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Tag: Direct and Inverse Proportions

Direct And Inverse Proportions | Study
Direct And Inverse Proportions | Study

Direct And Inverse Proportions | Study
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Pre – Requisite

English Version
Direct and Inverse Proportions | Speed Notes
Notes For Quick Recap
Variations: If the values of two quantities depend on each other in such a way that a change in one causes corresponding change in the other, then the two quantities are said to be in variation. (Scroll down to continue …)
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Direct Variation or Direct Proportion:
Extra:
Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains
constant. That is if
=k [k is a positive number, then x and y are said to vary directly.
In such a case if y₁, y₂are the values of y corresponding to the values x₁, x of x
respectively then = .
If the number of articles purchased increases, the total cost also increases. More than money deposited in a bank, more is the interest earned.
Quantities increasing or decreasing together need not always be in direct proportion, same in the case of inverse proportion.
When two quantities x and y are in direct proportion (or vary directly), they are
written as
. Symbol
stands for ‘is proportion to’.
Inverse Proportion: Two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant. That is, if xy
= k, then x and y are said to vary inversely. In this case if y₁, y₂are the values of y
corresponding to the values x₁, x₂of x respectively then
^x1^{, Y}1 = ^x2^{, y}2 or
=
When two quantities x and y are in inverse proportion (or vary inversely), they are
written as x
. Example: If the number of workers increases, time taken to finish
the job decreases. Or If the speed will increase the time required to cover a given distance decreases.

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November 5, 2023
Direct And Inverse Proportions | Study
Assess
Interact
Pre-Requisires
Test & Enrich
Pre – Requisite

English Version
Direct and Inverse Proportions | Speed Notes
Notes For Quick Recap
Variations: If the values of two quantities depend on each other in such a way that a change in one causes corresponding change in the other, then the two quantities are said to be in variation. (Scroll down to continue …)
Study Tools
Audio, Visual & Digital Content
Direct Variation or Direct Proportion:
Extra:
Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains
constant. That is if
=k [k is a positive number, then x and y are said to vary directly.
In such a case if y₁, y₂are the values of y corresponding to the values x₁, x of x
respectively then = .
If the number of articles purchased increases, the total cost also increases. More than money deposited in a bank, more is the interest earned.
Quantities increasing or decreasing together need not always be in direct proportion, same in the case of inverse proportion.
When two quantities x and y are in direct proportion (or vary directly), they are
written as
. Symbol
stands for ‘is proportion to’.
Inverse Proportion: Two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant. That is, if xy
= k, then x and y are said to vary inversely. In this case if y₁, y₂are the values of y
corresponding to the values x₁, x₂of x respectively then
^x1^{, Y}1 = ^x2^{, y}2 or
=
When two quantities x and y are in inverse proportion (or vary inversely), they are
written as x
. Example: If the number of workers increases, time taken to finish
the job decreases. Or If the speed will increase the time required to cover a given distance decreases.

1. Distance and Time
Time (hours) Distance (km) Formula
0 0
$d = 60 \times t$ $\Rightarrow d = 60 \times t$
1 60
2 120
3 180

2. Cost of Groceries
Number of Apples Total Cost ($) Formula
0 0 $C = 2n ⇒$
1 2
2 4
5 10

3. Cooking Ingredients
Number of Servings Amount of Flour (cups) Formula
0 0 $F = 0.5 s$
4 2
6 3
8 4

4. Speed and Fuel Consumption
Distance (km) Fuel Consumed (liters) Formula
0 0 $F = \frac{d}{15}$
15 1
30 2
45 3

5. Salary and Hours Worked
Hours Worked Total Earnings ($) Formula
0 0 $E = 15 h$
1 15
5 75
10 150

Hindi Version
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Topic:
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August 25, 2023

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