Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Solve each equation. 1. Multiply. 3.
5. 7.
48
2. 5m 18
3.6
4.
10
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Change each percent to a decimal.
8. 1
0.006
0.01
0.6
73
6. 112
0.73
1.12
Change each fraction to a decimal.
9.
10.
0.5
3

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Vocabulary
ratio scale rate
scale model cross products scale
drawing proportion unit rate percent
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Additional Example 1 Using Ratios
The ratio of the number of bones in a humans
ears to the number of bones in the skull is 311.
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.
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Check It Out! Example 1
The ratio of red marbles to green marbles is 65.
There are 18 red marbles. How many green marbles
are there?
Write a ratio comparing green to red marbles.
Write a proportion. Let x be the number green
marbles.
Since x is divided by 18, multiply both sides by
18.
15 x
There are 15 green marbles.
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Additional Example 2 Finding Unit Rates
Ralf Laue of Germany flipped a pancake 416 times
in 120 seconds to set the world record. Find the
unit rate. Round your answer to the nearest
hundredth.
Write a proportion to find an equivalent ratio
with a second quantity of 1.
3.47 x
Divide on the left side to find x.
The unit rate is approximately 3.47 pancake flips
per second.
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Check It Out! Example 2a
Find the unit rate. Round to the nearest
hundredth if necessary.
Cory earns 52.50 in 7 hours.
Write a proportion to find an equivalent ratio
with a second quantity of 1.
7.50 x
Divide on the left side to find x.
The unit rate is 7.50 per hour.
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Check It Out! Example 2b
Find the unit rate. Round to the nearest
hundredth if necessary.
A machine seals 138 envelopes in 23 minutes.
Write a proportion to find an equivalent ratio
with a second quantity of 1.
6 x
Divide on the left side to find x.
The unit rate is 6 envelopes seals per minute.
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Additional Example 3A Solving Proportions
Solve the proportion.
Use cross products.
3(m) 9(5)
3m 45
Divide both sides by 3.
m 15
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Additional Example 3B Solving Proportions
Solve the proportion.
Use cross products.
6(7) 2(y 3)
42 2y 6
Add 6 to both sides.
Divide both sides by 2.
24 y
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Check It Out! Example 3a
Solve the proportion. Check your answer.
Use cross products.
5(8) 2(y)
40 2y
Divide both sides by 2.
20 y
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Check It Out! Example 3a Continued
Solve the proportion. Check your answer.
Check
Substitute 20 for y.
?
2.5 2.5
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Check It Out! Example 3b
Solve the proportion. Check your answer.
Use cross product.
4(g 3) 5(7)
4g 12 35
Subtract 12 from both sides.
Divide both sides by 4.
g 5.75
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Check It Out! Example 3b Continued
Solve the proportion. Check your answer.
Check
Substitute 5.75 for b.
?
1.75 1.75
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Additional Example 4A Percent Problems
Find 30 of 80.
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the part.
100x 2400
Find the cross product. Since x is multiplied by
100, divide both sides to undo the multiplication.
x 24
30 of 80 is 24.
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Additional Example 4B Percent Problems
230 is what percent of 200?
Method 2 Use an equation.
Write an equation. Let x represent the percent.
230 x ? 200
230 200x
Since x is multiplied by 200, divide both sides
by 200 to undo the multiplication.
1.15 x
The answer is a decimal.
Write the decimal as a percent. This answer is
reasonable 230 is more than 100 of 200.
115 x
230 is 115 of 200.
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Additional Example 4C Percent Problems
20 is 0.4 of what number?
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the whole.
Cross multiply.
2000 0.4x
Since x is multiplied by 0.4, divide both sides
by 0.4.
5000 x
20 is 0.4 of 5000.
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Check It Out! Example 4a
Find 20 of 60.
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the part.
100x 1200
Find the cross product. Since x is multiplied by
100, divide both sides to undo the multiplication.
x 12
20 of 60 is 12.
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Check It Out! Example 4b
48 is 15 of what number?
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the whole.
4800 15x
Find the cross product. Since x is multiplied by
15, divide both sides by 15 to undo the
multiplication.
x 320
48 is 15 of 320.
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Proportions are used to create scale drawings and
scale models. A scale is a ratio between two sets
of measurements, such as 1 in.5 mi. A scale
drawing, or scale model, uses a scale to
represent an object as smaller or larger than the
actual object. A map is an example of a scale
drawing.
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Additional Example 5A Scale Drawings and Scale
Models
A contractor has a blueprint for a house drawn to
the scale 1 in.3 ft.
A wall on the blueprint is 6.5 inches long. How
long is the actual wall?
Write the scale as a fraction.
Let x be the actual length.
Use cross products to solve.
x ? 1 3(6.5)
x 19.5
The actual length is 19.5 feet.
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Additional Example 5B Scale Drawings and Scale
Models
A contractor has a blueprint for a house drawn to
the scale 1 in.3 ft.
A wall in the house is 12 feet long. How long is
the wall on the blueprint?
Write the scale as a fraction.
Let x be the blueprint length.
Use cross products to solve.
x ? 3 1(12)
x 4
The blueprint length is 4 inches.
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Check It Out! Example 5a
The actual distance between North Chicago and
Waukegan is 4 mi. What is the distance between
these two locations on the map?
Write the scale as a fraction.
Let x be the map distance.
18x 4
Use cross products to solve.
x 0.2
The distance on the map is about 0.2 in.
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Check It Out! Example 5b
A scale model of a human heart is 16 ft long. The
scale is 321 How many inches long is the actual
heart that the model represents?
Write the scale as a fraction.
Let x be the actual distance.
Use cross products to solve.
32x 16
x 0.5
The actual heart is 0.5 feet or 6 inches.
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Lesson Quiz Part l
1. In a school, the ratio of boys to girls is
43. There are 216 boys. How many girls are
there?
162
Find each unit rate. Round to the nearest
hundredth if necessary.
2. Nuts cost 10.75 for 3 pounds.
3.58/lb
3. Sue washes 25 cars in 5 hours.
5 cars/h
Solve each proportion.
4.
5.
16
6
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Lesson Quiz Part ll
6. Find 20 of 80.
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7. What percent of 160 is 20?
12.5
114.3
8. 35 of what number is 40?
9. A scale model of a car is 9 in. long. The
scale is 118. How many inches long is the actual
car the model represents?
162 in.