worldofcalcsRatio and Proportion Calculator
Simplest form
2 : 3 : 5
Divide every part by their HCF, 6.
Ratio and proportion
A ratio compares quantities of the same kind, such as 4 : 6, and is usually written in its simplest form, 2 : 3. A proportion says two ratios are equal, a : b = c : d, so a × d = b × c. This calculator simplifies ratios of two or more parts, finds the missing term of a proportion, and divides an amount, such as money or ingredients, in a given ratio.
Ratio formulas
a : b = c : x ⇒ x = (b × c) ÷ a · Share of a part = amount × part ÷ (sum of parts)
To simplify a ratio, divide every part by their HCF. Decimals are first turned into whole numbers by multiplying every part by the same power of 10.
Good to know
- Ratios compare like quantities in the same unit: 50 paise : ₹2 is 50 : 200 = 1 : 4.
- In a : b = c : d, a and d are the extremes and b and c the means; the product of the extremes equals the product of the means.
- The mean proportional of a and b is √(ab): for 4 and 9 it is 6, since 4 : 6 = 6 : 9.
- Partners in a business often share profit in the ratio of their investments.
- Scaling a recipe or a map uses proportion: double every part to keep the same ratio.
Worked examples
- 12 : 18 : 30: the HCF is 6, so the ratio is 2 : 3 : 5
- 1.5 : 2 = 15 : 20 = 3 : 4
- 2 : 3 = 8 : x ⇒ x = (3 × 8) ÷ 2 = 12
- Divide ₹12,000 in 2 : 3 : 5: the parts add to 10
- Shares: ₹12,000 × 2/10 = ₹2,400, × 3/10 = ₹3,600 and × 5/10 = ₹6,000
Dividing ₹12,000 in common ratios
The share of each part.
| Ratio | Shares |
|---|---|
| 1 : 1 | ₹6,000 / ₹6,000 |
| 1 : 2 | ₹4,000 / ₹8,000 |
| 2 : 3 | ₹4,800 / ₹7,200 |
| 3 : 5 | ₹4,500 / ₹7,500 |
| 1 : 2 : 3 | ₹2,000 / ₹4,000 / ₹6,000 |
| 2 : 3 : 5 | ₹2,400 / ₹3,600 / ₹6,000 |
Each share = amount × part ÷ sum of parts.