Dividing a Number According to a Ratio

Introduction to Ratio and Division

Understanding the division of a number according to a given ratio is a fundamental concept in mathematics. We often encounter situations where it is necessary to distribute a total amount into parts according to a specified ratio. In this article, we will walk through the process of dividing 360 into two parts in the ratio of 3:2 and determine the smallest share.

Step-by-Step Guide for Dividing 360 in the Ratio 3:2

Let's walk through the process of dividing 360 in the ratio 3:2 and find out the smallest share.

Step 1: Calculate the Total Parts

The first step is to determine the total number of parts in the given ratio. In the ratio 3:2, we have 3 parts and 2 parts combined. Therefore, the total number of parts is:

3 2 5

Step 2: Find the Value of One Part

To find the value of one part, divide the total amount by the total number of parts. We have 360 to be divided among 5 parts:

Value of one part 360 / 5 72

Step 3: Calculate the Shares

Now, we can find the individual shares by multiplying the value of one part by the number of parts in each share.

First Share (3 parts)

3 parts 3 x 72 216

Second Share (2 parts)

2 parts 2 x 72 144

The Smallest Share

From the above calculations, the smallest share is:

144

Alternative Methods for Division by Ratio

There are various methods to approach the same problem, and these methods are as follows:

Method 1: Using Basic Division

Another way to solve this is by directly dividing the total amount by the total parts and then multiplying the result by the respective parts:

Total Shares 5, Value of One Share 360 / 5 72

Smaller Share 72 x 2 144

Method 2: Proportional Division

Alternatively, we can use proportional division:

Total Parts 5, Smaller Share 2/5 x 360 2 x 72 144

Method 3: Algebraic Approach

We can also use algebra to solve the problem:

x/y 3/2, x 1.5y, 3y 2y 360

5y 360, y 72, Smaller Share 2 x 72 144

Conclusion

In conclusion, dividing 360 into a ratio of 3:2 results in the smallest share of 144. This process can be applied to various real-world scenarios, such as dividing assets, shares, or resources based on a proportional division of a given amount.

Additional Resources

If you require further assistance or more detailed explanations, consider exploring additional resources or consulting a mathematics expert.