How do you simplify a ratio?

To simplify a ratio, find the Greatest Common Divisor (GCD) of all parts and divide each part by it. Example: simplify 12:8. GCD of 12 and 8 is 4. Divide both by 4: 12/4 : 8/4 = 3:2. The simplified ratio is 3:2. A ratio is fully simplified when the parts share no common factors other than 1.

How do you find a missing value in a proportion?

A proportion states that two ratios are equal: a/b = c/d. To find the missing value, use cross-multiplication: a x d = b x c. Example: 3/4 = x/12. Cross multiply: 3 x 12 = 4 x x. So 36 = 4x. Therefore x = 9. Always check by substituting back: 3/4 = 9/12 = 3/4.

What is the difference between a ratio and a fraction?

A fraction represents a part of a whole (e.g. 3/4 means 3 out of 4 equal parts). A ratio compares two or more quantities to each other and does not have to represent a part of a whole. Example: a ratio of 3:4 (boys to girls in a class) means for every 3 boys there are 4 girls - the total could be 7, 14, 21, or any multiple. A fraction 3/4 always means exactly 3 parts out of 4 equal parts of one thing.

Ratio Calculator

Q: What is a ratio and how is it different from a fraction?

A ratio compares two or more quantities and shows their relative sizes. It can be written as a:b, a/b, or 'a to b'. A fraction represents a part of a whole (numerator/denominator), while a ratio compares two separate quantities. However, the ratio a:b is numerically equivalent to the fraction a/b and can be treated mathematically the same way.

Q: How do I simplify a ratio?

To simplify a ratio, divide both numbers by their Greatest Common Divisor (GCD). Example: to simplify 24:36, find GCD(24,36) = 12, then 24÷12:36÷12 = 2:3. The simplified ratio 2:3 expresses the same relationship as 24:36. You can verify: 24/36 = 2/3 ✓.

Q: How do I find a missing value in a proportion?

Use cross-multiplication. If a:b = c:d, then a×d = b×c. To find d when a=3, b=4, c=9: 3/4 = 9/d → d = 9×4/3 = 12. So 3:4 = 9:12 ✓. This is the fundamental method for solving any proportion problem.

Q: How do I scale a ratio to a specific total?

If a ratio is a:b and you need the total to equal N, then: Part A = N × a/(a+b) and Part B = N × b/(a+b). Example: mix concrete in a 1:2:3 ratio (cement:sand:gravel) for 60 kg total → cement = 60 × 1/6 = 10 kg, sand = 20 kg, gravel = 30 kg.

Simplify ratios, solve proportions, find missing values, and scale ratios instantly.

⚖️ What is a Ratio?

A ratio is a mathematical comparison of two or more quantities that shows their relative sizes. Ratios are written as a:b (read "a to b"), as a fraction a/b, or occasionally using the word "to" (e.g., "3 to 5"). The fundamental property of a ratio is that it expresses a relationship, not an absolute amount - the ratio 3:5 means that for every 3 of the first quantity, there are 5 of the second, regardless of the actual numbers involved.

Ratios appear everywhere in daily life. Recipe scaling uses ratios (double all ingredients keeping the same ratio). Mixing paint, concrete, or cleaning solutions involves ratios. Maps use scale ratios (1:50,000 means 1 cm on the map = 50,000 cm = 500 m in reality). Exchange rates are ratios between currencies. Aspect ratios describe screen proportions (16:9 for widescreen, 4:3 for older TVs). Financial ratios like Price-to-Earnings (P/E) compare stock price to earnings per share.

A proportion is an equation stating that two ratios are equal: a:b = c:d. Proportions are used to scale up or down, find unknown values, and solve many practical problems. If a car travels 120 km on 10 litres of fuel, how far will it travel on 25 litres? Set up the proportion 120:10 = x:25, and cross-multiply to find x = 120 × 25 / 10 = 300 km.

To simplify a ratio, divide all terms by their Greatest Common Divisor (GCD). The simplified ratio expresses the same relationship using the smallest possible whole numbers. For example, 48:36:24 simplifies by dividing by GCD(48,36,24) = 12, giving 4:3:2. Simplification makes ratios easier to understand, compare, and work with.

📐 Ratio Formulas

Simplify: a:b → (a÷GCD):(b÷GCD)

Proportion (find D): A:B = C:D → D = B × C ÷ A

Scale to total N: Part A = N × a / (a+b+c) | Part B = N × b / (a+b+c)

GCD = Greatest Common Divisor (largest number dividing both terms)

Cross-multiplication: If A/B = C/D then A×D = B×C

📖 How to Use This Calculator

Three calculation modes

Simplify: Enter two values A and B to reduce the ratio to its simplest form. Also shows decimal equivalent and percentage split.

Find Missing: Enter any 3 values in A:B = C:D and leave the 4th blank (or 0) to solve for the unknown - uses cross-multiplication.

Scale to Total: Enter a ratio (2 or 3 parts) and a total quantity - the calculator divides the total in exactly that ratio (e.g. split ₹90,000 in the ratio 3:2:1).

