How to Calculate Whole Number Ratios

Examples of whole numbers

It may be convenient to express a proportion as the ratio of two whole numbers. Common examples are the odds of an event occurring and the relative sizes of two objects. If you have a ratio already in this form, reducing it to a simpler form may make it more meaningful. If the accuracy of the ratio is not critical, an approximation can be used to reduce the ratio to even smaller numbers. These operations can be performed by hand, but with the use of Microsoft Excel they become much easier.

Things You'll Need

• Computer with Microsoft Excel installed

Instructions

Reducing a Ratio

1. Load and run Excel.

2. Load the Analysis ToolPak in Excel by selecting "Tools" and "Add-ins" from the menu. When the Add Ins dialog box comes up, check the "Analysis ToolPak" box and click "OK." The Analysis ToolPak includes the Greatest Common Divisor (GCD) function that is needed in the following step.

3. In cells A1 and B1 enter the two numbers for which you want the ratio.

4. In cell C1 of the worksheet type the following formula:

   =A1/GCD(A1,B1)&":"&B1/GCD(A1,B1)

   Press "Enter." The ratio, reduced to its simplest form, will be the shown in cell C1.

Approximating Ratios

1. Follow the procedures in the first section to find the simplest ratio of two numbers.

2. In the same worksheet, show the decimal result of dividing the two numbers by entering the following formula in cell D1:

   =A1/B1

3. Copy the contents of cells A1 through D1 into cells A2 through D2. These will be used for approximations of the ratio.

4. In cell E2, find the error in the approximation by entering the formula:

   =100*ABS((D2-D1)/D1)

   The result will initially be 0 because you haven't manipulated the numbers yet.

5. Try different values in cells A2 and B2 and evaluate the effect on the ratio in C2 and the error in E2. Try to achieve a simple quotient in cell D2 such as decimals that are ratios of whole numbers like 0.67, 0.25, 0.5 and 0.8.

6. Practice using this setup with larger numbers. For example, reduce the the ratio of the numbers 55 and 36 to a simpler approximation. Keep the error less than 5 percent

   Enter 55 in cell A1 and 36 in cell B1. The ratio shown in cell C1 is 55:36 and the decimal representation is about 1.53. By entering smaller values in cell A2 you may discover that a value of 54 results in a ratio of 3:2 and the error shown in cell D2 is only about 1.9 percent. With less than a 5 percent error, the proportion can be expressed as the very simple ratio 3:2.

References

• Spreadsheet Page: Excel Tips: How to Calculate a Ratio
• Microsoft Excel 2007 help files: GCD, ABS