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Learn it your way
A short class with Sarah and her students. The other ways are under More.
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Today, we're going to learn about direct proportion. Can anyone tell me what happens to the cost if I buy more kilograms of sugar?
The cost increases as we buy more sugar!
"Exactly! If 1 kg costs
Let's look at another example involving petrol and distance. If 4 litres of petrol takes a car 60 km, how far will it go with 12 litres?
It should travel 180 km.
Exactly! The distance is three times because the petrol consumed is three times more. Can anyone explain why we can say there is a direct proportion here?
Because both the petrol and distance increase in the same ratio.
Right! Let's make a quick table together to visualize this information.
What do we put in the table?
We'll fill in the litres of petrol and corresponding distances! This will help us see the pattern. Remember, for direct proportions, you can check if the ratios stay the same!
Now, let’s do an activity with a clock's minute hand. When we record the time and angle, what will we find out?
We’ll see if the angle changes the same with every minute?
Exactly! Make sure to observe how they relate to each other. If they keep the same ratio, then they are in direct proportion. Let's start recording!
In this table, as time increases, the angle turns too. Looks like they do stay proportional!
Great job! This is a classic example of direct proportion in motion.
Can anyone think of a situation where direct proportion applies? Perhaps in cooking or shopping?
In recipes! If you double the servings, you double the ingredients!
Exactly! And what about when we buy certain items? Let's brainstorm some other examples.
When we buy fruits, if I buy more apples, I pay more money but the price per apple stays the same!
Well said! It’s so important to understand how these quantities affect each other in life.
Finally, let's understand that not all relationships are direct proportion. Can anyone provide an example?
Changes in age between friends?
Correct! Age changes, but not in a constant ratio. It's critical to identify these cases too.
So we have to be careful about how we classify relationships in math?
Yes! Always evaluate if the ratios hold true to ensure they are in direct proportion.
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.
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.
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.
Let the map distance be cm and actual distance be cm, then:
or
Since :
Thus, two cities, which are 5 cm apart on the map, are actually m or 2500 km away from each other.
When one goes up, the other stays true, that's direct proportion just for you!
Imagine two friends, Sam and Tim. When Sam eats more, Tim eats the same. If Sam eats two sandwiches, Tim has two too. This shows how they are in direct proportion!
Remember: DR⇒ Direct & Ratio. Direct proportion is all about maintaining a ratio.
P.A.R. - Proportion Always Remains! Keep this in mind when assessing direct proportions.
Term
What is direct proportion?
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Term
What is a ratio?
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A relationship between two quantities where an increase in one leads to a proportionate increase in the other.
A relationship between two numbers indicating how many times the first number contains the second.
A fixed value that maintains the ratio between two quantities in direct proportion.
The quality of a relationship where two variables change in a consistent ratio.
This section introduces direct proportion, highlighting its significance and applications through practical examples.
In this section, direct proportion is explored through various examples such as the relationship between cost and quantity of sugar, petrol consumption and distance traveled, and more. The concept is illustrated with interactive activities and real-life applications, reinforcing the idea that two quantities in direct proportion change consistently in relation to one another.
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.
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.
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 cm and actual distance be cm, then:
or
Since :
Thus, two cities, which are 5 cm apart on the map, are actually m or 2500 km away from each other.