How do you simplify a ratio?

To simplify a ratio, divide both values by their Greatest Common Divisor (GCD). GCD is the largest number that divides both values without a remainder. Example: simplify 24:16. GCD(24, 16) = 8. Divide both: 24 / 8 = 3, 16 / 8 = 2. Simplified ratio = 3:2. This reads 'for every 3 of A, there are 2 of B.' Ratios can also have three parts - 2:3:5 means the parts are in proportion 2, 3, and 5. To simplify a three-part ratio, find the GCD of all three numbers and divide each. Simplified ratios make proportional reasoning clearer by removing unnecessary common factors.

What is a proportion and how do I find a missing value?

A proportion states two ratios are equal: A:B = C:D, or equivalently A/B = C/D. When three of four values are known, find the fourth by cross-multiplication: A x D = B x C, so D = (B x C) / A. Example: a car travels 60 km in 1 hour. How far in 2.5 hours? Set up: 60:1 = x:2.5. Cross-multiply: 60 x 2.5 = 1 x x, so x = 150 km. Proportions are used in cooking (scaling recipes), construction (mixing concrete), map reading (scale distances), and currency conversion. Whenever two quantities change at the same rate, their relationship is proportional.

What is GCD and how is it calculated?

GCD (Greatest Common Divisor), also called HCF (Highest Common Factor), is the largest positive integer that divides two or more numbers exactly with no remainder. The most efficient method is the Euclidean algorithm: GCD(a, b) = GCD(b, a mod b), repeating until the remainder is 0. Example: GCD(48, 36). 48 mod 36 = 12. GCD(36, 12). 36 mod 12 = 0. GCD = 12. So 48:36 simplifies to 4:3 (divide both by 12). When GCD equals 1, the numbers are coprime - they share no common factors and the ratio is already in its simplest form. GCD(7, 11) = 1, so 7:11 cannot be simplified further.

How do I convert a ratio to a percentage?

For ratio A:B, compute (A / (A + B)) x 100 for each part's share of the whole, or (A / B) x 100 to express A as a percentage of B specifically. Example: ratio 3:7. A's share of total = (3/10) x 100 = 30%, B's share = 70%. Alternatively, A as a percentage of B = (3/7) x 100 = 42.9%. The choice depends on context: in a profit-split scenario, percentage-of-total (30% and 70%) is usually more meaningful. In a comparison context like speed ratio, A as a percentage of B is more natural.

How are ratios used in finance and investing?

Ratios are fundamental to investing. P/E ratio (Price-to-Earnings) = Stock Price / EPS - tells you how much you pay per rupee of earnings; under 20 is generally reasonable for Indian stocks. Debt-to-equity ratio = Total Debt / Shareholder Equity - under 1 is considered healthy. Current ratio = Current Assets / Current Liabilities - should be above 1.5. For personal finance, the 50/30/20 rule (50% needs, 30% wants, 20% savings) is itself a ratio-based budgeting framework.

How do I divide a quantity in a given ratio?

To divide a quantity in ratio A:B:C, sum all parts (A + B + C) to get total shares. Each party's amount = their share x (Total quantity / Total shares). Example: divide Rs. 1,80,000 among three partners in ratio 2:3:5. Total shares = 10. Each share = Rs. 18,000. Partner A = 2 x Rs. 18,000 = Rs. 36,000. Partner B = Rs. 54,000. Partner C = Rs. 90,000. Check: all three sum to Rs. 1,80,000. This method works for any number of parties and applies directly to partnership profit splits, inheritance distributions, and concrete mix proportions (cement:sand:aggregate).

What is inverse proportion?

Two quantities are inversely proportional when one increases as the other decreases at the same rate - their product stays constant. If A and B are inversely proportional: A x B = constant. Example: 8 workers complete a job in 15 days. How many days for 12 workers? Workers x Days = 8 x 15 = 120. Days for 12 workers = 120 / 12 = 10 days. More workers, fewer days - inverse proportion. Other examples: speed and travel time for a fixed distance (double the speed = half the time); gas pressure versus volume at constant temperature (Boyle's Law). Recognising inverse proportion prevents the common error of applying direct proportion when the relationship is actually inverse.

