Defining Proportional Relationships In Math
Mathematics is based on the concept of proportional relationships. They can help us to understand the relationship between two quantities and their changes together. A proportional relationship is a relationship where one quantity and the other remain constant. If you want to put it another way, when one quantity is changed, the second quantity also changes proportionally.
Let’s look at the relationship between a car’s speed and its distance. Let's suppose a vehicle travels at 60 miles an hour. The distance travelled is directly proportional with the amount of time spent. If the car is driven for an hour, then it covers 60 miles. If it drives for two hours, then it covers 120 miles. The ratio between distance and time is always 60 miles per minute.
You can represent proportional relationships in many ways. These include equations and tables. Ratio tables is one way to show proportional relations. A ratio-table is a chart that shows how two quantities are related in relation to each other. Let’s look at the relationship between apples and cost. Assume we purchase apples for $0.50 each. In this instance, the price of buying apples will be directly proportional to how many apples you buy. You can show this relationship using a table of ratios, like the one below.
| Apples | Price |
|---|---|
| 1 | $0.50 |
| 2 | $1.00 |
| 3 | $1.50 |
| 4 | $2.00 |
| … | … |
This table shows that the cost per apple remains at $0.50.
Graphs can be used to represent proportional relationships. A graph of proportional relationships is a horizontal line that goes through the origin. The slope represents the constant relationship between the two amounts. Take, for instance, the graph that shows the relationship between speed and time required to travel a certain distance.
GRAPH INSERT
The slope of this line represents the speed of a car traveling at 60 miles per hour.
Indirect proportions and direct proportions are both types of proportional relationships. Direct proportion is the change of two quantities in the same way. Inverse proportion occurs when two quantities move in the opposite direction. Let’s look at some examples.
- Direct proportion: Earn more money by working more hours.
- Inverse Proportion: The shorter the time taken to complete a job, the greater number of tasks that can be completed in a specified time.
As a summary, proportional relations are a basic concept in math that helps us understand how quantities relate to one another. You can represent them through tables, graphs, or equations. Direct proportion and inverse ratio are two different types of proportional relationships. Understanding proportional relationship can be used to solve a variety of real-life situations, such as calculating a person’s cost, calculating if he or she is driving fast, etc.
