Question 1: Calculate the fractional scale factor used to reduce a model of a building from 120 meters to a scaled model of 30 meters.

Answer: 0.25

Question 2: A map shows a park that measures 8 km across. The map's scale uses a reduction factor of \( \frac{1}{4} \). What is the actual distance across the park?

Answer: 32 km

Question 3: A photograph of a sculpture measures 15 cm in height. The sculpture's actual height is 2.4 meters. What is the scale factor used in the photograph?

Answer: 1/16

Question 4: Construct a triangle on the grid with sides measuring 3 cm, 4.5 cm, and 6 cm. Then, reduce each side by a scale factor of \( \frac{1}{3} \).

Answer: Sides 1 cm, 1.5 cm, and 2 cm

Question 5: A photograph of a car is scaled down by a factor of \( \frac{2}{5} \). The photograph's length is 12 cm. What is the actual length of the car?

Answer: 30 cm

Question 6: A model airplane has a wingspan of 18 cm. The real airplane's wingspan is 9 meters. What scale factor is used in the model?

Answer: 1/50

Question 7: A city map shows a river that is 16 km long. The reduction scale factor from the real river to the map is \( \frac{1}{200} \). What is the length of the river on the map?

Answer: 0.08 km or 80 meters

Question 8: A photograph of a statue measures 20 cm in height. The actual height is 3.2 meters. Determine the scale factor of the photograph.

Answer: 1/16

Question 9: A blueprint shows a room that measures 5 meters in length. The blueprint's scale factor is \( \frac{1}{50} \). What is the length of the room on the blueprint?

Answer: 0.1 meters or 10 cm

Question 10: Identify and correct the mistake in this statement: 'The reduction scale factor from a model to the real object is 2.'

Answer: The scale factor should be less than 1 for reduction; a scale factor of 2 indicates enlargement, not reduction.