Question 1: Calculate the reduced length of a side that measures 24 cm when scaled by a fractional scale factor of 3/4.

Answer: 18

Question 2: A triangle with sides 10 cm, 14 cm, and 18 cm is reduced by a scale factor of 2/3. Calculate the lengths of the sides after reduction.

Answer: {"side1":6.67,"side2":9.33,"side3":12}

Question 3: A map shows a park that is 150 meters long. If the map is scaled with a reduction scale factor of 2/5, what is the actual length of the park?

Answer: 60

Question 4: Construct a rectangle with a length of 12 units and a width of 8 units. Reduce the rectangle using a scale factor of 3/4. Show the new dimensions.

Answer: {"new_width":6,"new_length":9}

Question 5: A sculpture is scaled down from 150 cm to 90 cm. Find the scale factor used. Is this a reduction or enlargement?

Answer: {"type":"reduction","scale_factor":"3/5"}

Question 6: Explain why multiplying by a scale factor greater than 1 results in enlargement, while a scale factor less than 1 results in reduction.

Answer: Because a scale factor greater than 1 increases the size, leading to enlargement, whereas less than 1 decreases the size, leading to reduction.

Question 7: A photograph measures 20 cm in width and is reduced by a scale factor of 2/3. What is the new width of the photograph?

Answer: 13.33

Question 8: A scale drawing of a building has a length of 8 cm. If the actual building is 24 meters long, what is the scale factor of the drawing?

Answer: 1/3

Question 9: Identify and correct the mistake in this statement: "Reducing a shape by a scale factor of 4/3 will make it smaller."

Answer: Since 4/3 is greater than 1, it causes enlargement, not reduction.

Question 10: A model car is 1/4 the size of the actual car. If the actual car is 4.8 meters long, what is the length of the model in meters?

Answer: 1.2

Question 11: A student claims that reducing a figure always results in a smaller shape, regardless of the scale factor. Is this correct? Explain your reasoning.

Answer: No, only scale factors less than 1 result in reduction. Factors greater than 1 enlarge the shape.