How To Teach Students To Resolve Proportions?
Yes, it is true that many students feel difficulty in resolving proportions. The maximum audience in this category belongs to either grade 6 or 7. The basic reason for this difficulty is the weak base. No doubt the proportion is an advanced form of ratios, but a little bit of variance is involved in the concept.
Adding more, you can now use a free proportion calculator as well to simplify proportions in mathematics. Not only this but the tool is loaded with a very simple user interface that allows you to enter the inputs and get results in a matter of seconds. Also, you can download the results in a pdf file or share it with other mates for group study purposes.
Coming back to the topic of discussion now, the following article will help you to understand proportions and the way you can easily resolve them.
So let’s get started now!
What Is Proportion?
In mathematics;
A proportion is considered a relation between two ratios.
The basic concept behind the definition involves two daughter concepts. These include:
- Fractions
- Ratios
You may consider the proportion as an expression that equates to two ratios.
Mathematical Form:
A proportion can be written as follows:
a:b::c:d
Where the sign “::” represents the proportion.
Types of Proportion:
Basically, there are two types of proportions that include the following and can also be solved by a proportion calculator online:
Direct Proportion:
It is a type of proportion in which an increase in one quantity gives rise to another quantity as well.
Mathematically:
a ∝ b
For Example:
Suppose you are driving a car. Now if you press more accelerator, the car will run fast and cover more distance. Conversely, running the car at a lower speed will cover less distance.
For verification, you may enter the speeds and distances in the proportion calculator and get clear results. This will let you know how the quantities change with respect to each other.
Inverse Proportion:
This type of proportion is exactly the opposite to direct one. In the thai situation, where the one quantity increases, the other in the relation decreases automatically.
Mathematically:
A ∝ 1/b
For example:
Considering the same example of the car, running the car at high speed will cover more distance in less amount of time.
Characteristics of Proportions:
If you want to master proportions, then you need to understand teh following characteristics of them:
Addendo:
If a : b = c : d
Then a + c : b + d
Subtrahendo:
If a : b = c : d
Then a – c : b – d
Dividendo:
If a : b = c : d
Then a – b : b = c – d : d
Componendo:
If a : b = c : d
Then a + b : b = c + d : d
Alternendo:
If a : b = c : d
Then a : c = b: d
Invertendo:
If a : b = c : d
Then b : a = d : c
Componendo and Dividendo:
If a : b = c : d
Then a + b : a – b = c + d : c – d
All of these properties are also considered by the free proportion calculator when resolving proportions in seconds. This way, you will also get an idea of how to calculate these parameters in mathematics by hand.
A Few Words About Proportion Calculator:
This advanced tool is one of the best methods to get instant solutions to your proportion-related problems. Let’s discuss how!
- After you lad on to the tool page, enter any of the three inputs
- Now tap Calculate and the calculator will give you immediate results right there on your device screen
Features of the tool:
- Highly compatible
- Free to use
- 100% accurate results
- User-friendly interface
- You may also share the results with your mates for group study purposes
Instant Tips To Resolve Proportion:
Here in this section, we have packed in all necessary tips that may help you to simplify proportions. These tips will certainly assist you to pass analytical examinations.
- a/b = c/d ⇒ ad = bc
- a/b = c/d ⇒ b/a = d/c
- a/b = c/d ⇒ a/c = b/d
- a/b = c/d ⇒ (a + b)/b = (c + d)/d
- a/b = c/d ⇒ (a – b/b = (c – d)/d
- a/(b + c) = b/(c + a) = c/(a + b) and a + b + c ≠0, then a = b = c.
- a/b = c/d ⇒ (a + b)/(a – b) = (c + d)/(c – d)
Continued Proportions:
Continued proportions are discussed for three quantities instead of two. The definition states that:
In a continued proportion, the ratio of first and second values must be equal to the second and third values. The ratio between the first and second quantities in a set of four quantities will be equal to the ratio between the third and fourth quantities.
Conclusion:
Mathematical literacy for learners includes giving them the knowledge and abilities to solve proportional problems. To emphasise how important it is to grasp proportions and how to apply them, it is crucial to put these abilities in a practical, real-world setting.
Understanding proportions lets you resolve a lot of complicated concepts in higher calculus and algebra. This is why it is a must to learn how to solve for proportions. And using an online proportion calculator can also assist you to simplify these mathematical concepts in keen detail.