💡 Example Calculations

Example 1 - Simplify a ratio: 48:36

Find GCD(48, 36): factors of 48 = 1,2,3,4,6,8,12,16,24,48; factors of 36 = 1,2,3,4,6,9,12,18,36. GCD = 12.

48 ÷ 12 = 4 | 36 ÷ 12 = 3 → Simplified: 4:3

4:3 means for every 4 of A, there are 3 of B. Decimal: 1.333. Split: 57.1% vs 42.9%.

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Example 2 - Find missing value: 5:8 = 15:?

Cross-multiply: 5 × D = 8 × 15 = 120

D = 120 ÷ 5 = 24

5:8 = 15:24. Verify: 5/8 = 0.625 and 15/24 = 0.625 ✓

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Example 3 - Split ₹90,000 in ratio 3:2:1 (three business partners)

Total parts = 3+2+1 = 6

Partner A = 90,000 × 3/6 = ₹45,000

Partner B = 90,000 × 2/6 = ₹30,000 | Partner C = 90,000 × 1/6 = ₹15,000

Total check: 45,000 + 30,000 + 15,000 = ₹90,000 ✓

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❓ Frequently Asked Questions

What is a ratio and how is it different from a fraction?+

A ratio compares two or more separate quantities and shows their relative sizes (e.g. 3 boys to 5 girls). A fraction represents a part of a whole (3 out of 8 students). Mathematically, the ratio a:b equals the fraction a/b and can be handled the same way - but conceptually, ratios compare independent quantities while fractions describe parts of a single total.

How do I simplify a ratio?+

Divide both numbers by their Greatest Common Divisor (GCD). Example: to simplify 24:36, find GCD(24,36) = 12, then divide: 24÷12 : 36÷12 = 2:3. To find GCD, list factors of both numbers and find the largest common one, or use the Euclidean algorithm: GCD(24,36) = GCD(24, 36-24) = GCD(24,12) = GCD(12, 24-2×12) = GCD(12,0) = 12.

How do I find a missing value in a proportion?+

Use cross-multiplication. If a:b = c:d, then a×d = b×c. Rearrange for the unknown: if d is unknown, d = b×c÷a. Example: 3:4 = 9:d → d = 4×9÷3 = 12. Check: 3/4 = 0.75 and 9/12 = 0.75 ✓. This works for any proportion problem including recipe scaling, map distances, and unit conversion.

How do I scale a ratio to a specific total?+

Add up all parts of the ratio to find the total shares. Divide each part by the total shares, then multiply by your target total. Example: split ₹12,000 in the ratio 5:3: total shares = 8, Part A = 12,000 × 5/8 = ₹7,500, Part B = 12,000 × 3/8 = ₹4,500. Verify: 7,500 + 4,500 = ₹12,000 ✓.

What is the difference between a ratio and a rate?+

A ratio compares two quantities of the same unit (e.g. 3 boys : 5 girls - both are people; the ratio is dimensionless). A rate compares two quantities of different units (e.g. 60 km per hour - distance divided by time). Speed, price per kilogram, interest rate, and exchange rates are all rates. Both use the same mathematical operations, but rates always carry units in the result.

What is the golden ratio and why is it significant?+

The golden ratio (φ ≈ 1.618) is the ratio where a:b = (a+b):a. It appears in geometry, art, and nature - spiral shells, flower petal arrangements, and the proportions of classical architecture. In design, rectangles with a 1:1.618 aspect ratio are considered aesthetically pleasing. The golden ratio is related to the Fibonacci sequence: consecutive Fibonacci numbers (1, 1, 2, 3, 5, 8, 13...) form ratios that approach φ as the sequence grows.

What is the difference between ratio and proportion?+

A ratio compares two quantities (3:4 or 3/4). A proportion is a statement that two ratios are equal: a/b = c/d. "3 apples to 4 oranges" is a ratio. "3 apples to 4 oranges is the same as 9 apples to 12 oranges" is a proportion. Proportions are solved by cross-multiplication: if a/b = c/d, then ad = bc.

How are ratios used in real life?+

Ratios appear everywhere: recipe scaling (double a recipe by multiplying all ratios by 2), mixing paint (e.g., 3 parts blue to 1 part white), map scales (1:50,000), aspect ratios in screens and photos (16:9, 4:3), financial ratios (P/E ratio, debt-to-equity), and pharmacy (drug concentrations). Understanding ratios is essential for proportional reasoning in everyday decisions.

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📌 Quick Tips

💡To simplify a ratio, divide both values by their Greatest Common Divisor (GCD). For example, 12:8 → GCD is 4 → simplified to 3:2.

💡A ratio a:b is equivalent to the fraction a/b. To compare two ratios, convert them to fractions with a common denominator, or convert to decimals.

💡The golden ratio φ ≈ 1.618 (approximately 1.618:1) appears throughout art, architecture, and nature. The ratio of consecutive Fibonacci numbers approaches φ.