Final answer:
To write a proportion, you set two equivalent ratios equal to each other. You use the unit scale ratio to compare the measurements of a scale model or drawing to the actual object's dimensions. When solving for a missing dimension, you use the given scale factor and measurements to establish and solve the proportion.
Step-by-step explanation:
To write up a proportion or similar statement, you first need equivalent ratios. Equivalence of ratios signifies that two fractions are equal when their respective numerators and denominators are multiplied by the same factor. Proportions are used to show that two ratios or rates are equivalent, such as the scale of a map or a model in comparison to the real object.
Example Steps for Writing Proportions
- Determine the two pairs of measurements or quantities you want to compare.
- Write the ratios using the measurements. For instance, if you have lengths in inches, set up a ratio, such as 4 inches to 12 inches (4/12).
- Next, write a second ratio that represents the same relationship but with different measurements. Using the previous example, this could be 1 inch to 3 inches (1/3).
- Finally, set the two ratios equal to each other to establish a proportion: 4/12 = 1/3.
When utilizing a unit scale, like 1 inch representing 100 feet (1 inch/100 feet), you would create proportions by setting each dimension ratio to the unit scale ratio. For example, if an object’s length in a scale drawing is 14 inches, and the unit scale is 1 inch for every 10 feet, the proportion is 14/1 = 1/10.
To find a missing dimension using a scale factor, write the proportion with the known scale factor and the given measurement, then solve for the unknown value. A missing dimension problem with a scale factor of 2 inches to 3 feet (2":3') and a scale measurement of 6 inches (6") would have the initial proportion as 2/3 = 6/x, where x is the actual dimension in feet.