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Use cross products to match each proportion to the equation that can be used to solve it.
9/2.5 = 8/x
2.5x = 9(8)
9/x = 8/2.5
OOO
8x = 2.5(9)
9/2.5 = x/8
2.5(8) = 9x

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Final answer:

To solve proportions, cross-multiplication is used to find the missing value by equating the product of the extremes with the product of the means. This technique is applied to scales, unit conversions, and other situations requiring proportional reasoning.

Step-by-step explanation:

To solve problems involving proportions, especially when dealing with scale models or conversions, it's important to use the cross-multiplication technique. Cross-multiplication helps us find missing values in a proportion which is an equation that shows two equivalent ratios.

Example Problems

Basic Proportion:

For instance, to solve the proportion 1 foot/12 inches = 12 feet/x inches, we would cross multiply to get 1x = 12 × 12, which simplifies to x = 144 inches. This means that 12 feet equals to 144 inches.

Scale Model Proportion:

In scale model problems, if you have a scale where the length on the model is 1/50 of the actual length and the model’s length is 0.5 inches, to find the actual length (w) when the model is 30 inches long, you would use the proportion 1/50 = 0.5/30 and cross multiply to calculate w.

Another scenario could involve converting units, like turning gallons into quarts. You can set up the proportion 1 gallon/4 quarts = 3 gallons/x quarts and cross multiply to obtain 1x = 3 × 4, which results in x being equal to 12 quarts.

When applying cross multiplication to the original question, 9/2.5 = 8/x, we get 2.5x = 9 × 8. After performing the multiplication, we find that x equals 72 divided by 2.5, which leads us to the solution for x.

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