Goals
1. Grasp the concept of ratio.
2. Learn how to calculate basic ratios.
3. Apply the idea of ratio to everyday scenarios, such as a car's speed and a map's scale.
4. Work through problems connecting fractions and ratios of two quantities.
Contextualization
In our daily lives, we often come across comparisons between quantities, such as a vehicle's speed, the population density of a town, or the scale of a map. These comparisons are practical instances of using ratios, enabling us to comprehend and interpret the world around us quantitatively. For instance, when we look at a car's speed, we relate the distance covered to the time taken. A map's scale helps us understand the relation between the distance shown on the map and the actual distance. Thus, ratios serve as essential tools for converting data into meaningful information.
Subject Relevance
To Remember!
Concept of Ratio
A ratio is a way to compare two quantities of the same kind, usually written as a fraction. For example, if we have two quantities A and B, the ratio can be expressed as A/B or A:B.
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A ratio compares two quantities.
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It can be represented as a fraction, like A/B.
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It's a method to compare quantities quantitatively.
Calculation of Simple Ratios
To calculate a simple ratio, we divide one quantity by another. For instance, if someone drives 100 km in 2 hours, the ratio of distance to time becomes 100/2, resulting in a speed of 50 km/h.
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Divide one quantity by the other.
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For example, 100 km in 2 hours gives a speed of 50 km/h.
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It's a straightforward way to compare two quantities.
Application of Ratio in Practical Contexts
Ratios are used in many practical situations, such as calculating a car's average speed or interpreting a map's scale. For example, a map with a scale of 1:100000 indicates that 1 cm on the map represents 100,000 cm in real life.
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Useful for calculating average speed.
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Helps in understanding map scales.
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Crucial for practical analysis.
Relationship between Fraction and Ratio of Two Quantities
Understanding the relationship between fractions and ratios is key for tackling comparison problems. A fraction like 2/3 can illustrate the ratio of two parts of one quantity to three parts of another.
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Fractions and ratios are linked.
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Fraction 2/3 shows the ratio of two parts of one quantity to three parts of another.
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Vital for solving comparison challenges.
Practical Applications
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Engineers rely on ratios to assess material strength.
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Economists study financial ratios to interpret data.
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Game developers utilize ratios to ensure balanced gameplay.
Key Terms
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Ratio: A way to compare two quantities of the same kind.
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Fraction: A mathematical expression showing the division between two numbers.
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Average Speed: The ratio of distance travelled to the time taken.
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Map Scale: A ratio that depicts the relationship between distance on a map and actual distance.
Questions for Reflections
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How can grasping ratios assist in making informed choices in your daily life?
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In which ways are ratios used in careers you're interested in pursuing?
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Think of a common scenario where you use ratios without even realising it. How might this understanding enhance your mathematical skills?
Map Scale Challenge
In this mini-challenge, you will work with a map's scale to calculate real distances.
Instructions
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Select a printed or digital map with a defined scale (e.g., 1:50000).
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Pick two points on the map and measure the distance between them with a ruler.
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Use the map's scale to calculate the actual distance between the two points you measured.
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Write a brief paragraph explaining the calculation method you used and the actual distance you found.
