Ch. 7 Learning Goal: Ratios & Proportions
• Learn to find equivalent ratios to create proportions (7-1)
• Learn to work with rates and ratios (7-2)
• Learn to use one or more conversion factors to solve rate
problems (7-3)
• Learn to solve proportions (7-4)
• Learn to identify and create dilations of plane figures (7-5)
• Learn to determine whether figures are similar, to use scale
factors, and to find missing dimensions similar figures (7-6)
• Learn to make comparisons between and find dimensions of
scale drawings and actual objects (7-7)
• Learn to make comparisons between and find dimensions of
scale models and actual objects (7-8)
• Learn to make scale models of solid figures (7-9)
Page 353 #8-14 Answers
7-4 Solving Proportions
Pre-Algebra Homework
Page 358
#15-28
Mid-Chapter 7 Chop Chop Quiz Tomorrow!
Pre-Algebra
7-4
7-4 Solving
SolvingProportions
Proportions
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
7-4 Solving Proportions
Warm Up
Find two ratios that are equivalent to
each given ratio.
Possible answers:
2. 10
1. 3 6 , 9
12
5 10 15
3. 45 3 , 90
30 2 60
Pre-Algebra
4.
5 , 20
6 24
8 16 , 24
9 18 27
7-4 Solving Proportions
Problem of the Day
Replace each • with a digit from 1 to 7 to
write a proportion. Use each digit once. The
digits 2 and 3 are already shown.
23 = ••
••
•
Pre-Algebra
23 = 14
Possible answer:
56
7
7-4 Solving Proportions
Today’s Learning Goal Assignment
Learn to
solve
proportions.
Pre-Algebra
7-4 Solving Proportions
Vocabulary
cross product
Pre-Algebra
7-4 Solving Proportions
Unequal masses will not balance on a fulcrum
if they are an equal distance from it; one side
will go up and the other side will go down.
Unequal masses will balance when the
following proportions is true:
mass 1 =
length 2
mass 2
length 1
Mass 2
Mass 1
Length 1
Length 2
Fulcrum
Pre-Algebra
7-4 Solving Proportions
One way to find whether ratios, such as those
above, are equal is to find a common denominator.
The ratios are equal if their numerators are equal
after the fractions have been rewritten with a
common denominator.
6 = 72
8
96
9 = 72
12
96
6 = 9
8
12
Pre-Algebra
7-4 Solving Proportions
Pre-Algebra
7-4 Solving Proportions
Helpful Hint
The cross product represents the numerator of
the fraction when a common denominator is
found by multiplying the denominators.
Pre-Algebra
7-4 Solving Proportions
Additional Example 1A: Using Cross Products to
Identify Proportions
Tell whether the ratios are proportional.
? 4
6
=
A.
15 10
6
15
4
10
60
60
Find cross products.
60 = 60
Since the cross products are equal, the ratios are
proportional.
Pre-Algebra
7-4 Solving Proportions
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 Set up ratios.
4 parts gasoline =
1 part oil
5 quarts oil
4 • 5 = 20
1 • 15 = 15
Find the cross
products.
20 ≠ 15
The ratios are not equal. The mixture will not be
correct.
Pre-Algebra
7-4 Solving Proportions
Try This: Example 1A
Tell whether the ratios are proportional.
A.
? 2
5 =
10
4
5
10
2
4
20
20
Find cross products.
20 = 20
Since the cross products are equal, the ratios are
proportional.
Pre-Algebra
7-4 Solving Proportions
Try This: 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 • 4 = 12
1 • 12 = 12
Set up ratios.
Find the cross
products.
12 = 12
The ratios are equal. The mixture will be correct.
Pre-Algebra
7-4 Solving Proportions
When you do not know one of the four
numbers in a proportion, set the cross
products equal to each other and solve.
Pre-Algebra
7-4 Solving Proportions
Additional Example 2: Solving Proportions
Solve the proportion.
p =5
12 6
6p = 12 • 5 Find the cross products.
6p = 60
p = 10
Pre-Algebra
Solve.
10 = 5
6
12
; the proportion checks.
7-4 Solving Proportions
Try This: Example 2
Solve the proportion.
14 = 2
3
g
14 • 3 = 2g
42 = 2g
21 = g
Pre-Algebra
Find the cross products.
Solve.
14 = 2
21
3
; the proportion checks.
7-4 Solving Proportions
Additional Example 3: Physical Science Application
Allyson weighs 55 lbs and sits on a seesaw 4
ft away from its center. If Marco sits 5 ft
away from the center and the seesaw is
balanced, how much does Marco weigh?
mass 2
mass 1
= length 1 Set up the proportion.
length 2
Let x represent Marco’s
55 = x
weight.
5
4
Find the cross products.
55 • 4 = 5x
220 = 5x
Multiply.
220 = 5x
5
5
44 = x
Solve. Divide both
sides by 5.
Pre-Algebra
Marco weighs 44 lb.
7-4 Solving Proportions
Try This: Example 3
Robert weighs 90 lbs and sits on a seesaw 5 ft
away from its center. If Sharon sits 6 ft away
from the center and the seesaw is balanced,
how much does Sharon weigh?
mass 2
mass 1
= length 1 Set up the proportion.
length 2
Let x represent Sharon’s
90 = x
weight.
6
5
Find the cross products.
90 • 5 = 6x
450 = 6x
Multiply.
450 = 6x
6
6
75 = x
Solve. Divide both
sides by 5.
Pre-Algebra
Sharon weighs 75 lb.
7-4 Solving Proportions
Lesson Quiz
Tell whether each pair of ratios is proportional.
? 16 yes
1. 48 =
42
14
? 3
2. 20 =
no
15
4
Solve each proportion.
3. n = 45
12
18
n = 30
4. 6 = n
9
24
n = 16
5. Two weights are balanced on a fulcrum. If a 6lb
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
Pre-Algebra