Scale Factors

What is a scale factor?

• A ratio that compares the size of an object in a drawing to its actual size.

• The measurement used to determine the weight of an object.

• The time it takes for an object to travel a certain distance.

• The temperature at which an object freezes.

Answer explanation

A scale factor is a ratio that compares the size of an object in a drawing or model to its actual size. It tells you how much smaller or larger the representation is compared to the real object or place. For example, if a scale factor is 1 in = 10 ft, it means that one inch on the drawing is 10 feet of the actual object.

Tags

CCSS.7.G.A.1

Sophia is making a scale drawing of her backyard. The length of the yard on her drawing is 5 inches, while the actual length is 40 feet. What is the scale of Sophia's drawing?

• 1 in = 10 ft

• 1 in = 8 ft

• 1 in = 6 ft

• 1 in = 5 ft

Answer explanation

To find the scale of Sophia's drawing, write the comparison as a fraction with the length on her drawing (5 inches) on top and the actual length of the yard (40 feet) on the bottom. Simplify the fraction by dividing the top and bottom quantities by their greatest common factor (5). The fraction simplifies to 1/8, so 1 inch represents 8 feet, resulting in a scale of 1 in = 8 ft.

Tags

CCSS.7.RP.A.2C

Andrew is making a scale model of a plane. The wingspan of the model plane is 12 inches, and the actual wingspan of the plane is 60 feet. What is the scale of Andrew's model?

• 1 in = 10 ft

• 1 in = 8 ft

• 1 in = 6 ft

• 1 in = 5 ft

Answer explanation

To find the scale of Andrew's model, write the comparison as a fraction with the wingspan of the model plane (12 inches) on top and the actual wingspan of the plane (60 feet) on the bottom. Simplify the fraction by dividing the top and bottom quantities by their greatest common factor (12). The fraction simplifies to 1/5, so 1 inch represents 6 feet, resulting in a scale of 1 in = 5 ft.

Tags

CCSS.7.G.A.1

Selena is creating a scale model of a national park. The width of the model park is 20 centimeters, and the actual width of the park is 60 kilometers. What is the scale of Sophia's model?

• 1 cm = 3 km

• 1 cm = 1 km

• 1 cm = 2 km

• 1 cm = 6 km

Answer explanation

To find the scale of Selena's model, write the comparison as a fraction with the width of the model park (20 centimeters) on top and the actual width of the park (60 kilometers) on the bottom. Simplify the fraction by dividing the top and bottom quantities by their greatest common factor (20). The fraction simplifies to 1/3, so 1 centimeter represents 3 kilometers, resulting in a scale of 1 cm = 3 km.

Tags

CCSS.7.G.A.1

Owen is drawing a map of a city. The distance between two landmarks on the map is 4 inches, and the actual distance between the landmarks is 28 miles. What is the scale of Owen's map?

• 1 in = 12 mi

• 1 in = 5 mi

• 1 in = 7 mi

• 1 in = 24 mi

Answer explanation

To find the scale of Owen's model, write the comparison as a fraction with the distance between the landmarks in the model (4 centimeters) on top and the actual distance between the landmarks (28 miles) on the bottom. Simplify the fraction by dividing the top and bottom quantities by their greatest common factor (4). The fraction simplifies to 1/7, so 1 centimeter represents 7 miles, resulting in a scale of 1 in = 7 mi.

Tags

CCSS.7.RP.A.2C