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Ratio Calculator

Simplify ratios and solve proportions. Enter A:B to get the simplified form, decimal, and percentage equivalent.

About the Ratio Calculator

Ratios and proportions underpin everything from recipe scaling to financial analysis to map reading. A ratio expresses the relationship between two quantities; a proportion states that two ratios are equal. Simplifying a ratio to its lowest terms (by dividing by the GCD) reveals the fundamental relationship. Proportional reasoning is one of the most widely applicable mathematical skills in business and daily life.

Ratio and Proportion

Simplified ratio A:B = (A/GCD):(B/GCD) · Proportion A:B = C:D means A×D = B×C · Missing value D = (B×C)/A

GCD = Greatest Common Divisor · Percentage from ratio: A/(A+B) × 100 · Ratio to decimal: A/B · Compound ratio: (A:B) × (C:D) = (A×C):(B×D)

Worked Example

Business profit split between partners in ratio 3:5 on total profit of ₹2.4 lakh

Profit:₹2,40,000

Split ratio:3:5

Total parts:3 + 5 = 8

Partner A = (3/8) × ₹2,40,000 = ₹90,000 · Partner B = (5/8) × ₹2,40,000 = ₹1,50,000

Tips & Insights

1
GST split CGST:SGST is always 1:1 regardless of the total GST rate. On an 18% GST product, CGST is 9% and SGST is 9% - understanding this ratio matters when reconciling input tax credit.
2
Compound ratios arise in business: if efficiency ratio is 4:3 and output ratio is 5:4, compound = 20:12 = 5:3. Compounding two ratios is just cross-multiplication - useful in multi-step proportion problems.
3
Map scales are ratios: 1:50,000 means 1 cm on map = 50,000 cm = 500 m in reality. Topo maps used for trekking in Himachal and Uttarakhand typically use 1:25,000 or 1:50,000 scales.
4
Concrete mix ratios (1:2:4 for cement:sand:aggregate) can be by volume or by weight - the two give different results. Always confirm which system the specification uses before mixing to avoid structural issues.
5
Financial ratios like P/E, debt-to-equity, and current ratio are all proportional relationships. A company with ₹10 crore earnings and ₹200 crore market cap has P/E = 20. Comparing P/E ratios across companies in the same sector is one of the most widely used equity valuation shortcuts.
6
In photography, aspect ratios (4:3, 16:9, 1:1) determine the shape of the final image. Social media platforms crop to fixed ratios: Instagram 1:1 (square) or 4:5 (portrait), YouTube thumbnails 16:9. Knowing these ratios avoids composition being cut off.
7
For dilution problems (chemistry, pharma, paints), the ratio method is faster than cross-multiplication. To dilute a 30% solution to 10%, the required ratio of solution:water is 1:2 (1 part solution + 2 parts water = 3 parts total at 10%).

Why this matters for you

Proportional thinking is central to financial analysis (P/E ratios, debt-to-equity), cooking (recipe scaling), construction (material mixing), and data analysis (survey proportions). Mastering ratios makes quantitative reasoning faster and more intuitive across a wide range of professional and daily contexts.

In competitive exams like CAT, GMAT, and SSC CGL, ratio and proportion questions are among the most frequently tested quantitative topics. The ability to quickly set up a proportion, identify the missing value, and verify the answer is a time-saver that separates strong scorers from average ones. Practicing with real-world contexts - not just abstract numbers - builds the intuition that makes this fast.

Business partnership agreements almost always specify profit-sharing in ratios. Understanding how to compute each partner's share, adjust for changes in capital contribution mid-year, or convert a ratio split into rupee amounts is a practical skill for anyone running or joining a small business or startup. Compound ratio calculations are especially useful when investment amounts and time periods both differ between partners.