ch. 7 learning goal: ratios & proportions
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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
Pre-Algebra
7-4 Solving Proportions
Pre-Algebra Homework
Page 358
#15-28Mid-Chapter 7 Chop Chop Quiz Tomorrow!
Pre-Algebra
7-4 Solving Proportions7-4 Solving Proportions
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
7-4 Solving Proportions
Warm UpFind two ratios that are equivalent to each given ratio.
Pre-Algebra
7-4 Solving Proportions
35
1.
4530
3. 9060
32
,
1012
2. 2024
56
,
89
4. 2427
1618
,
915
610
,Possible answers:
Pre-Algebra
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
••= 14
723
56=Possible answer:
Pre-Algebra
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 2length 1
mass 1length 2
=
Mass 1
Mass 2
Fulcrum
Length 1 Length 2
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.
7296
68
= 7296
912
=
912
68
=
Pre-Algebra
7-4 Solving Proportions
Pre-Algebra
7-4 Solving Proportions
The cross product represents the numerator of the fraction when a common denominator is found by multiplying the denominators.
Helpful Hint
Pre-Algebra
7-4 Solving Proportions
Tell whether the ratios are proportional.
410
615
A.
Since the cross products are equal, the ratios are proportional.
60
=?
Additional Example 1A: Using Cross Products to Identify Proportions
60 = 60
Find cross products.60410
615
Pre-Algebra
7-4 Solving 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?
4 parts gasoline1 part oil
=? 15 quarts gasoline5 quarts oil
4 • 5 = 20 1 • 15 = 15
20 ≠ 15
The ratios are not equal. The mixture will not be correct.
Set up ratios.
Find the cross products.
Additional Example 1B: Using Cross Products to Identify Proportions
Pre-Algebra
7-4 Solving Proportions
Tell whether the ratios are proportional.
Try This: Example 1A
Since the cross products are equal, the ratios are proportional.
20
20 = 20
Find cross products.2024
510
24
510
A. =?
Pre-Algebra
7-4 Solving Proportions
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?
Try This: Example 1B
3 parts tea 1 part sugar
=? 12 tablespoons tea4 tablespoons sugar
3 • 4 = 12 1 • 12 = 12
12 = 12
The ratios are equal. The mixture will be correct.
Set up ratios.
Find the cross products.
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
Solve the proportion.
6p = 12 • 5
p = 10
6p = 60
Find the cross products.
Solve.
Additional Example 2: Solving Proportions
56
p12
=
; the proportion checks.56
1012
=
Pre-Algebra
7-4 Solving Proportions
Solve the proportion.
14 • 3 = 2g
21 = g
42 = 2g
Find the cross products.
Solve.
Try This: Example 2
23
14g
=
; the proportion checks.23
1421
=
Pre-Algebra
7-4 Solving Proportions
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?
5x5
2205
=
44 = x
Set up the proportion.
Let x represent Marco’s weight.
Find the cross products.
Multiply.
Solve. Divide both sides by 5.
Marco weighs 44 lb.
Additional Example 3: Physical Science Application
220 = 5x
55 • 4 = 5x
x4
555
=
mass 1length 2
= mass 2length 1
Pre-Algebra
7-4 Solving Proportions
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?
Try This: Example 3
6x6
4506
=
75 = x
Set up the proportion.
Let x represent Sharon’s weight.
Find the cross products.
Multiply.
Solve. Divide both sides by 5.
Sharon weighs 75 lb.
450 = 6x
90 • 5 = 6x
x5
906
=
mass 1length 2
= mass 2length 1
Pre-Algebra
7-4 Solving Proportions
Lesson Quiz
Tell whether each pair of ratios is proportional.
4842 =? 16
141. 20
15 =? 34
2.
Solve each proportion.
3. 4.
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?
yes no
n = 30 n = 16
0.5 ft
4518
n12 = n
2469 =
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