How to divide a quantity in a given ratio eg. Divide 12 in the ratio 3:2:1

To divide a quantity in a given ratio, you'll follow a systematic process. Let's break it down into steps:

### Step 1: Understand the Ratio
Let's say you have a quantity and you want to divide it in a given ratio, such as 2:3. This ratio means that for every 2 parts of the quantity, 3 parts are allocated elsewhere.

### Step 2: Find the Total Parts
Add up the parts in the ratio to determine the total parts. In the example 2:3, the total parts would be 2 + 3 = 5.

### Step 3: Determine the Share for Each Part
Divide the quantity by the total parts to find the value of each part. This value represents one part of the ratio.

Value of each part = Total Quantity ÷ Total Parts

### Step 4: Calculate Individual Shares
Multiply the value of each part by the respective ratio components (called "terms") to find the share for each part. In the example 2:3, you would multiply the value of each part by 2 for the first part and 3 for the second part.

### Example:
Let's say you have 100 units of a quantity and you want to divide it in a 2:3 ratio.

1. **Understand the Ratio:** 2:3
2. **Find the Total Parts:** 2 + 3 = 5
3. **Determine the Value of Each Part:** 100 ÷ 5 = 20
4. **Calculate Individual Shares:**
- For the first part (2): 20 × 2 = 40
- For the second part (3): 20 × 3 = 60

So, in the 2:3 ratio, you would allocate 40 units for the first part and 60 units for the second part, totaling the original 100 units.

Remember, these steps can be adjusted for different ratios, and the key is to maintain the proportional relationship between the parts as specified by the given ratio. In other words, the original ratio and the calculated ratio must be equivalent. This can be checked easily:

40:60 (divide both terms by 20) gives 2:3, which corresponds to the original ratio.