Introduction
Let’s start with the basics. A ‘ratio’ is simply a comparison of two or more quantities. For example, if you are looking at a recipe that calls for 2 cups of flour and 1 cup of sugar, the ratio of flour to sugar is 2:1. Ratios can be expressed in a variety of ways, including fractions, decimals, percentages, and proportions. Understanding how to calculate and use ratios can be incredibly useful in a variety of different contexts, from financial analysis to project management.
Types of Ratios
There are two main types of ratios: simple and compound. Simple ratios compare two quantities to each other, while compound ratios compare more than two quantities. For example, a simple ratio might be the ratio of boys to girls in a classroom (2:3), while a compound ratio might be the ratio of lemons to limes to oranges in a fruit basket (2:3:4).
Ratios can also be expressed in different ways. Proportions are ratios that have been simplified to their lowest terms (for example, 1:2 is the same as 2:4, but 1:2 is the proportion). Percentages are ratios that have been converted to a percentage (for example, a ratio of 1:4 can be expressed as 25%).
Let’s take a look at some examples of each type of ratio:
Simple Ratio:
- The ratio of boys to girls in a classroom is 2:3.
- The ratio of red to blue marbles in a jar is 3:5.
Compound Ratio:
- The ratio of lemons to limes to oranges in a fruit basket is 2:3:4.
- The ratio of nitrogen to oxygen to carbon dioxide in the atmosphere is 78:21:1.
Proportion:
- The proportion of dogs to cats in a neighborhood is 1:4.
- The proportion of apples to oranges in a fruit basket is 3:2.
Percentage:
- The percentage of students who received an ‘A’ in a class is 25%.
- The percentage of savings on a sale item is 20%.
Finding Ratio in Different Scenarios
Let’s take a look at how to find ratio in different scenarios. We’ll start with financial analysis and then move on to work-related projects.
Financial Analysis
One common use of ratio is in financial analysis. Ratios can be used to evaluate the financial health of a company or to compare the performance of different companies. Some common ratios used in financial analysis include:
- Liquidity ratios, which measure a company’s ability to meet short-term financial obligations.
- Profitability ratios, which measure a company’s ability to generate profit.
- Debt ratios, which measure a company’s debt load and its ability to repay debt.
Let’s take a look at how to calculate some of these ratios:
Liquidity Ratio:
The Current Ratio is a commonly used liquidity ratio that measures a company’s ability to meet its short-term financial obligations. The formula for calculating the current ratio is:
Current Ratio = Current Assets / Current Liabilities
For example, if a company has $100,000 in current assets and $50,000 in current liabilities, the current ratio would be:
Current Ratio = $100,000 / $50,000 = 2
Profitability Ratio:
The Return on Equity (ROE) ratio measures a company’s profitability by comparing its net income to its shareholder equity. The formula for calculating ROE is:
ROE = Net Income / Shareholder Equity
For example, if a company has $10,000 in net income and $100,000 in shareholder equity, the ROE would be:
ROE = $10,000 / $100,000 = 0.1 or 10%
Work-related Projects
Ratio can also be helpful in planning work-related projects. For example, if you are trying to improve productivity, you might use ratio to compare the number of hours worked to the amount of work completed. Some common ratios used in work-related projects include:
- Productivity ratios, which measure the amount of output relative to the amount of input.
- Efficiency ratios, which measure the number of units produced in a given amount of time.
- Quality ratios, which measure the number of errors or defects in a product.
Let’s take a look at how to calculate some of these ratios:
Productivity Ratio:
The Labor Productivity Ratio measures the amount of output relative to the amount of input. The formula for calculating the labor productivity ratio is:
Labor Productivity Ratio = Units Produced / Hours Worked
For example, if a team of workers produces 1,000 units in a week and works a total of 100 hours, the labor productivity ratio would be:
Labor Productivity Ratio = 1,000 / 100 = 10
Efficiency Ratio:
The Overall Equipment Effectiveness (OEE) ratio measures the number of units produced in a given amount of time. The formula for calculating the OEE ratio is:
OEE = (Good Units Produced x Ideal Cycle Time) / Total Time
For example, if a machine produces 100 good units in an hour, with an ideal cycle time of 1 minute per unit, the OEE ratio would be:
OEE = (100 x 1) / 60 = 1.67
Quality Ratio:
The Defects Per Million (DPM) ratio measures the number of errors or defects in a product. The formula for calculating the DPM ratio is:
DPM = (Number of Defects / Total Units Produced) x 1,000,000
For example, if a product has 5 defects in a batch of 1,000 units, the DPM ratio would be:
DPM = (5 / 1,000) x 1,000,000 = 5,000
Common Mistakes and Pitfalls
As with any mathematical concept, there are some common mistakes and pitfalls to avoid when working with ratio. Some common mistakes include:
- Not simplifying ratios to their lowest terms before using them.
- Not converting ratios to the same units before comparing them.
- Confusing the order of the quantities in the ratio.
- Dividing or multiplying the wrong quantities when calculating ratios.
To avoid these and other common mistakes, be sure to double-check your work and take the time to simplify and convert ratios as necessary.
Common Ratios Used in Different Fields
Now that we’ve covered the basics of how to find ratio, let’s take a look at some of the most commonly used ratios in different fields:
| Field | Common Ratio | Formula |
|---|---|---|
| Business | Current Ratio | Current Assets / Current Liabilities |
| Engineering | Overall Equipment Effectiveness | (Good Units Produced x Ideal Cycle Time) / Total Time |
| Medicine | Body Mass Index (BMI) | (Weight in kg) / (Height in m)^2 |
Keep in mind that these ratios are just a few examples of the many different ratios used in different industries. Be sure to research and understand the ratios that are most relevant to your field or industry.
Practice Problems or Exercises
Now that we’ve covered the basics of how to find ratio, it’s time to put your skills to the test with some practice problems! Here are three different scenarios that require you to find and use ratios:
1. A company has $10,000 in current assets and $5,000 in current liabilities. What is the current ratio for the company?
2. A manufacturing plant has a capacity to produce 1,000 units per hour. If the plant produces 800 units in an hour, what is the efficiency ratio?
3. A patient weighs 75 kg and is 1.8 m tall. What is the patient’s BMI?
Conclusion
Ratio is a powerful tool that can be used in a wide variety of different contexts, from financial analysis and work-related projects to engineering and medicine. By understanding the basics of how to find ratio, you’ll be better equipped to make informed decisions, analyze data, and communicate effectively in your field or industry.
