Proportion is one of the most important concepts in arithmetic and quantitative reasoning. It helps us compare two ratios and check if they represent the same relationship between quantities. Whether you're comparing prices, scaling recipes, solving map-related problems, or attempting exam questions, the proportion formula makes calculations simple and accurate. The idea is straightforward: if two ratios are equal, the quantities are said to be in proportion.
Proportion Formula - Quick Overview
| Part | Meaning | When It Is Used |
|---|---|---|
| Formula | a : b = c : d | To compare two ratios |
| a, b, c, d | Four terms of proportion | Marks, money, distance, quantities |
| Extremes | a and d | First and last terms |
| Means | b and c | Middle terms |
| Use Case | Check equality of ratios | Exams (CUET, SSC, Banking), real-life problems |
What is Proportion in Maths?
A proportion describes the relationship between four quantities such that the ratio of the first pair equals the ratio of the second pair. The standard form of proportion is:
a : b = c : d
or
a/b = c/d
If these two ratios are equal, then the numbers a, b, c, and d are said to be in proportion.
For example:
2/4 = 3/6, so 2, 4, 3, and 6 are in proportion.
Steps to Check Proportion:
- Write the two ratios (a : b and c : d).
- Convert them to fractions (a/b and c/d).
- Cross multiply → a × d and b × c.
- If both products are equal, the ratios are in proportion.
Proportion plays a key role in exam topics like ratio–proportion, percentages, averages, and speed–distance problems. It is also useful in real-life situations such as price comparison, recipe adjustments, map reading, and construction measurements.
Solved Examples on Proportion Formula
Example 1: Check if 2, 4, 6, 12 are in proportion.
Step 1: Ratios → 2 : 4 and 6 : 12
Step 2: Fractions → 2/4 = 0.5 and 6/12 = 0.5
Step 3: Both values are equal.
Yes, they are in proportion.
Example 2: Is 5 : 15 = 10 : 30?
Step 1: Write as fractions → 5/15 and 10/30
Step 2: Simplify → 1/3 and 1/3
Step 3: Both are equal.
Yes, they are in proportion.
FAQs about Proportion Formula
Q1. What is the main condition for proportion?
Two ratios must be equal, meaning a/b = c/d.
Q2. What are extremes and means in proportion?
In a : b = c : d, a and d are extremes, while b and c are means.
Q3. How is proportion useful in real life?
It helps in recipe adjustments, map scaling, business comparisons, and construction measurements.
Q4. How is proportion different from ratio?
A ratio compares two numbers; proportion compares two ratios.
Q5. Is proportion important for exams?
Yes, it is frequently asked in CUET, SSC, Banking, JEE, and school aptitude tests.
Q6. Can proportion involve decimals or fractions?
Yes, ratios with fractions or decimals can be in proportion, such as 0.5/1 = 2.5/5.