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Inverse Proportion

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Crystal Hi

on 3 March 2011

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Transcript of Inverse Proportion

Inverse Proportion Definition of Inverse Proportion When quantities are related this way we say that they are in inverse proportion. That is, when two quantities change by reciprocal factors, they are inversely proportional. Two quantities, A and B, are in inverse proportion if by whatever factor A changes, B changes by the multiplicative inverse, or reciprocal, of that factor. Inverse Proportions/Variations Two values x and y are inversely proportional to each other when their product xy is a constant.

This means that when x increases y will decrease, and vice versa, by an amount such that xy remains the same. Knowing that the product does not change also allows you to form an equation to find the value of an unknown variable. It takes 4 men 6 hours to repair a road. How long will it take 8 men to do the job if they work at the same rate? The number of men is inversely proportional to the time taken to do the job. 4 x 6 = 8 x t -> 8 x t = 24 -> t = 3hour Usually, you will be able to decide from the question whether the values are directly proportional or inversely proportional. Examples~ Let’s look at an example: Given y is directly proportional to , write an equation connecting x, y and a constant k.

So, in simple terms, when y increases, x increases too. Inverse (Indirect) Proportion statement:
Given y is inversely proportional to , write an equation connecting x, y and a constant k.
This is similar to the situation when a See-Saw is in Up-Down position. y is up while (x+2) is down. You can also see it from another point: y is in the numerator while (x+2) is in the denominator or when y increases, x decreases. As noted in the definition above, two proportional variables are sometimes said to be directly proportional. This is done so as to contrast direct proportionality with inverse proportionality.

Two variables are inversely proportional (or varying inversely, or in inverse variation, or in inverse proportion or reciprocal proportion) if one of the variables is directly proportional with the multiplicative inverse reciprocal of the other, or equivalently if their product is a constant. It follows that the variable y is inversely proportional to the variable x if there exists a non-zero constant k such that
The constant can be found by multiplying the original x variable and the original y variable.
Basically, the concept of inverse proportion means that as the absolute value or magnitude of one variable gets bigger, the absolute value or magnitude of another gets smaller, such that their product (the constant of proportionality) is always the same.
For example, the time taken for a journey is inversely proportional to the speed of travel; the time needed to dig a hole is (approximately) inversely proportional to the number of people digging.
The graph of two variables varying inversely on the Cartesian coordinate plane is a hyperbola. The product of the X and Y values of each point on the curve will equal the constant of proportionality (k). Since k can never equal zero, the graph will never cross either axis.
Two quantities are inversely proportional when one is multiplied or divided by any number, the other is divided or multiplied by the same number. The relation is also commonly denoted as
The graph of two variables that are inversely proportional is a hyperbola
Speed and time are inversely proportional because as the speed increases, the time it takes to reach the destination decreases.
Examples~ 3 workers build a wall in 12 hours. How long would it have taken for 6 equally productive workers?
In this example, the number of workers and the time are inversely proportional, because when the quantity of people decreases, the total time increases and when the quantity of people increases, the total time decreases. Follow these steps to complete an inverse proportionality word problem. Write down the ratio using one type of term (number of workers or time). Invert one of the ratios (flip it upside down).
Cross-multiply, divide and solve (the same method used for direct proportions)
And there we have it Bibliography http://www.vitutor.com/arithmetic/ratio/inverse_proportion.html
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