- Dividing quantities in a given ratio

Understanding How to Divide Quantities in a Given Ratio

Dividing quantities in a given ratio is a fundamental mathematical skill, often used in real-life situations such as sharing costs, distributing resources, or splitting profits. This process ensures that each part receives a fair share according to the specified ratio.

What Is a Ratio?

A ratio is a way to compare two or more quantities, showing how many times one value contains or is contained within the other. For example, a ratio of 2:3 means for every 2 parts of the first quantity, there are 3 parts of the second.

Steps to Divide a Quantity in a Given Ratio

1. Add the Parts of the Ratio:
   • For a ratio of a:b, add a + b to get the total number of parts.
2. Divide the Total Quantity by the Total Number of Parts:
   • This gives the value of one part.
3. Multiply Each Part of the Ratio by the Value of One Part:
   • This gives the actual amounts for each share.

Example Problem

Question: Divide 60 in the ratio 2:3.

• Total parts = 2 + 3 = 5
• Value of one part = 60 ÷ 5 = 12
• First share = 2 × 12 = 24
• Second share = 3 × 12 = 36

Answer: The two shares are 24 and 36.

Tips for Dividing Quantities in a Ratio

• Always check that the sum of the shares equals the original total.
• Ratios can involve more than two parts (e.g., 2:3:5). Add all parts together before dividing.
• Ratios can be simplified before calculations if possible.

Dividing quantities in a given ratio is a practical skill used in budgeting, recipe adjustments, and group work. Mastering this concept helps in fair and accurate distribution.