Week 16, Day Four
HW # 57 - p. 234-235 # 6-30 even and 31, 32, 33
Extra Credit: Keyword: MT8CA Health
Read the article, provide a 3 sentence summary, answer the
math questions at the bottom of the page.
Warm up
Find two ratios that are equivalent to
each given ratio.
Possible answers:
2. 10
1. 3 6 , 9
12
5 10 15
5 , 20
6 24
3. 45 3 , 90
4. 8 16 , 24
30 2 60
9 18 27
Put your “duck” warm ups in the center of the table so that I can
collect them.
Warm Up Response
24
Homework Check
p. 230-231 # 17-29 odd
17) 14 points/game
19) 16 beats/measure
21) ~ 50 beats/minute
23) ~ 4 apples/lb
25) $3.75; $ 4.50; 2/3 lb
27) ~ $ 110/day
29)The student divided the number of shirts by the
cost instead of the cost by the number of shirts
• 5-3 Proportions
• Worksheet
• Cereal- MARS task (list as CW and get a
signature)
Vocabulary
proportion
cross products
An equation that states that two ratios are
equivalent is called a proportion. For example, the
equation, or proportion, 2 = 4 states that the ratios
3
6
2
4
3 and 6 are equivalent. Ratios that are equivalent
are said to be proportional, or in proportion.
a
c
, the products a ∙ d and b ∙ c
b = d
are called cross products.
In the proportion
a
c
b = d
a∙ d = b ∙ c
Proportion
Cross Products
One way to find whether two ratios are equivalent is to
find their cross products.
Additional Example 1A: Using Cross Products to
Identify Proportions
Tell whether the ratios are proportional.
? 4
6 =
15 10
6 =? 4
15 10
Find the cross products.
?
6  10 = 4  15
60 = 60
Since the cross products are equal, the ratios are
proportional.
Additional Example 1B: Using Cross Products to
Identify Proportions
A mixture of fuel for a certain small engine
should be 4 parts gasoline to 1 part oil. If
you combine 5 quarts of oil with 15 quarts
of gasoline, will the mixture be correct?
? 15 quarts gasoline
4 parts gasoline =
1 part oil
5 quarts oil
4 =? 15
1
5
?
Set up equal
ratios.
Find the cross
products.
4  5 = 1  15
20  15
The ratios are not equal. The mixture will not be correct.
Check It Out! Example 1A
Tell whether the ratios are proportional.
?
5 =
10
5 =?
10
5

?
2
4
2
4
4=2
Find the cross products.

10
20 = 20
Since the cross products are equal, the ratios are
proportional.
Check It Out! Example 1B
A mixture for a certain brand of tea should be
3 parts tea to 1 part sugar. If you combine 4
tablespoons of sugar with 12 tablespoons of
tea, will the mixture be correct?
? 12 tablespoons tea
3 parts tea =
1 part sugar 4 tablespoons sugar
3 =? 12
1
4
3
Set up equal
ratios.
Find the cross
products.
?
4 = 1  12
12 = 12

The ratios are equal. The mixture will be correct.
Additional Example 2: Using Properties of Equality
to Solve Proportions
The ratio of the length of the actual height of a
person to the length of the shadow cast by the
person is 1:3. At the same time, a lighthouse casts a
shadow that is 36 meters long. What should the
length of its shadow be?
height of person
length of shadow
1= x
3 36
1
3
Write a ratio comparing height of
a person to shadow length.
Set up the proportion. Let x
represent the shadow length.
1
x Since x is divided by 36, multiply
= (36)
3
36 both sides of the equation by 36.
12 = x
The length of the lighthouse’s shadow should be 12 meters.
(36)
Check It Out! Example 2
For most cats, the ratio of the length of their head to
their total body length is 1:5. If a cat is 20 inches in
length, what should the total length of their head be?
head length
total length
1
5
1= x
5 20
(20)
1
x
= (20)
5
20
Write a ratio comparing head
length to total length.
Set up the proportion. Let x
represent the length of the cat's
head.
Since x is divided by 20, multiply
both sides of the equation by 20.
4=x
The length of the cat's head should be 4 inches.
Additional Example 3: Using Cross Products to
Solve Proportions
Allyson weighs 55 pounds and sits on a seesaw 4 feet
away from it center. If Marco sits on the seesaw 5 feet
away from the center and the seesaw is balanced, how
much does Marco weigh?
Set up a proportion using the information. Let w represent
Marco’s weight.
weight 1 = weight 2
length 2
length 1
55 = w
5
4
55 ∙ 4 = 5w
Find the cross products.
220
= 5w
5
5
44 = w
Divide both sides by 5.
Simplify.
Marco weighs 44 lb.
Check It Out! Example 3
Austin weighs 32 pounds and sits on a seesaw 6 feet away
from it center. If Kaylee sits on the seesaw 4 feet away
from the center and the seesaw is balanced, how much
does Kaylee weigh?
Set up a proportion using the information. Let w represent
Kaylee’s weight.
weight 1 = weight 2
length 2
length 1
32 = w
4
6
32 ∙ 6 = 4w
Find the cross products.
192
4w
=
4
4
48 = w
Divide both sides by 4.
Simplify.
Kaylee weighs 48 lbs.
Additional Example 4: Business Application
Nate has 225 envelopes to prepare for mailing. He takes
30 minutes to prepare 45 envelopes. If he continues at
the same rate, how many more minutes until he has
completed the job?
Let x represent the number of minutes it takes to complete the
job.
30 = x
Set up the proportion.
45
225
30 ∙ 225 = 45x
Find the cross products.
6750
45x
=
45
45
150 = x
Divide both sides by 45.
Simplify.
It will take 150 minutes to complete the job. Nate has
already spent 30 minutes, so it will take him 150 – 30 =
120 more minutes to finish the job.
Check It Out! Example 4
Nemo has to make 160 muffins for the bake sale. He
takes 21 minutes to make 24 muffins. If he continues at
the same rate, how many more minutes until he has
completed the job?
Let m represent the number of minutes it takes to complete
the job.
21 = m
Set up the proportion.
24
160
21 ∙ 160 = 24m
3360
24m
=
24
24
140 = m
Find the cross products.
Divide both sides by 24.
Simplify.
It will take 140 minutes to complete the job. Nemo has
already spent 21 minutes, so it will take him 140 – 21 =
119 more minutes to finish the job.
Lesson Quiz: Part I
Tell whether the ratios are proportional.
? 16 yes
1. 48 =
42
14
? 3
2. 40 =
no
15
4
3. The ratio of violins to violas in an orchestra is 5:3.
t The orchestra has 9 viola players. How many
t violinists are in the orchestra?
15
4. Two weights are balanced on a fulcrum. If a 6 lb
weight is positioned 1.5 ft from the fulcrum, at
what distance from the fulcrum must an 18 lb
weight be placed to keep the weights balanced?
0.5 ft
Lesson Quiz: Part II
5. An elevator travels 342 feet as it goes from the
lobby of an office building to the top floor. It
takes 7 seconds to travel the first 133 feet. If
the elevator travels at the same rate, how much
longer does it take to reach the top floor?
11 s