. A student scored 96% on a test with 50 questions. How
many questions were missed?
2. Ramon spent 40% of his savings on new shoes. He has
saved $275. How much were the shoes?
3. In a survey, people were asked to name their favorite sport.
30 said Baseball, 42 football, and 8 soccer. What percent like
baseball best?
4. Minimum wage in the CNMI has increased from $4.60 to
$5.55 in the past two years. What is the percent increase?
5. You are 15 years old and have lived 18% of your life. At
what age will you die?
3. Ratios, Proportions, & Rates
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.
4. Solving Proportions
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.)
5. 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) DFE. Find
DE.
C
E
Set up the
18 cm proportion:
21 cm x
15 = 21
D F 10 x
10 cm
A
B
15 cm
6. Example 1: Writing Ratios in Simplest Form
Write the ratio 15 bikes to 9 skateboards in simplest
form.
bikes = 15 Write the ratio
skateboards 9 as a fraction.
15 ÷ 3
= = 5 Simplify.
9÷3 3
The ratio of bikes to skateboards is 5 , 5:3, or 5 to 3.
3
7. 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.
8. 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.
9. The ratio of left handed to right handed students at
North High is 2:21. North High has an enrollment of
1058 students. How many left handers are at the
school?
10. Solving Rate Problems
A rate is a ratio of two quantities with different units, such as
Rates are usually written as unit rates. A unit rate is a rate with a
second quantity of 1 unit, such as or 17 mi/gal. You can
convert any rate to a unit rate.
13. (1) Mindy has 72 candy bars. If the ratio
of Mars to Snickers is 8:4, Find the
number of each type of candy.
(2) Explain what this ratio tell us.
14. Rate Problems:
Example 1
Cory earns $52.50 in 7 hours. Find the unit rate.
Write a proportion to find an equivalent
ratio with a second quantity of 1.
Divide on the left side to find x.
The unit rate is $7.50.
15. Converting Rates of Different
Units
A cheetah can run at a rate of 60 miles per hour in short
bursts. What is this speed in feet per minute?
Step 1 Convert the speed to feet per hour.
Step 2 Convert the speed to feet per minute.
To convert the first quantity in a
rate, multiply by a conversion
factor with that unit in the first
quantity.
The speed is 5280 feetfeet per hour.
316,800 per minute.
16. Example 2
A cyclist travels 56 miles in 4 hours. What is the cyclist’s speed
in feet per second? Round your answer to the nearest tenth,
and show that your answer is reasonable.
Step 1 Convert the speed to feet per hour.
Change to miles in 1 hour.
To convert the first quantity in a
rate, multiply by a conversion
factor with that unit in the
second quantity.
The speed is 73,920 feet per hour.
17. (1) You have 150 different shirts. The ratio of
blue to black shirts is 20 . How many black
shirts do you have? 30
