Proportions Help

Subject Areas

Tools / Misc

bCalc

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scrnGC3: f(x) Plot Input

scrnGC4: g(x) Plot Input

The inputs above will be hidden when the program finally gets launched. Currently, I am not hiding them even when you close the calculator. The purpose of the inputs is to help in debugging. This allows you to enter simple code on the calculator screen but the program translates the input to javascript math. Give it a try and see if you notice any obvious problems or have suggestions for improvements.

gCalc

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Select precision* of answer:

Select angle mode:

Enter expression to evaluate here:

The answer is shown below:

Enter function to be plotted:

f(x) =

Enter 2nd function, if needed:

g(x) =

Change or reset the x-y scaling below:

x_min =

x_max =

y_min =

y_max =

Accuracy Disclaimer

The javascript math object methods used for this calculator are not accurate for very large or very small numbers. In particular, the trigonometric functions may yield very small answers that should actually be zero or very large answers that should be infinite. This typically occurs at 90° or pi/2 intervals.

DO NOT USE WHERE HIGH PRECISION IS REQUIRED. USE AT YOUR OWN RISK.

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Proportions are nothing more than a pair of ratios that are equal to each other.

Example 1: 12 = 24

The cross-products of a proportion are equal. Cross-multiplication is the process of multiplying the numerator of one of the ratios times the denominator of the other ratio.

In example 1, above, note that 1•4 = 2•2 or 4 = 4.

This is a very helpful tool that can often be used to solve routine, daily problems. For example, given that you can buy 3 oranges for $1.50, how many oranges can you buy for $5? Solve the problem as shown in example 2, below.

Example 2: 3 oranges$1.50= X oranges$5.00

Notice how the ratios included the dimensions. Although you may not be accustomed to seeing the dimensions and the numbers, this practice can be helpful in deciding what numbers go where. Note that all the numerators have the same dimension and all the denominators have the same dimension. The cross-multiplication leaves us with the following cross-products:

Example 2 Solution: ($1.50)•(X oranges) = ($5.00)•(3 oranges)

1.5 X $oranges = 15 $oranges

Divide both sides by 1.5 $oranges and cancel where possible.

1.5 X $oranges = 15 $oranges

1.5 $oranges 1.5 $oranges

X = 10

Note, how we were left with $oranges on both sides of the equation. If the problem had been set up incorrectly we might have had $•$ on one side of the equation and oranges•oranges on the other side, making it an equality.

Notice how the X-term was put on the left side of the equation when we did the cross-product. It really doesn't matter which side of the equation the unknown is placed, however many people find it easier to solve this way.