Then the long piece, being what was left of the original piece after I cut off s meters, must have a length of 21 — s. Then my ratio, in fractional rather than in odds format, is:. Because there are two parts of this proportion that contain variables, I can't use the shortcut to solve.
Instead, I'll cross-multiply, and proceed from there. Referring back to my set-up for my equation, I see that I defined " s " to stand for the length of the s horter piece, with the unit of length being meters.
Then the length of the longer piece is given by:. Now that I've found both required values, I can give my answer, complete with the correct units:. Try always to clearly define and label your variables. Also, be sure to go back and re-check the word problem for what it actually wants. This exercise did not ask me to find "the value of a variable" or "the length of the shorter piece".
By re-checking the original exercise, I was able to provide an appropriate response, being the lengths of each of the two pieces, including the correct units of meters.
All right reserved. Web Design by. Skip to main content. Purplemath Solving proportions is simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross-multiplying , and solving the resulting equation. Content Continues Below. First, I convert the colon-based odds-notation ratios to fractional form:. Affiliate WyzAnt Tutoring.
Share This Page. Terms of Use Privacy Contact. Advertising Linking to PM Site licencing. Visit Our Profiles. Juanita could also have set up the proportion to compare the ratios of the container sizes to the number of servings of each container. Sometimes you will need to figure out whether two ratios are, in fact, a true or false proportion. Below is an example that shows the steps of determining whether a proportion is true or false.
Is the proportion true or false? The units are consistent across the numerators. The units are consistent across the denominators. Write each ratio in simplest form. Since the simplified fractions are equivalent, the proportion is true.
The proportion is true. Identifying True Proportions. To determine if a proportion compares equal ratios or not, you can follow these steps. Check to make sure that the units in the individual ratios are consistent either vertically or horizontally.
For example, or are valid setups for a proportion. Express each ratio as a simplified fraction. If the simplified fractions are the same, the proportion is true ; if the fractions are different, the proportion is false. Sometimes you need to create a proportion before determining whether it is true or not. An example is shown below. One office has 3 printers for 18 computers. Another office has 20 printers for computers.
Is the ratio of printers to computers the same in these two offices? Identify the relationship. Write ratios that describe each situation, and set them equal to each other.
Printers check. Check that the units in the numerators match. Computers check. Check that the units in the denominators match. Simplify each fraction and determine if they are equivalent.
Since the simplified fractions are not equal designated by the sign , the proportion is not true. The ratio of printers to computers is not the same in these two offices. There is another way to determine whether a proportion is true or false. To cross multiply, you multiply the numerator of the first ratio in the proportion by the denominator of the other ratio.
Then multiply the denominator of the first ratio by the numerator of the second ratio in the proportion. If these products are equal, the proportion is true; if these products are not equal, the proportion is not true. Below is an example of finding a cross product, or cross multiplying. Both products are equal, so the proportion is true. Below is another example of determining if a proportion is true or false by using cross products. Identify the cross product relationship.
Use cross products to determine if the proportion is true or false. Since the products are not equal, the proportion is false. The proportion is false. A True. The cross products are equal, so the proportion is true. The correct answer is true.
Finding an Unknown Quantity in a Proportion. We can also use cross products to find a missing term in a proportion. Here's an example. 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.
A inch tall model building was also used in the movie. How tall did the building seem in the movie? First, write the proportion, using a letter to stand for the missing term. We find the cross products by multiplying 20 times x, and 50 times
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