Proportions are used to compare two ratios or sets of data. Ratios are comparisons between two different quantities that can be expressed as fractions or decimals. Proportions usually involve unknown quantities, and they help us by setting up an equation to find the unknown value. Understanding how to proportion” title=”How to make a mathematical proportion”>make a is an essential skill that will help you analyze different data sets and become a more proficient problem solver.

To make a proportion, we need to follow a few fundamental steps:

Step #1: Identify the given ratios

The first step is to find out the two ratios that we need to compare. For example, let us say we have two sets of data: 3 out of 10 apples are red, and 2 out of 5 oranges are ripe. In this case, we have two ratios:

Ratio A: 3 red apples in 10 apples

Ratio B: 2 ripe oranges in 5 oranges

Step #2: Write the ratios as fractions

Once we have identified the two ratios, the next step is to write them as fractions. We do this by putting the number of units in the numerator and the total number of units in the denominator. In the above example, we write:

Ratio A: 3/10

Ratio B: 2/5

Step #3: Compare the ratios

To make a proportion, we need to compare the two ratios and write them as an equation. We can do this by either cross-multiplying or setting up a ratio table.

Cross-multiplying is a way of multiplying the numerator of one fraction by the denominator of the other, and vice versa. For example, if we want to compare ratio A to ratio B, we write:

3/10 = 2/5

Cross-multiplying gives us:

3 x 5 = 10 x 2

15 = 20

The equation is not balanced since 15 is not equal to 20. Therefore, we can’t compare ratio A to ratio B.

A ratio table is another way to compare ratios. It helps organize the information and makes it easier to find the proportion. To set up a ratio table, we write the two ratios side by side and multiply the denominators by the opposite numerator. For example, let us set up a ratio table for the two ratios above:

| Ratio A | Ratio B |
| — | — |
| 3 | 2 |
| 10 | 5 |
| 30 | 20 |

To check for proportion, we compare the two products, which are 30 and 20. If they are equal, then the ratios are proportional. In this case, since 30 is equal to 20, we have a proportion:

3/10 = 2/5

Step #4: Solve for the unknown value

Once we have a proportion, we can use it to solve problems that involve an unknown value. For example, let us say that we want to know how many apples we need to buy to get six red apples. We can use the proportion we found earlier:

3/10 = 6/x

We know that 3/10 and 6/x are equivalent ratios since we have a proportion. We can cross-multiply and solve for x:

3x = 60

x = 20

We need to buy 20 apples to get six red apples.

In conclusion, making a proportion requires identifying the given ratios, writing them as fractions, comparing them using cross-multiplication or a ratio table, and solving for the unknown value. These steps help us solve problems that involve ratios and proportions and become more efficient problem solvers.

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