Question 1: If a drawing is reduced by a scale factor of 1:4, and the original length of a side is 20 cm, what is the length of the side in the reduced drawing?

Answer: 5

Question 2: A model of a building is scaled down with a scale factor of 1:10. If the actual building height is 50 meters, what is the height of the model?

Answer: 5

Question 3: Calculate the scale factor if a photograph measures 15 cm and the actual object measures 75 cm.

Answer: 1:5

Question 4: Construct a rectangle on the grid with a length of 6 units and a width of 4 units. Then, reduce the rectangle by a scale factor of 1:3 and draw the reduced rectangle on the same grid.

Answer: Length: 2 units, Width: 1.33 units (or approximately 1 1/3 units)

Question 5: A scale drawing of a car is made with a scale factor of 1:25. If the length of the drawing is 12 cm, what is the actual length of the car?

Answer: 300

Question 6: A poster image of an airplane is scaled down by a factor of 1:50. If the picture's wingspan measures 4 cm on the poster, what is the actual wingspan?

Answer: 200

Question 7: In a drawing, the original length of an object is 30 units. When it is reduced by a scale factor of 1:6, what is the length of the reduced object? Show your working.

Answer: 5 units

Question 8: A model train is built with a scale factor of 1:87. If the model's length is 15 cm, what is the length of the actual train? Show your working.

Answer: 1305 cm or 13.05 meters

Question 9: A photo of a monument measures 8 cm in height on paper. The actual monument is 64 meters tall. What is the scale factor of the drawing to the real monument?

Answer: 1:800

Question 10: Identify and correct the mistake in this reduction calculation: "A scale factor of 1:10 was used to reduce a length of 40 cm, resulting in a length of 4 cm. The correct reduced length should be 4 cm."

Answer: The mistake is the reduction; 40 cm reduced by 1:10 should be 4 cm, which is correct. But, if the student says it's wrong, explain that the calculation is correct, the mistake could be in misreading the scale or the original length.