Short Answer
A compound ratio is a ratio formed by combining two or more ratios into one. It is obtained by multiplying the corresponding terms of the given ratios.
For example, if the ratios are 2:3 and 4:5, the compound ratio is found by multiplying them as (2×4):(3×5), which gives 8:15. It helps in solving problems involving multiple comparisons.
Detailed Explanation:
Compound Ratio
Meaning of Compound Ratio
A compound ratio is a type of ratio that is formed by combining two or more ratios. It is used when we want to compare multiple quantities together in a single ratio. Instead of working with separate ratios, we combine them into one simple ratio.
The compound ratio is obtained by multiplying the first terms (antecedents) of the given ratios together and the second terms (consequents) together. The result gives a new ratio that represents all the given ratios combined.
For example, if we have two ratios 3:4 and 5:6, the compound ratio will be (3×5):(4×6), which is 15:24. This can further be simplified if needed.
How to Find Compound Ratio
To find a compound ratio, follow these simple steps:
First, write down the given ratios clearly.
Second, multiply all the first terms together.
Third, multiply all the second terms together.
Finally, write the result in ratio form.
For example, consider three ratios: 2:3, 4:5, and 6:7.
Multiply the first terms: 2 × 4 × 6 = 48
Multiply the second terms: 3 × 5 × 7 = 105
So, the compound ratio is 48:105
This method can be used for any number of ratios.
Importance of Compound Ratio
Compound ratios are very useful in mathematics, especially when dealing with multiple relationships. They help in combining different ratios into one, which makes calculations easier and more organized.
They are also used in solving problems related to proportion and comparison. Instead of solving each ratio separately, we can use a compound ratio to get the result quickly.
Use in Real Life
Compound ratios are used in many real-life situations. For example, in business, if we need to combine ratios of cost, profit, and sales, compound ratios can be helpful. In science, they are used to compare multiple quantities at once.
They are also useful in problems involving speed, distance, and time, where more than one ratio is involved.
Simplifying Compound Ratio
After finding a compound ratio, it can be simplified just like any other ratio. This is done by dividing both terms by their common factor.
For example, if the compound ratio is 12:18, it can be simplified by dividing both terms by 6, giving 2:3. This makes the ratio easier to understand and use.
Conclusion
A compound ratio is a useful way to combine two or more ratios into one. It simplifies calculations and helps in comparing multiple quantities easily. Understanding compound ratios is important for solving many mathematical and real-life problems.