Ratios and Proportions

CHAPTER 8

Ratios 8.1

• Ratio- Uses division to compare two numbers.

• Equivalent ratios- Two ratios are equivalent ratios when they have the same value.

Writing a RatioWORDS

• Wins to losses

• wins losses

• Wins:Losses

ALGEBRA A to B, where b is nonzero

A B, where B is nonzero

A:B where B is nonzero

NUMBERS

18 to 13

18 13

18:13

Writing Ratios in Simplest Form

• A water ride lasts 2 min. Suppose you wait in line for 1 ½ hours to ride the water ride. Follow the steps below to find the ratio of time spent in line to time spent on the water ride.

• Write hours as minutes so that the units are the same.

1h+1/2h=60min+30min =90 min• Write the ratio of time

spent in line to time spent on the ride.

Time in line= 90 Time on ride 2 = 45 1

Comparing RatiosNicole and Taylor

compared their CD collections.

To determine who has a greater ratio of rock CDs to pop CDs, write the ratios.

Rock

Pop Hip-Hop

Nicole

9 24 16

Taylor

42 70 25

Taylor:Rock = 42Pop 70

=0.6

Nicole: Rock =9 Pop 24 =0.375

Rates 8.2

• Rate- is a ratio of two quantities measured in different units.

• Unit Rate- is a rate that has a denominator of 1 unit rates below are equivalent.

Finding a Unit Rate

• During Spring, a sunflower can grow 6 in. in 12 hrs. What is the growth rate of Sunflower in in. per hour?

• 6in.= 6in./12 12h 12h/12Divide numerator and

denominator by 12 = 0.5 in. simplify 1 hAnswer: The growth

rate of Sunflower is about 0.5 in. per hour.

Finding an average speed• An ice skater took 2

min. 30 sec. to complete a 1500 meter race. What was the skater’s average speed?

- Divide numerator and denominator by 150.

- Simplify

• Rewrite the time so that the units are the same.

2min+30sec=120sec+30sec=150secFind the average speed1500m=1500m/150150sec 150sec/150 =10m 1secAnswer: the ice skater’s

average speed was 10m per sec.

Writing and solving proportions 8.4

•Proportion- is an equation that states that two ratios are equivalent.

Proportions

• Numbers: 3 = 6 The Proportion is read

5 10 “3 is to 5 as 6 is to 10.”

• Algebra: a = c Where b and d are b d nonzero

numbers.

Solving proportions

• Solve: 6 = x Write original proportion 10 25 25x 6 = 25x x Multiply each side by 25 10 25 150 = X Simplify 10 15=x Simplify Fraction Answer: The solution is 15.

Solving proportions Using Cross Products

8.5

• Cross Products- In a proportion a/b = c/d where b = 0, the cross products are ad and bc

Cross products property

• Words: The cross products of a proportion are equal

• Numbers: 3 = 15 4 x 15 = 60

4 20 3 x 20 = 60

• Algebra: If a/b = c/d where b and d are nonzero numbers, then ad = bc.

Solving a Proportion Using Cross Products

• Use the cross products property to solve:

4/8 = 5/d.

1. Write original proportion. 2/1 = 6/d

2. Cross products property. 2d = 1 x 6

3. Divide each side by 2. 2d/2 = 1 x 6/2

4. Simplify d = 3

Scale Drawings and Models 8.6

• Scale drawing- a diagram of an object in which the dimensions are in proportion to the actual dimensions of the object.

• Scale- On a scale drawing tells how the drawing’s are related.

• Scale model- a model of an object in which the dimensions are in proportion to the actual dimensions of the object.

Finding a Dimension on a Scale Model

A scale model of the White House appears Japan. The scale used is 1:2. The height h of the main building of the White House is 76ft. Find the height on the Model.

1 = h scale model

2 76 building

1 x 76 = 2 x h Cross products property.

38 = h divide each side by 2.

Vocabulary•Ratio A. Uses division t

o compare two numbers.

B. Two ratios are equivalent ratios when they have the same value.

Vocabulary• Equivalent

ratiosA. Uses division t

o compare two numbers.

B. Two ratios are equivalent ratios when they have the same value.

Write the ratio of the first number to the second number in three ways.

1. 1,1

1:1 1/1 1 to 1

Vocabulary•Rate A. Rate that has

a denominator of 1 unit.

B. Ratio of two quantities measured in different units.

Vocabulary•Unit rate A. A rate that has

a denominator of one unit.

B. Is a ratio of two quantities measured in different units.

Match the rate with the equivalent unit rate.

• 18ft 3 sec

A. 2.2 ft/sec B. 4.5 ft/sec C. 6 ft/sec

Vocabulary

• Proportion A. Equation that states that two rates are equivalent.

B. Equation that states that two ratios are equivalent.

Use equivalent ratios to solve the proportion

• 20 = x 10 2

A. -2 B. 4 C.2 D. -4

Vocabulary

• Cross products A. The cross products of a proportion are equal.

B. In a proportion a/b = c/d where b non equal to 0 and d non equal to 0, the cross products are ad and bc

Use the cross products property to solve the proportion.

• 8 = 2 4 n

A. -1 B. 2 C. 1 D. -2

Vocabulary

• Scale drawing A. Diagram of an object in which the dimensions are in proportion to the actual dimensions of the object

B. Tells how the drawing’s dimensions are related.

Vocabulary

• Scale A. Tells how the drawing’s dimensions and the actual dimensions are related.

B. Model of an object in which the dimensions are in proportion to the actual dimensions of the object.

Vocabulary

• Scale model A. Model of an object in which the dimensions are in proportion to the actual dimensions of the object

B. Diagram of an object in which the dimensions are in proportion to the actual dimensions of the object

The scale on a map is 1cm: 25mi. Find the actual distance in miles for the given length on the map.

• 10cm

A. 225miles B. 250miles C. 275miles