Problem Solving With Proportions

Problem Solving With Proportions-77
For instance if one package of cookie mix results in 20 cookies than that would be the same as to say that two packages will result in 40 cookies.$$\frac=\frac$$ A proportion is read as "x is to y as z is to w" $$\frac=\frac \: where\: y,w\neq 0$$ If one number in a proportion is unknown you can find that number by solving the proportion.

For instance if one package of cookie mix results in 20 cookies than that would be the same as to say that two packages will result in 40 cookies.$$\frac=\frac$$ A proportion is read as "x is to y as z is to w" $$\frac=\frac \: where\: y,w\neq 0$$ If one number in a proportion is unknown you can find that number by solving the proportion.

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The cross products of a proportion is always equal If we again use the example with the cookie mix used above $$\frac=\frac$$ $$\cdot =\cdot =40$$ It is said that in a proportion if $$\frac=\frac \: where\: y,w\neq 0$$ $$xw=yz$$ If you look at a map it always tells you in one of the corners that 1 inch of the map correspond to a much bigger distance in reality. We often use scaling in order to depict various objects. Thus any measurement we see in the model would be 1/4 of the real measurement.

Scaling involves recreating a model of the object and sharing its proportions, but where the size differs. If we wish to calculate the inverse, where we have a 20ft high wall and wish to reproduce it in the scale of 1:4, we simply calculate: $$20\cdot 1:4=20\cdot \frac=5$$ In a scale model of 1: X where X is a constant, all measurements become 1/X - of the real measurement.

We can also use cross products to find a missing term in a proportion. In a horror movie featuring a giant beetle, the beetle appeared to be 50 feet long.

However, a model was used for the beetle that was really only 20 inches long.

The following proportion is read as "twenty is to twenty-five as four is to five." In problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion.

To find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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$$\frac=\frac\: \: or\: \: \frac=\frac$$ If we write the unknown number in the nominator then we can solve this as any other equation $$\frac=\frac$$ Multiply both sides with 100 $$\, \frac=\, \frac$$ $$x=\frac$$ $$x=10$$ If the unknown number is in the denominator we can use another method that involves the cross product.

The cross product is the product of the numerator of one of the ratios and the denominator of the second ratio.

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