Direct Proportion
Direct proportion is a fundamental concept in mathematics that describes a relationship between two variables, where an increase in one variable results in a proportional increase in the other. This section outlines the basic principles of direct proportion through several relatable examples and exercises. If the cost of 1 kg of sugar is
36, then the cost of 3 kg is
108, demonstrating that as the quantity of sugar increases, the cost also increases in a consistent ratio.
Key Concepts
- Definition: Two quantities are said to be in direct proportion when their ratio remains constant.
- Examples provided include the use of petrol and the distance traveled by a car, and the relationship between the length of cloth and its cost.
Applications
This section also includes practical activities such as measuring the angle turned by a clock's minute hand and drawing direct comparisons between ages and their ratios. It concludes with exercises that require the application of the direct proportion concept in various scenarios, reinforcing the understanding of how different variables are interconnected.
Example
The scale of a map is given as 1:500000. Two cities are 5 cm apart on the map. Find the actual distance between them.
Solution: Let the map distance be \( x \) cm and actual distance be \( y \) cm, then:
\[ 1:500000 = \frac{x}{y} \]
or
\[ 500000 \cdot x = y \]
Since \( x = 5 \):
\[ 500000 \cdot 5 = y \]
Thus, two cities, which are 5 cm apart on the map, are actually \( 500000 \cdot 5 = 2500000 \) m or 2500 km away from each other.