Pre-Algebra 7-7 Scale Drawings HW: Page 370 #1-6 and #21-26

Pre-Algebra

7-7 Scale Drawings

HW: Page 370 #1-6 and #21-26

Pre-Algebra

7-7 Scale Drawings

Pre-Algebra Homework

Page 374

#7-12 & #30-34

(Spiral Review)

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)

Pre-Algebra

7-7 Scale Drawings7-7 Scale Drawings

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

7-7 Scale Drawings

Warm UpEvaluate the following for x = 16.

1. 3x 2. x

Evaluate the following for x = .

3. 10x 4. x

48 12

4

Pre-Algebra

7-7 Scale Drawings

34

25

14

110

Pre-Algebra

7-7 Scale Drawings

Problem of the Day

An isosceles triangle with a base length of 6 cm and side lengths of 5 cm is dilated by a scale factor of 3. What is the area of the image?

108 cm2

Pre-Algebra

7-7 Scale Drawings

Today’s Learning Goal Assignment

Learn to make comparisons between and find dimensions of scale drawings and actual objects.

Pre-Algebra

7-7 Scale Drawings

Vocabulary

scale drawingscalereductionenlargement

Pre-Algebra

7-7 Scale Drawings

A scale drawing is a two-dimensional drawing that accurately represents an object. The scale drawing is mathematically similar to the object.

A scale gives the ratio of the dimensions in the drawing to the dimensions of the object. All dimensions are reduced or enlarged using the same scale. Scales can use the same units or different units.

Pre-Algebra

7-7 Scale Drawings

The scale a:b is read “a to b.” For example, the scale 1 cm:3 ft is read “one centimeter to three feet.”

Reading Math

Scale Interpretation

1:20 1 unit on the drawing is 20 units.

1 cm: 1 m 1 cm on the drawing is 1 m.

in. = 1 ft in. on the drawing is 1 ft.1 4

1 4

Pre-Algebra

7-7 Scale Drawings

A. The length of an object on a scale drawing is 2 cm, and its actual length is 8 m. The scale is 1 cm: __ m. What is the scale?

Additional Example 1A: Using Proportions to Find Unknown Scales or Lengths

1 cmx m = 2 cm

8 m Set up proportion using scale length .actual length

1 8 = x 2 Find the cross products.

8 = 2x

Solve the proportion.

The scale is 1 cm:4 m.

4 = x

Pre-Algebra

7-7 Scale Drawings

A. The length of an object on a scale drawing is 4 cm, and its actual length is 12 m. The scale is 1 cm: __ m. What is the scale?

Try This: Example 1A

1 cmx m = 4 cm

12 m Set up proportion using scale length .actual length

1 12 = x 4 Find the cross products.

12 = 4x


The scale is 1 cm:3 m.

3 = x

Pre-Algebra

7-7 Scale Drawings

B. The length of an object on a scale drawing is 1.5 inches. The scale is 1 in:6 ft. What is the actual length of the object?

Additional Example 1B: Using Proportions to Find Unknown Scales or Lengths

1 in.6 ft = 1.5 in.

x ft Set up proportion using scale length .actual length

1 x = 6 1.5 Find the cross products.

x = 9 Solve the proportion.

The actual length is 9 ft.

Pre-Algebra

7-7 Scale Drawings

B. The length of an object on a scale drawing is 2 inches. The scale is 1 in:4 ft. What is the actual length of the object?

Try This: Example 1B

1 in.4 ft = 2 in.

x ft Set up proportion using scale length .actual length

1 x = 4 2 Find the cross products.

x = 8 Solve the proportion.

The actual length is 8 ft.

Pre-Algebra

7-7 Scale Drawings

A scale drawing that is smaller than the actual object is called a reduction. A scale drawing can also be larger than the object. In this case, the drawing is referred to as an enlargement.

Pre-Algebra

7-7 Scale Drawings

Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length?

Additional Example 2: Life Sciences Application

scale length actual length

1000 x = 1 8 Find the cross products.

x = 0.008

The actual length of the amoeba is 0.008 mm.

1000 1 = 8 mm

x mm


Pre-Algebra

7-7 Scale Drawings

Under a 10,000:1 microscope view, a fiber appears to have length of 1mm. What is its actual length?

Try This: Example 2


10,000 x = 1 1 Find the cross products.

x = 0.0001

The actual length of the fiber is 0.0001 mm.

10,000 1 = 1 mm

x mm


Pre-Algebra

7-7 Scale Drawings

A drawing that uses the scale in. = 1 ft

is said to be in in. scale. Similarly, a

drawing that uses the scale in. = 1 ft is

in in. scale.

1 4

1 4

1 2

1 2

Pre-Algebra

7-7 Scale Drawings

Additional Example 3A: Using Scales and Scale Drawings to Find Heights


0.25 x = 1 4 Find the cross products.

x = 16

The wall is 16 ft tall.

0.25 in. 1 ft = 4 in.

x ft.

A. If a wall in a in. scale drawing is 4 in. tall, how tall is the actual wall?

14

Length ratios are equal.


Pre-Algebra

7-7 Scale Drawings

B. How tall is the wall if a in. scale is used?

Additional Example 3B: Using Scales and Scale Drawings to Find Heights

12


0.5 x = 1 4 Find the cross products.

x = 8

The wall is 8 ft tall.

0.5 in. 1 ft = 4 in.

x ft.Length ratios are equal.


Pre-Algebra

7-7 Scale Drawings

Try This: Example 3A


0.25 x = 1 0.5 Find the cross products.

x = 2

The wall is 2 ft thick.

0.25 in. 1 ft = 0.5 in.



A. If a wall in a in. scale drawing is 0.5 in. thick, how thick is the actual wall?

14

Pre-Algebra

7-7 Scale Drawings

B. How thick is the wall if a in. scale is used?

Try This: Example 3A Continued

12


0.5 x = 1 0.5 Find the cross products.

x = 1

The wall is 1 ft thick.

0.5 in. 1 ft = 0.5 in.



Pre-Algebra

7-7 Scale Drawings

1. What is the scale of a drawing in which a 9 ft wall is 6 cm long?

2. Using a in. = 1 ft scale, how long would a

drawing of a 22 ft car be?

3. The height of a person on a scale drawing is

4.5 in. The scale is 1:16. What is the actual height

of the person?

The scale of a map is 1 in. = 21 mi. Find each length on the map.

4. 147 mi 5. 5.25 mi

Lesson Quiz

5.5 in.

1 cm = 1.5 ft.

72 in.

7 in. 0.25 in.

14

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Pre-Algebra 7-7 Scale Drawings HW: Page 370 #1-6 and #21-26