The formula for calculating Proportion is used to check if two ratios are equal. Proportion helps us compare four quantities in pairs. and the formula is: a : b = c : d or a/b = c/d
Where:
- a, b, c, d = four terms of proportion
- a, d = extreme terms
- b, c = middle terms
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 ?
Proportion is the relation between four quantities such that the ratio of the first two is equal to the ratio of the last two.
Standard Form:
a : b = c : d or a/b = c/d
The proportion formula works by comparing two ratios. If two ratios are equal, they are said to be in proportion.
For example : if 2/4 = 3/6, then the numbers 2, 4, 3, and 6 are in proportion.
Steps:
- Write two ratios (a : b and c : d).
- Convert them into fractions (a/b and c/d).
- Cross multiply: a × d = b × c.
- If equal, then they are in proportion.
Proportion is widely used in mathematics exams (CUET, SSC, Banking, JEE) and in daily life—such as scaling recipes, comparing prices, distances, or maps.
Solved Examples on Proportion formula
Example 1: Check if 2, 4, 6, 12 are in proportion.
Solution :
Step 1: Ratios → 2 : 4 and 6 : 12
Step 2: Fractions → 2/4 = 0.5, 6/12 = 0.5
Step 3: Both are equal.
Yes, they are in proportion.
Example 2: Is 5 : 15 = 10 : 30?
Solution :
Step 1: Write as 5/15 and 10/30
Step 2: Simplify it → ⅓ and ⅓
Step 3: Hence they are in Equal ratios.
Yes, they are in proportion.
FAQs about Proportion formula
Q1. What is the main condition for proportion?
Two ratios must be equal, i.e., a/b = c/d.
Q2. What are extremes and means in proportion?
In a : b = c : d, a and d are extremes, b and c are means.
Q3. How is proportion useful in real life?
It is used in cooking recipes, map scaling, business profit comparisons, and construction measurements.
Q4. How is proportion different from ratio?
A ratio compares two quantities, while proportion compares two ratios.
Q5. Is proportion important for exams?
Yes, questions on ratio and proportion are common in CUET, SSC, Banking, and JEE aptitude sections.
Q6. Can proportion involve decimals or fractions?
Yes, proportion can be checked with whole numbers, fractions, or decimals. Example: 0.5/1 = 2.5/5.