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

2023
Views:

134

Pages:

3
Author:

Lawak A

Problems in Comparing Results and Scale: An In-Depth Discussion 1. Meaning of Comparison Comparison is a very important thing in mathematics, as well as in our daily lives. As an illustration, consider the following example: a. Father is 45 years old and mother is 40 years old, while Ali is 15 years old and Ani is 10 years old. Age ratio of father and mother = 45 years : 40 years = 45 : 40 = 9 : 8 Ali and Ani Age Comparison = 15 years : 10 years = 15 : 10 = 3 : 2 Father and Ali's age ratio = 45 years : 15 years = 45 : 15 = 3 : 1 b. Dewa's height is 160 cm, Dewi's height is 120 cm and Gita's height is 60 cm. Height comparison of Dewa and Goddess = 160 cm:120 cm = 160:120 = 4:3 Height ratio of Dewi and Gita = 120 cm:60 cm = 120:60 = 2:1 Height ratio of Dewa and Gita = 160 cm:60 cm = 160:60 = 8:3 From this example, it can be seen that to compare two quantities, we need to consider : a. Compare one quantity with another b. Equalize the units c. Simplify the comparison form From the description and example of the problem above, we can get the meaning of comparison as follows: a. The ratio between a and b is written in simple form or a : b, where a and b are natural numbers, and b 0. b. The two units being compared must be the same. c. Comparison in simple form means that a and b have no common factors except 1. 2. Scale We often encounter the term scale when we open a map/atlas. If the map says scale 1: 5,000,000, it means : 1 cm on a map represents 5,000,000 cm of actual distance, or 1 cm on a map represents 50,000 m of actual distance, or 1 cm on a map represents 50 km of actual distance Scale is the comparison of the size in the figure (cm) with the actual size (cm) It appears that the scale uses cm units for the two quantities being compared Keep in mind that : 1 km = 1,000 m = 100,000 cm. The following example explains how we use scale on a map. a. On a map, the distance between places A and B is 3 cm, whereas the distance between A and B is actually 450 km. Determine the scale used on the map! Answer: Scale = Size on the map: Actual size = 3 cm : 450 km = 3 cm : 45,000,000 cm (the scale must use cm units) = 3 : 45.000.000 = 1 : 15.000.000 b. On a map the distance from city A to city B is 8 cm. If the scale of the map is 1: 500,000, then what is the actual distance between the two cities? Answer: A scale of 1 = 500,000 means that 1 cm on a map represents 500,000 cm of actual distance, or 1 cm on a map represents 5 km of actual distance. c. A map using a scale of 1 : 25.000.000 . If the distance between two places is actually 300 km, what is the distance between the two places on the map? Answer: Scale 1: 25.000.000 This means that 1 cm on a map represents 25,000,000 cm of actual distance, or 1 cm on a map represents 250 km of actual distance. So the distance between the two places on the map is 300 : 250 = 1.2 cm Now you have learned comparison, scale and its use, easy isn't it?