University:
University of Cambridge
Course:
0580 IGCSE | Mathematics
Academic year:

2023
Views:

53

Pages:

3
Author:

Lawak A

Understanding the Challenges of Comparing and Rating Scale Answers In an inverse value comparison, : a1/a2 = b2/b1 Problem and Discussion on Scale and Comparison Class VII Junior High School 1. The distance between the two cities on the map is 12 cm. The actual distance between the two cities is 144 km. Determine the size of the scale! Solution: Unknown: Distance on the map = 12 cm Actual distance = 144 km = 14,400,000 cm Ask: Scale Answe r: Scale = Distance on the map: Actual distance Scale = 12 : 14.400.000 Scale = 1 : 1,200,000 Thus, the scale is 1: 1,200,000. 2. The distance between two cities on the map is 17 cm. On the map, it is known that the scale is 1: 1.500.000. What is the original distance between the two cities? Solution: Unknown: Distance on the map = 17 cm Scale on the map = 1: 1,500,000 Question: Actual distance Answer: Scale = Distance on the map : Actual distance Actual distance = Distance on map : scale lOMoARcPSD|26370826 Actual distance = 17 : (1 : 1,500,000) Actual distance = 17 x 1,500,000 Actual distance = 25,500,000 cm Actual distance = 255 km Thus, the actual distance is 255 km. 3. The distance from Palembang to Bengkulu is about 450 km. If Cemerlang Junior High School students are asked to draw a map with a scale of 1: 75,000,000, then what is the distance between Palembang and Bengkulu on the map? Solution: Unknown: Actual distance = 450 Km = 45,000,000 cm Scale = 1:75,000,000 Asked: Distance on the map Answer: Scale = Distance on the map : Actual distance Distance on map = Scale x Actual distance Distance on map = (1: 75,000,000) x 450,000,000cm Distance on map = 6 cm Therefore, the distance that the students of Cemerlang Junior High School have to make is 6 cm. 4. A rectangle is 50 cm long and 12.5 cm wide. Find the ratio between the perimeter and the length of the rectangle! Solution: Unknown: Length = 50 cm Width = 12.5 cm Ask: The ratio of the perimeter to twice the length of the rectangle Answer: Perimeter of rectangle = 2 x (Length + Width) Perimeter of rectangle = 2 x (50 cm + 12.5 cm) Perimeter of rectangle = 2 x (62.5 cm) Perimeter of the rectangle = 125 cm Twice the length = 2 x the length of the rectangle Twice the length = 2 x 50cm Twice the length = 100cm lOMoARcPSD|26370826 Comparison = Perimeter : Twice the length of the rectangle Comparison = 125 cm : 100 cm Comparison = 5 : 4 Therefore, the ratio is 5: 4.