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A direct and inverse proportion are very useful in showing that how the quantities and amount are related to each other. A direct and inverse proportion are also known as directly proportional or inversely proportional. ‘∝’ this is the symbol of the proportionality.
For instance, if we have to say x is proportional to y, then it should be represented as “x ∝ y”, and if we say x is inversely proportional to y, then it is represented as “x ∝ 1/y. The proportionality rules governed these relations.
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Moreover, when the increase in quantity brings the decrease in the quantity of the other value or when the decrease in the quantity increases the quantity of the other value, is known as inverse proportion. The product of the given two values is equal to a constant value, whereas, when the two quantity increases or decreases together, is known as direct proportion.
DIRECT PROPORTION
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The definition of the direct proportion states that, “Two quantities are said to be in the direct proportion when the value of both the quantities increases or decreases together or when the ratio of the two given values remain constant. This means,
a/b = k
the quantities a and b are said to vary directly, where k is a positive number.
If the values b1, b2 of b corresponding to the values a1, a2 of a, respectively then it becomes,
A1/b1 = a2/b2
The direct proportion is also called direct variation.
Also Read: Direct Proportion
DIRECTLY PROPORTIONAL SYMBOL
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The symbol that is used to represent the direct proportion is ‘∝’.
Suppose,
X is directly proportional to Y
By using the symbol, this can be written as:
x ∝ y
Let’s, take the other statement, a = 2b
This statement shows that a is directly proportional to b, and the value of the one variable can only be found, if the value of the other variable is given.
For instance:
Let b = 7
Therefore, a = 2 x 7 = 14
Likewise, if we take the value of “a” as 14, then only we will find the value of b.
Such as
14 = 2 x b
14/2 = b
Therefore, b =7
INVERSE PROPORTION
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When the one quantity increases, the other quantity of the value decreases. Similarly, when the one quantity decreases, the other quantity of the value increases. The corresponding ratios remains constant, this is known as inverse proportion or indirect variation. However, the proportionality symbol is used in many different ways.
PROPERTIES OF DIRECT AND INDIRECT PROPORTION
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The properties of the direct proportion are as follows-
- As one quantity increases, the other quantity increases as well.
- As one quantity decreases, the other quantity decreases as well.
- The given ratios always remain constant
- The direct proportion is also called ‘direct variation’
The properties of indirect proportion are given below-
- When one quantity increases, moreover, the other quantity decreases
- When one quantity decreases, further the other quantity increases
- The given ratios always vary inversely
- The indirect proportion is also known as indirect variation.
HOW TO WRITE DIRCET AND INDIRECT PROPORTION EQUATION?
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Follow the steps given below to write the proportionality whether is direct or indirect-
- Step1- Firstly, write down the proportional statement
- Step2- By using the constant of proportionality, convert the statement as an equation
- Step3- From the information given, find the constant of proportionality.
- Step4- Substitute in an equation, after finding the constant of proportionality.
THINGS TO REMEMBER
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- A direct and inverse proportion are very useful in showing that how the quantities and amount are related to each other.
- When the increase in quantity brings the decrease in the quantity of the other value or when the decrease in the quantity increases the quantity of the other value, is known as inverse proportion.
- The definition of the direct proportion states that, “Two quantities are said to be in the direct proportion when the value of both the quantities increases or decreases together or when the ratio of the two given values remain constant.
- ‘∝’ this is the symbol of the proportionality.
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FAQS
Question1- How can we know if a question is direct or inverse proportion?
Answer1- The direct or inverse proportions are also known as directly proportional or inversely proportional. The symbol of the proportionality is very useful in showing whether the question is direct or inverse proportion. For example- if we say, x is proportional to y, then it will be represented as x ∝ y. similarly, if we say x is inversely proportional to x, then it will be represented as x ∝ 1/y.
Question2- How to apply direct and inverse proportion in daily life?
Answer- Suppose, the earning of a member is directly proportional to the working hours. The statement, “work more hours to urge more pay” suggests the rise within the value of one quantity also increases the worth of the other quantity. Similarly, if the value of the one quantity decreases, the worth of the other quantity decreases itself.
Question3- What are the steps involved in solving the problems related to the direct inverse proportion?
Answer- The steps that are involved in solving the problems involving the direct inverse proportion are mentioned bellow-
- Step1- Firstly, write the proportional relationship
- Step2- By using a constant of proportionality, convert it into an equation
- Step3- To find the constant of the proportionality, use the given information
- Step4- Now, substitute it to an equation
Question4- Differentiate between the direct proportion and inverse proportion.
Answer- When the value of both the quantities increases or decreases together or when the ratio of the two given values remain constant, is termed as direct proportion, whereas, when the quantity of one variable increase with a decrease in the value of the other variable and decreases with an increase in the quantity of the other value, is known as inverse proportion.
Question5- Give an example of direct proportion.
Answer- The example for the direct proportion is, when the number of the commodities increases, the cost of the commodities increases too. However, the price or cost is directly proportional to number of the commodities.
Question6- Give an example of inverse proportion.
Answer- The example for the inverse proportion is as follows- time is inversely proportional to speed. As if the speed of a vehicle increases, then it takes less time for the vehicle to cover the distance.
Question7- Explain the characteristics of direct and inverse proportion.
Answer- In the direct proportion, when the one quantity increases, the other quantity increases too. Likewise, when the one quantity decreases, the other quantity decreases itself. The corresponding ratios remains constant. The direct proportion is also termed as direct variation.
Though, in the inverse proportion, when the one quantity increases, the other quantity decreases. Similarly, if one quantity decrease, the other quantity increase. The corresponding ratio vary inversely. The inverse proportion is also termed as indirect variation.
Question8- In inverse proportion, what does ‘∝’ symbol represents?
Answer- In the inverse proportion, the symbol ‘∝’ denotes the relationship between two quantities. This symbol implies as a ∝ b, when we say a is proportional to b. Similarly, this symbol implies as a ∝ 1/b, when we say a is inversely proportional to b.
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