Understanding the Ratio Between A, B, and C: A Step-by-Step Guide

Ratios are a fundamental part of mathematics and are used in various fields, including biology, physics, finance, and more. When dealing with problems involving multiple ratios, it can be challenging to understand how to find the relationship between different quantities. In this article, we will walk through a step-by-step process to solve a specific ratio problem. If A : B 1 : 2 and B : C 2 : 3, what is A : C?

Given Information and Initial Setup

Let's break down the problem and set up the initial equations:

A : B 1 : 2 B : C 2 : 3

These can be translated into the following algebraic expressions:

A/B 1/2 B/C 2/3

Solving the Equations

Now, let's solve these equations step by step to find the relationship between A and C:

Step 1: Express B in Terms of A

From A/B 1/2, we can deduce that B 2A.

Step 2: Express B in Terms of C

From B/C 2/3, we can deduce that B (2/3)C.

Step 3: Setting the Expressions for B Equal

We now set 2A equal to (2/3)C, as B is the same quantity in both expressions: 2A (2/3)C Dividing both sides by 2, we get A (1/3)C

Step 4: Determine the Ratio A : C

From A (1/3)C, we can deduce that A/C 1/3 Therefore, the ratio A : C is 1 : 3

Conclusion

By systematically solving the given ratios, we found that the ratio A : C is 1 : 3. This solution demonstrates the importance of proportional reasoning in mathematics and its practical applications.

Resources and Further Reading

If you're interested in learning more about ratios and their applications, you may want to explore the following resources:

Textbooks on basic mathematics and algebra Online courses on ratios and proportions Practice problems with solutions

Related Questions

Here are some common questions related to this topic:

How do you solve ratio problems? Can ratios be expressed as fractions? What are some real-life applications of ratios?

If you have any further questions or need additional assistance, feel free to reach out. Happy solving!