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Math Coach Amy
Amy Ferguson Moncure

7th Grade Math · Unit 6

Scale
Drawings

A scale drawing multiplies every actual length by the same scale factor. A factor less than 1 shrinks the drawing. A factor greater than 1 enlarges it.

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Key Ideas Easy Medium Hard
What to Remember

Drawing and actual

Drawing length = scale factor × actual length.

A scale factor less than 1 is a reduction. A scale factor greater than 1 is an enlargement.

From actual to drawing

When you know the actual length, multiply by the scale factor.

From drawing to actual

When you know the drawing length, divide by the scale factor.

Keep the unit

The drawing and the actual object use the same unit in the answer.

A tenth in the length is still an exact value. Do not round it.

Level 1

Easy

The scale factor is 2, 3, 4, one half, or one fourth.

Example
The scale factor is 2. The actual length is 5 cm. Find the drawing length.

scale factor = 21

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 2 × 5

drawing = 10

Answer: 10 cm

1
The scale factor is 2. The drawing length is 6 in. Find the actual length.
Show Answer

scale factor = 21

drawing = scale factor × actual

drawing = scale factor × actual

6 = 2 × actual

Divide by the scale factor.

actual = 3

Answer: 3 in

2
The scale factor is 3. The actual length is 4 ft. Find the drawing length.
Show Answer

scale factor = 31

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 3 × 4

drawing = 12

Answer: 12 ft

3
The scale factor is 4. The actual length is 3 m. Find the drawing length.
Show Answer

scale factor = 41

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 4 × 3

drawing = 12

Answer: 12 m

4
The scale factor is 12. The actual length is 10 cm. Find the drawing length.
Show Answer

scale factor = 12

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 12 × 10

drawing = 5

Answer: 5 cm

5
The scale factor is 12. The drawing length is 4 in. Find the actual length.
Show Answer

scale factor = 12

drawing = scale factor × actual

drawing = scale factor × actual

4 = 12 × actual

Divide by the scale factor.

actual = 8

Answer: 8 in

6
The scale factor is 14. The actual length is 12 ft. Find the drawing length.
Show Answer

scale factor = 14

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 14 × 12

drawing = 3

Answer: 3 ft

7
The scale factor is 14. The drawing length is 2 m. Find the actual length.
Show Answer

scale factor = 14

drawing = scale factor × actual

drawing = scale factor × actual

2 = 14 × actual

Divide by the scale factor.

actual = 8

Answer: 8 m

8
The scale factor is 3. The drawing length is 9 cm. Find the actual length.
Show Answer

scale factor = 31

drawing = scale factor × actual

drawing = scale factor × actual

9 = 3 × actual

Divide by the scale factor.

actual = 3

Answer: 3 cm

9
The scale factor is 4. The drawing length is 8 in. Find the actual length.
Show Answer

scale factor = 41

drawing = scale factor × actual

drawing = scale factor × actual

8 = 4 × actual

Divide by the scale factor.

actual = 2

Answer: 2 in

10
The scale factor is 2. The actual length is 7 ft. Find the drawing length.
Show Answer

scale factor = 21

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 2 × 7

drawing = 14

Answer: 14 ft

Level 2

Medium

The denominator of the scale factor is 3, 5, 6, 8, 10, or 12.

Example
The scale factor is 13. The actual length is 15 cm. Find the drawing length.

scale factor = 13

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 13 × 15

drawing = 5

Answer: 5 cm

1
The scale factor is 23. The actual length is 9 in. Find the drawing length.
Show Answer

scale factor = 23

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 23 × 9

drawing = 6

Answer: 6 in

2
The scale factor is 15. The actual length is 20 ft. Find the drawing length.
Show Answer

scale factor = 15

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 15 × 20

drawing = 4

Answer: 4 ft

3
The scale factor is 35. The drawing length is 9 m. Find the actual length.
Show Answer

scale factor = 35

drawing = scale factor × actual

drawing = scale factor × actual

9 = 35 × actual

Divide by the scale factor.

actual = 15

Answer: 15 m

4
The scale factor is 16. The actual length is 18 cm. Find the drawing length.
Show Answer

scale factor = 16

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 16 × 18

drawing = 3

Answer: 3 cm

5
The scale factor is 56. The actual length is 12 in. Find the drawing length.
Show Answer

scale factor = 56

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 56 × 12

drawing = 10

Answer: 10 in

6
The scale factor is 18. The drawing length is 2 ft. Find the actual length.
Show Answer

scale factor = 18

drawing = scale factor × actual

drawing = scale factor × actual

2 = 18 × actual

Divide by the scale factor.

actual = 16

Answer: 16 ft

7
The scale factor is 38. The actual length is 16 m. Find the drawing length.
Show Answer

scale factor = 38

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 38 × 16

drawing = 6

Answer: 6 m

8
The scale factor is 110. The actual length is 30 cm. Find the drawing length.
Show Answer

scale factor = 110

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 110 × 30

drawing = 3

Answer: 3 cm

9
The scale factor is 310. The drawing length is 6 in. Find the actual length.
Show Answer

scale factor = 310

drawing = scale factor × actual

drawing = scale factor × actual

6 = 310 × actual

Divide by the scale factor.

actual = 20

Answer: 20 in

10
The scale factor is 512. The actual length is 24 ft. Find the drawing length.
Show Answer

scale factor = 512

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 512 × 24

drawing = 10

Answer: 10 ft

Level 3

Hard

A length may be a tenth. The result is still exact.

Example
The scale factor is 2. The actual length is 2.5 cm. Find the drawing length.

scale factor = 21

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 2 × 52

drawing = 5

Answer: 5 cm

1
The scale factor is 4. The actual length is 1.5 in. Find the drawing length.
Show Answer

scale factor = 41

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 4 × 32

drawing = 6

Answer: 6 in

2
The scale factor is 2. The actual length is 3.5 ft. Find the drawing length.
Show Answer

scale factor = 21

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 2 × 72

drawing = 7

Answer: 7 ft

3
The scale factor is 12. The actual length is 5 m. Find the drawing length.
Show Answer

scale factor = 12

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 12 × 5

drawing = 52

Answer: 2.5 m

4
The scale factor is 15. The actual length is 2.5 cm. Find the drawing length.
Show Answer

scale factor = 15

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 15 × 52

drawing = 12

Answer: 0.5 cm

5
The scale factor is 12. The drawing length is 2.5 in. Find the actual length.
Show Answer

scale factor = 12

drawing = scale factor × actual

drawing = scale factor × actual

52 = 12 × actual

Divide by the scale factor.

actual = 5

Answer: 5 in

6
The scale factor is 14. The actual length is 10 ft. Find the drawing length.
Show Answer

scale factor = 14

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 14 × 10

drawing = 52

Answer: 2.5 ft

7
The scale factor is 2. The actual length is 4.5 m. Find the drawing length.
Show Answer

scale factor = 21

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 2 × 92

drawing = 9

Answer: 9 m

8
The scale factor is 23. The actual length is 1.5 cm. Find the drawing length.
Show Answer

scale factor = 23

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 23 × 32

drawing = 1

Answer: 1 cm

9
The scale factor is 25. The actual length is 7.5 in. Find the drawing length.
Show Answer

scale factor = 25

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 25 × 152

drawing = 3

Answer: 3 in

10
The scale factor is 54. The actual length is 6 ft. Find the drawing length.
Show Answer

scale factor = 54

drawing = scale factor × actual

drawing = scale factor × actual

drawing = 54 × 6

drawing = 152

Answer: 7.5 ft

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