Understanding the Concept of Ratio

Oct 13, 2025 by windailys.com 26 views

Introduction

In mathematics, dividing a quantity in a specific ratio is a common problem that requires a clear understanding of proportions and fractions. The given problem is to divide the number 720 in the ratio 5:4:3. This means that the total quantity of 720 will be divided into three parts, with the first part being 5 parts, the second part being 4 parts, and the third part being 3 parts. In this article, we will explore the concept of dividing a quantity in a specific ratio and provide a step-by-step solution to the given problem.

Understanding the Concept of Ratio

A ratio is a way of comparing two or more numbers by division. It is a fraction that shows the relationship between two or more quantities. In the given problem, the ratio 5:4:3 means that for every 5 parts of the first quantity, there are 4 parts of the second quantity and 3 parts of the third quantity. This ratio can be written as 5:4:3 or 5/4:3/4.

Dividing a Quantity in a Specific Ratio

To divide a quantity in a specific ratio, we need to follow these steps:

Add the parts of the ratio to find the total number of parts.
Divide the total quantity by the total number of parts to find the value of each part.
Multiply the value of each part by the corresponding number of parts to find the value of each part of the quantity.

Step-by-Step Solution to the Problem

Let's apply the above steps to the given problem.

Step 1: Add the parts of the ratio

The ratio is 5:4:3, so the total number of parts is 5 + 4 + 3 = 12.

Step 2: Divide the total quantity by the total number of parts

The total quantity is 720, and the total number of parts is 12. So, the value of each part is 720 ÷ 12 = 60.

Step 3: Multiply the value of each part by the corresponding number of parts

Now, we multiply the value of each part (60) by the corresponding number of parts:

For the first part (5 parts), the value is 5 × 60 = 300.
For the second part (4 parts), the value is 4 × 60 = 240.
For the third part (3 parts), the value is 3 × 60 = 180.

Conclusion

In conclusion, the number 720 can be divided in the ratio 5:4:3 as follows:

The first part is 300.
The second part is 240.
The third part is 180.

This solution is based on the concept of dividing a quantity in a specific ratio, which involves adding the parts of the ratio, dividing the total quantity by the total number of parts, and multiplying the value of each part by the corresponding number of parts.

Frequently Asked Questions

Q: What is the ratio 5:4:3?

A: The ratio 5:4:3 means that for every 5 parts of the first quantity, there are 4 parts of the second quantity and 3 parts of the third quantity.

Q: How do I divide a quantity in a specific ratio?

A: To divide a quantity in a specific ratio, you need to add the parts of the ratio, divide the total quantity by the total number of parts, and multiply the value of each part by the corresponding number of parts.

Q: What is the value of each part in the ratio 5:4:3?

A: The value of each part in the ratio 5:4:3 is 60.

Q: How do I find the value of each part of the quantity?

A: To find the value of each part of the quantity, you need to multiply the value of each part (60) by the corresponding number of parts.

Example Problems

Problem 1: Divide 1200 in the ratio 3:2:1.

Solution:

Add the parts of the ratio: 3 + 2 + 1 = 6
Divide the total quantity by the total number of parts: 1200 ÷ 6 = 200
Multiply the value of each part by the corresponding number of parts:
- For the first part (3 parts), the value is 3 × 200 = 600
- For the second part (2 parts), the value is 2 × 200 = 400
- For the third part (1 part), the value is 1 × 200 = 200

Problem 2: Divide 900 in the ratio 2:3:4.

Solution:

Add the parts of the ratio: 2 + 3 + 4 = 9
Divide the total quantity by the total number of parts: 900 ÷ 9 = 100
Multiply the value of each part by the corresponding number of parts:
- For the first part (2 parts), the value is 2 × 100 = 200
- For the second part (3 parts), the value is 3 × 100 = 300
- For the third part (4 parts), the value is 4 × 100 = 400

Conclusion

In conclusion, dividing a quantity in a specific ratio is a common problem that requires a clear understanding of proportions and fractions. By following the steps outlined in this article, you can easily divide a quantity in a specific ratio and find the value of each part of the quantity.

Introduction

Dividing a quantity in a specific ratio is a common problem that requires a clear understanding of proportions and fractions. In this article, we will answer some frequently asked questions (FAQs) on dividing a quantity in a specific ratio.

Q&A

Q: What is the ratio 5:4:3?

A: The ratio 5:4:3 means that for every 5 parts of the first quantity, there are 4 parts of the second quantity and 3 parts of the third quantity.

Q: How do I divide a quantity in a specific ratio?

Q: What is the value of each part in the ratio 5:4:3?

A: The value of each part in the ratio 5:4:3 is 60.

Q: How do I find the value of each part of the quantity?

A: To find the value of each part of the quantity, you need to multiply the value of each part (60) by the corresponding number of parts.

Q: Can I divide a quantity in a ratio with more than three parts?

A: Yes, you can divide a quantity in a ratio with more than three parts. The process is the same as dividing a quantity in a ratio with three parts.

Q: How do I handle fractions in a ratio?

A: When a ratio contains fractions, you need to find the least common multiple (LCM) of the denominators and multiply each part of the ratio by the LCM.

Q: Can I divide a quantity in a ratio with negative numbers?

A: Yes, you can divide a quantity in a ratio with negative numbers. However, you need to be careful when multiplying the value of each part by the corresponding number of parts.

Q: How do I divide a quantity in a ratio with decimals?

A: When a ratio contains decimals, you need to multiply each part of the ratio by the decimal value.

Q: Can I divide a quantity in a ratio with mixed numbers?

A: Yes, you can divide a quantity in a ratio with mixed numbers. However, you need to convert the mixed numbers to improper fractions before dividing the quantity.

Q: How do I handle ratios with different units?

A: When a ratio contains different units, you need to convert the units to a common unit before dividing the quantity.

Q: Can I divide a quantity in a ratio with variables?

A: Yes, you can divide a quantity in a ratio with variables. However, you need to be careful when multiplying the value of each part by the corresponding number of parts.

Example Problems

Problem 1: Divide 1200 in the ratio 3:2:1.

Solution:

Add the parts of the ratio: 3 + 2 + 1 = 6
Divide the total quantity by the total number of parts: 1200 ÷ 6 = 200
Multiply the value of each part by the corresponding number of parts:
- For the first part (3 parts), the value is 3 × 200 = 600
- For the second part (2 parts), the value is 2 × 200 = 400
- For the third part (1 part), the value is 1 × 200 = 200

Problem 2: Divide 900 in the ratio 2:3:4.

Solution:

Add the parts of the ratio: 2 + 3 + 4 = 9
Divide the total quantity by the total number of parts: 900 ÷ 9 = 100
Multiply the value of each part by the corresponding number of parts:
- For the first part (2 parts), the value is 2 × 100 = 200
- For the second part (3 parts), the value is 3 × 100 = 300
- For the third part (4 parts), the value is 4 × 100 = 400