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Inversely Proportional

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Indirect proportionality is a relationship where a number either increases as another decreases or decreases as another increases. Inversely proportional is the opposite of directly proportional and in this page we will discuss about indirect proportionality. In the year 1864 indirect proportionality was first in use. The constant will be negative as the variables tend to be negatively proportional.
Product of two variables is constant in inverse proportionality and here as one quantity goes up the other quantity will go down. 


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Consider two variables l and m respectively. l varies inversely with m if and only if
$l$ $\alpha$ $\frac{1}{m}$ One variable is reciprocal of the other such that a constant n exists. ($n$ is not equal to zero).

$l$ = $\frac{n}{m}$
$l$ and $m$ denotes the values for inversely proportion.
$n$ is the proportionality constant
$n$ = $l$ $\times$ $m$
"$\alpha$" is inversely proportional symbol.


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Inverse proportion graph is a curve that never touches any of the axes. This form of graph is known as hyperbola.
The graph will never cross either axis because no variable is zero. Inversely proportional means that the product of the two quantities should be constant.

Given below is an example showing inverse proportionality
Example: Draw the graph of the inversely proportional function $y$ = -$\frac{5}{x}$


Plug in any values of $x$ to get $y$

When $x$ = - 2, $y$ = 2.5

When $x$ = - 1, $y$ = 5

When $x$ = 1,  $y$ = - 5

When $x$ = 2, $y$ = - 2.5

 - 2   - 1 
  1     2
$y$  2.5   5   - 5   - 2.5

Given below is the graph for the function $y$ = - $\frac{5}{x}$
Inversely Proportional Graph


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Example 1: Find $L$ when $M$ = 550, If $L$ is inversely proportional to $M$ and $L$ = 350, $M$ = 0.8

Given: Here $L$ and $M$ are in inverse proportionality to $M$ i.e.

$L$ = $N$ $\times$ $\frac{1}{M}$

Where $N$ is a constant and we get $N$ = $L x M$

Given that $L$ = 350 and $M$ = 0.8
We get $N$ = 350 $\times$ 0.8 = 280

Therefore $N$ = 280

Substitute value of $N$ and $M$  in equation, $N$ = $L x M$, we get

280 = $L \times$ 550

$L$ = $\frac{280}{550}$

$L$ = 0.51

Example 2: Number of boys in chemistry class are 28 and the ratio between girls and boys is 60  when compared to physics class. The ratio between girls and boys is 6 : 5 for mathematics class. Find out the number of girls present in biology class.


Given: Number of boys in chemistry class = 28

Ratio between boys and girls in physics class = 60

Let number of girls in biology class = $x$

We get $\frac{28}{x}$ = $\frac{6}{5}$

28 $\times$ 5 = 6 $\times$ $(x)$

140 = 6$x$

$x$ = $\frac{140}{6}$

$x$ = 23.33 
$x$ $\sim$ 23

Therefore number of girls in biology class is 23.