Using the LCM to Find the Relationship

Oct 13, 2025 by windailys.com 27 views

Introduction

Mathematics is a subject that deals with numbers, quantities, and shapes. It is a fundamental subject that is used in various aspects of life, including science, technology, engineering, and mathematics (STEM). In this discussion, we will explore a mathematical analogy that will help us find the value of 'x'. The analogy is 5 : 8 : : 91. 50 : x. This analogy is based on the concept of proportionality, where the ratio of two quantities remains constant.

Understanding the Analogy

The given analogy is 5 : 8 : : 91. 50 : x. To understand this analogy, we need to find the relationship between the numbers. The first part of the analogy is 5 : 8. This can be written as a ratio, which is 5/8. The second part of the analogy is 91. 50 : x. This can be written as a ratio, which is 91.50/x.

Finding the Relationship

To find the relationship between the numbers, we need to find the common factor between 5 and 8. The common factor between 5 and 8 is 1. However, we can also find the least common multiple (LCM) of 5 and 8, which is 40. The LCM is the smallest number that is a multiple of both numbers.

Using the LCM to Find the Relationship

Using the LCM, we can rewrite the ratio 5/8 as 40/320. This is because 5 x 8 = 40 and 8 x 8 = 64. Therefore, the ratio 5/8 is equal to 40/320.

Applying the Relationship to the Second Part of the Analogy

Now that we have found the relationship between the numbers, we can apply it to the second part of the analogy. The second part of the analogy is 91.50/x. We can rewrite this as 91.50/ (91.50 x 320/40).

Simplifying the Expression

To simplify the expression, we can cancel out the common factor between 91.50 and 320. The common factor between 91.50 and 320 is 1. However, we can also find the greatest common divisor (GCD) of 91.50 and 320, which is 1. The GCD is the largest number that divides both numbers.

Finding the Value of x

Now that we have simplified the expression, we can find the value of x. The expression is 91.50/ (91.50 x 320/40). We can simplify this expression by canceling out the common factor between 91.50 and 320. The expression becomes 91.50/ (320/40).

Calculating the Value of x

To calculate the value of x, we need to divide 91.50 by (320/40). This can be written as 91.50/ (8). Therefore, the value of x is 91.50/ (8).

Conclusion

In conclusion, the value of x is 91.50/ (8). This is the correct answer to the given analogy. The analogy is based on the concept of proportionality, where the ratio of two quantities remains constant. We used the least common multiple (LCM) to find the relationship between the numbers and then applied it to the second part of the analogy. We simplified the expression and found the value of x.

Final Answer

The final answer is 11.44.

Introduction

In our previous article, we explored a mathematical analogy that helped us find the value of 'x'. The analogy was 5 : 8 : : 91. 50 : x. In this article, we will provide a Q&A section to help clarify any doubts and provide further understanding of the concept.

Q&A

Q1: What is the concept behind the analogy 5 : 8 : : 91. 50 : x?

A1: The concept behind the analogy is proportionality, where the ratio of two quantities remains constant. We used the least common multiple (LCM) to find the relationship between the numbers and then applied it to the second part of the analogy.

Q2: How do we find the relationship between the numbers in the analogy?

A2: To find the relationship between the numbers, we need to find the common factor between 5 and 8. The common factor between 5 and 8 is 1. However, we can also find the least common multiple (LCM) of 5 and 8, which is 40.

Q3: What is the least common multiple (LCM) and how is it used in the analogy?

A3: The least common multiple (LCM) is the smallest number that is a multiple of both numbers. In the analogy, we used the LCM to rewrite the ratio 5/8 as 40/320.

Q4: How do we apply the relationship to the second part of the analogy?

A4: We can rewrite the second part of the analogy as 91.50/x. We can then apply the relationship we found earlier by rewriting this as 91.50/ (91.50 x 320/40).

Q5: What is the greatest common divisor (GCD) and how is it used in the analogy?

A5: The greatest common divisor (GCD) is the largest number that divides both numbers. In the analogy, we used the GCD to simplify the expression by canceling out the common factor between 91.50 and 320.

Q6: How do we find the value of x in the analogy?

A6: To find the value of x, we need to divide 91.50 by (320/40). This can be written as 91.50/ (8). Therefore, the value of x is 91.50/ (8).

Q7: What is the final answer to the analogy 5 : 8 : : 91. 50 : x?

A7: The final answer to the analogy 5 : 8 : : 91. 50 : x is 11.44.

Conclusion

In conclusion, the Q&A section provides further understanding of the concept behind the analogy 5 : 8 : : 91. 50 : x. We hope that this section has helped clarify any doubts and provided a better understanding of the concept.

Final Answer

The final answer is 11.44.