Make a ratio as simple as possible, and see it as a decimal and as a percentage of the total.
The greatest common divisor of both numbers is found using the Euclidean algorithm.
Dividing both sides by it reduces the ratio to its simplest whole-number form.
Decimal inputs are scaled to whole numbers first, so 1.5 : 3 still simplifies correctly to 1 : 2.
Simplified ratio: A ÷ GCD : B ÷ GCD
Share of A: A ÷ (A + B) × 100
A ratio compares two quantities by showing how many times one contains the other. The ratio calculator takes two numbers A and B, reduces A : B to its simplest whole-number form, and also shows A ÷ B as a decimal and each side's share of the total as a percentage. So 4,50,000 : 6,00,000 becomes 3 : 4, which is easier to read and use.
Ratios appear everywhere in Indian life: partners sharing profit in the ratio of their capital, recipes and concrete mixes, screen aspect ratios, map scales, and class 8 to 10 maths problems on proportion. Converting a ratio into percentage shares is often the step that makes it useful, for example when you need to split ₹70,000 of profit between two partners in the ratio of their investment.
1. Write the two quantities in the same unit, for example both in rupees or both in grams.
2. If either has decimals, multiply both by the same power of 10 to make them whole numbers.
3. Find the greatest common divisor (GCD) of the two whole numbers, using the Euclidean method of repeated remainders.
4. Divide both by the GCD to get the simplest ratio.
5. Decimal value = A ÷ B.
6. Share of A = A ÷ (A + B) × 100 and share of B = B ÷ (A + B) × 100.
Dividing both sides of a ratio by the same number does not change the comparison, just as 6/8 and 3/4 are the same fraction. The largest number that divides both sides exactly is the GCD. After dividing by it, the two sides share no common factor except 1, so the ratio cannot be reduced further. The Euclidean method finds the GCD quickly: replace the larger number by the remainder when divided by the smaller, and repeat until the remainder is 0.
A ratio A : B compares part to part. A fraction or percentage share compares part to whole. In a 3 : 4 ratio, the whole has 3 + 4 = 7 parts, so A's share is 3/7, about 42.9%, not 3/4. This difference causes many errors when splitting money. To divide an amount in a ratio, divide it into A + B equal parts and give A parts to the first person and B parts to the second.
Ratios with decimals, such as 1.5 : 2.5, are scaled to whole numbers first: multiply both by 10 to get 15 : 25, then simplify to 3 : 5. The order of terms matters. 3 : 4 is not the same as 4 : 3, and the decimal A ÷ B changes accordingly. If B is zero the ratio is still meaningful as a comparison, but A ÷ B is undefined, so the decimal form cannot be shown.
Gaurav and Salma started a printing shop in Bhopal. Gaurav invested ₹4,50,000 and Salma ₹6,00,000, and they agreed to share profit in the ratio of their capital.
Answer: Simplified ratio 3 : 4; As a decimal 0.75; Share of A 42.86%
Comparing quantities in different units, such as grams with kilograms.
Treating A : B as the fraction A/B when splitting a total, instead of A/(A + B).
Reversing the order of the ratio when writing the answer.
Rounding decimals before simplifying, which can give a wrong simplest form.
Splitting profit between business partners according to capital.
Scaling recipes or concrete and mortar mixes.
Checking aspect ratios of screens, photos and prints.
Solving ratio and proportion problems in school maths.
What does a ratio like 16:9 mean?
For every 16 units of the first amount, there are 9 of the second. On a screen, this means the width is 16/9 times the height, no matter the actual size of the screen.
What is the difference between a ratio and a fraction?
A ratio compares two parts to each other (2:3). A fraction compares one part to the whole (2/5). In a 2:3 ratio, the first part is actually two-fifths of the total, not two-thirds.